Opening
[Transcriber’s Note:
In this, the text file, italics delimited by underscores, and bold text delimited by equal signs.]
THE
MICROSCOPE
ITS HISTORY, CONSTRUCTION, AND APPLICATION
BEING A FAMILIAR INTRODUCTION TO THE USE OF THE INSTRUMENT, AND THE STUDY OF MICROSCOPICAL SCIENCE
BY JABEZ HOGG, M.R.C.S., F.R.M.S.,
FORMERLY AND FOR TWENTY-FIVE YEARS SURGEON TO THE ROYAL WESTMINSTER OPHTHALMIC HOSPITAL; PAST PRESIDENT OF THE MEDICAL MICROSCOPICAL SOCIETY; HONORARY FELLOW OF THE ACADEMY OF SCIENCES, PHILADELPHIA; OF THE MEDICO-LEGAL SOCIETY, NEW YORK; OF THE BELGIAN MICROSCOPICAL SOCIETY, ETC.; AUTHOR OF “ELEMENTS OF NATURAL PHILOSOPHY,” “A MANUAL OF OPHTHALMOSCOPIC SURGERY,” ETC.
_WITH UPWARDS OF NINE HUNDRED ENGRAVED AND COLOURED ILLUSTRATIONS BY TUFFEN WEST AND OTHER ARTISTS_
_FIFTEENTH EDITION RE-CONSTRUCTED, RE-WRITTEN, REVISED, AND ENLARGED THROUGHOUT_
LONDON AND NEW YORK GEORGE ROUTLEDGE & SONS, LIMITED 1898
BRADBURY, AGNEW, & CO. I.D., PRINTERS, LONDON AND TONBRIDGE.
PREFACE TO THE FIFTEENTH EDITION.
The First Edition of this work appeared in 1854, a time in the history of the Microscope when the instrument, as an aid to original scientific research, may be said to have been in its infancy. Then certainly it was seldom employed in the laboratory or the medical schools. Now, however, as I anticipated, it has asserted its proper position, and has at length become one of the most important auxiliaries to science, and a direct incentive to original work, while it has doubtless exercised considerable influence over the student’s power of observation, and materially assisted in his studies, let his ultimate object and pursuits be what they may.
The greater use made of the Microscope has likewise conferred benefits of untold value upon the arts and industries of the country, thereby adding to the national prosperity in ways as manifold as unique. The Microscope has also proved of immense value in the promotion of the health of the community, and the art and science of healing, since the theory of medicine has become a science, resting on the minute microscopical examination of animal tissues.
The work of research in the sister sciences and by other methods has, during the last decade, received a corresponding impetus, while it has undoubtedly tended towards elaboration and specialisation in all departments. In consequence, the progress of microscopical science has become more dependent upon the specialist for gaining accurate knowledge and for certain important details seen to be branching out in many directions. There never was a time when the instrument was so constantly and generally resorted to and with so much confidence and advantage, as the present. It has shown itself equal to the task imposed--that of teaching the eye to see things that are new, and also, what is perhaps of more importance, to perceive things which had been entirely overlooked. The older defects, perhaps, arose from two causes; the want of more careful training of the organ of vision, and the want of sufficient power and precision in the optical part of the Microscope itself. Both of these obstacles have been to a considerable extent removed, and all educational systems are looked upon as incomplete without a knowledge of the Microscope.
A step has already been taken in another direction, that of furnishing special forms of instruments, better adapted to the uses to which they will hereafter be put, and purposely designed for chemical and analytical processes, for petrological pursuits, the geometrical measurement of crystals, for special work in connection with manufacturing industries, for the dairyman, and the farmer. For the detection of adulterations--that of butter, for example--a newer form of instrument has been devised, namely, a “Butro-refractometer,” by the help of which any adulteration of this universal article of diet will at once be revealed. The form of instrument upon which the optician has expended a greater amount of skill than perhaps on any other is the Bacteriological Microscope, as may be inferred from the larger space I have devoted to this important adjunct, since by original research, there can be no doubt a still greater future is in store for science in this special department of microscopy. But perfect success in this direction remains very much with the practical optician, and the further improvements made in the optical part of the instrument, since it is admitted that the highest theoretical perfection has not yet been reached.
It is a commonplace remark that every question solved is a step towards new problems waiting solution. It is equally obvious that many difficulties must be encountered by every author who uses his best endeavours to supply a standard volume or even a fairly comprehensive text-book on the Microscope, one that will remain a sure guide for any lengthened period. Such a success I regard as scarcely possible. I may, however, notice that my earlier work has met with a great amount of appreciation, and its utility acknowledged in the past by a demand almost unprecedented, edition after edition being called for.
It is hardly necessary to add that my task has been accomplished with an earnest desire to assist in diffusing a love for an instrument which has been my constant companion for upwards of sixty years.[1] Moreover, I have a firm conviction of the real utility of the Microscope in the work of education, its practical value in many branches of science, art, and manufacturing industries. These are my chief reasons for applying myself once more to the task of revision, rewriting, and rearranging and bringing this book as far as possible into line with the knowledge gained in chemical pathology and bacteriology.
It will be noticed that in the first part, my subjects have as far as possible been treated from a historical point of view. This method has enabled me to affix dates of introduction of special inventions and improvements made in the instrument and its appliances. The enlargement of my pages has enabled me to devote more space to bacteriological processes, and by the further addition of plates and several hundred illustrations to more fully elucidate the subject matter of my text. In an Appendix I have introduced a selection of “Formulæ and Methods” of staining, mounting, etc., also tables of the “Metrical System,” now in general use in the laboratory; together with comparative thermometric values, all of which I trust may prove of service to the student.
Before bringing these few prefatory remarks to a close, a pleasing duty devolves upon me--that of tendering my thanks for cordial aid received from Professor Dr. EDGAR CROOKSHANK in dealing with his special subject, Bacteriology. From his valuable “Text-Book on Bacteriology” I have extracted much useful matter. I am equally indebted to Professor MARSHALL WARD, F.R.S., Cambridge, for much information on “Economic Botany,” and the great advances made in the knowledge of the uses of plants, and the industrial value of bacteria in particular. My acknowledgments are also due to the Messrs. WARNE for many illustrations placed at my disposal, and for useful facts derived from their “Royal Natural History.” It will, however, be seen that the results of a large amount of independent observation have been consigned to my pages. As the references show, recourse has been had to original sources for trustworthy, reliable information on many subjects. These are constantly, almost daily, being added to, as is made manifest by the numerous periodical publications of the day devoted to this and kindred sciences; the foremost and most important among which is that almost exclusively given to microscopical science, “The Journal of the Royal Microscopical Society of London,” the perusal of which I commend to my readers.
LONDON, JULY, 1898.
PREFACE TO THE FIRST EDITION.
The Author of this Publication entered upon his task with some hesitation and diffidence; but the reasons which influenced him to undertake it may be briefly told, and they at once explain his motives, and plead his justification, for the work which he now ventures to submit to the indulgent consideration of his readers.
It had been to him for some time a subject of regret that one of the most useful and fascinating studies--that which belongs to the domain of microscopic observation--should be, if not wholly neglected, at best but coldly and indifferently appreciated by the great mass of the general public; and he formed a strong opinion that this apathy and inattention were mainly attributable to the want of some concise, yet sufficiently comprehensive, popular account of the Microscope, both as regards the management and manipulation of the instrument, and the varied wonders and hidden realms of beauty that are disclosed and developed by its aid. He saw around him valuable, erudite, and splendid volumes, which, however, being chiefly designed for circulation amongst a special class of readers, were necessarily published at a price that renders them practically unattainable by the great bulk of the public. They are careful and beautiful contributions to the objects of science, but they do not adequately bring the value and charm of microscopic studies home, so to speak, to the firesides of the people. Day after day, new and interesting discoveries, and amplifications of truth already discerned, have been made, but they have been either sacrificed in serials, or, more usually, devoted to the pages of class publications; and thus this most important and attractive study has been, in a great measure, the province of the few only, who have derived from it a rich store of enlightenment and gratification: the many not having, however, participated, to any great extent, in the instruction and entertainment which always follow in the train of microscopical science.[2]
The manifold uses and advantages of the Microscope crowd upon us in such profusion, that we can only attempt to enumerate them in the briefest and most rapid manner in these prefatory pages.
It is not many years since this invaluable instrument was regarded in the light of a costly toy; it is now the inseparable companion of the man of science. In the medical world, its utility and necessity are fully appreciated, even by those who formerly were slow to perceive its benefits; now, knowledge which could not be obtained even by the minutest dissection is acquired readily by its assistance, which has become as essential to the anatomist and pathologist as are the scalpel and bedside observation. The smallest portion of a diseased structure, placed under a Microscope, will tell more in one minute to the experienced eye than could be ascertained by long examination of the mass of disease in the ordinary method. Microscopic agency, in thus assisting the medical man, contributes much to the alleviation of those multiplied “ills which flesh is heir to.” So fully impressed were the Council of the Royal College of Surgeons with the importance of the facts brought to light in a short space of time, that, in 1841, they determined to establish a Professorship of Histology, and to form a collection of preparations of the elementary tissues of both animals and vegetables, healthy and morbid, which should illustrate the value of microscopical investigations in physiology and medical science. From that time, histological anatomy deservedly became an important branch of the education of the medical student.
In the study of Vegetable Physiology, the Microscope is an indispensable instrument; it enables the student to trace the earliest forms of vegetable life, and the functions of the different tissues in the growth of plants. Valuable assistance is derived from its agency in the detection of adulterations. In the examination of flour, an article of so much importance to all, the Microscope enables us to judge of the size and shape of the starch-grains, their markings, their isolation and agglomeration, and thus to distinguish the starch-grains of one meal from those of another. It detects these and other ingredients, invisible to the naked eye, whether combined in atoms or aggregated in crystals, which adulterate our food, our drink, and our medicines. It discloses the lurking poison in the minute crystallisations which its solutions precipitate. “It tells the murderer that the blood which stains him is that of his brother, and not of the other life which he pretends to have taken; and as a witness against the criminal, it on one occasion appealed to the very sand on which he trod at midnight.”
The zoologist finds in the Microscope a necessary coadjutor. To the geologist it reveals, among a multiplicity of other facts, “that our large coal-beds are the ruins of a gigantic vegetation; and the vast limestone rocks, which are so abundant on the earth’s surface, are the catacombs of myriads of animal tribes, too minute to be perceived by the unaided vision.”
By “conducting the eye to the confines of the visible form,” the Microscope proves an effective auxiliary in defining the geometric properties of bodies. Its influence as an instrument of research upon the structure of bodies has been compared to that of the galvanic battery, in the hands of Davy, upon Chemistry. It detects the smallest structural difference, heretofore inappreciable, and, as an ally of Chemistry, enables us to discover the very small changes of form and colour effected by test-fluids upon solids; and dissects for us, so to speak, the most multiplex compounds. It opens out to the mind an extended and vast tract, opulent in wonders, rich in beauties, and boundless in extent.
The Microscope not only assists studies, and develops objects of profound interest, but also opens up innumerable sources of entertainment and amusement, in the ordinary conventional acceptation of these terms; disclosing to us peculiarities and attractions in abundance; impressing us with the wonderful and beautifully skilful adaptation of all parts of creation, and filling our minds with additional reverence and admiration for the beneficent and Almighty Creator.
The Author will conclude these prefatory observations with a few words in explanation of his arrangements, by way of dealing with the instrument and development of his subject. He has sought, in the volume that he now lays before the public, to point out and elucidate at once in a practical manner and in a popular style, the vast fund of utility and amusement which the Microscope affords, and has endeavoured to touch upon most of the interesting subjects for microscopic observation as fully as the restrictions of a limited space, and the nature of the succinct summary, would permit. To have dwelt upon each in complete detail would have necessitated the issue of many expensive volumes--and this would have entirely frustrated the aim which the writer had in view; he has, therefore, contented himself with the humble, but, he trusts, not useless, task of setting up a finger-post, so to say, to direct the inquirer into the wider road. In the section of the work devoted to the minuter portion of creation, he has ventured to dwell somewhat longer, in the belief that that department is more especially the province of the microscopist. He has arranged his topics under special headings, and in separate chapters, for the sake of perspicuity and precision; and has brought the ever-welcome aid of illustration to convey his explanatory remarks more vividly to the minds of his readers.
Finally, it is the Author’s hope that, by the instrumentality of this volume, he may possibly assist in bringing the Microscope, and its valuable and delightful studies, before the general public in a more familiar, compendious, and economical form than he found it at the period of its publication, so that, in these days of a diffused taste for reading and the spread of cheap publications, he may thus supply further exercise for the intellectual faculties; contribute to the additional amusement and instruction of the family circle, and aid the student of nature in investigating the wonderful and exquisite works of the Almighty. If it shall be the good fortune for this work, which is now confided with great diffidence to the consideration of the public, to succeed, in however slight a degree, in furthering this design, the Author will feel fully repaid for the amount of time and labour expended.
LONDON, May, 1854.
I. PAGE
EARLY HISTORY OF THE MICROSCOPE 1
Chapter I
LIGHT--ITS PROPAGATION--REFRACTION--SPHERICAL AND CHROMATIC ABERRATION--HUMAN EYE--FORMATION OF IMAGES--VISUAL ANGLE--ABBÉ’S THEORY OF MICROSCOPIC VISION--DEFINITION OF APERTURE--NUMERICAL APERTURE--ABBÉ’S APERTOMETER--STEREOSCOPIC BINOCULAR VISION 12
Chapter II
SIMPLE AND COMPOUND MICROSCOPES--EVOLUTION OF THE MODERN ACHROMATIC MICROSCOPE--IMPROVEMENTS IN THE MODERN MICROSCOPE: THE ROSS-JACKSON, POWELL AND LEALAND, BECK’S, BAKER’S, PILLISCHER, ZEISS, LEITZ, WATSON’S, VAN HEURCK’S EDINBURGH STUDENTS’, SWIFT’S, AND BACTERIOLOGICAL 72
Chapter III
APPLIED OPTICS--EYE-PIECES--ACHROMATIC OBJECTIVES AND CONDENSERS--MAGNIFYING POWER OF EYE-PIECES AND OBJECTIVES--METHOD OF EMPLOYING THE CONDENSER--ITS ILLUMINATION MIRROR--ACCESSORIES OF THE MICROSCOPE--FINDERS--MICROMETERS--CAMERA-LUCIDA--MICROSCOPE IN POSITION FOR DRAWING--ABBÉ’S TEST-PLATE--MICRO-PHOTOGRAPHY--POLARISATION OF LIGHT--THE MICRO-SPECTROSCOPE 139
Chapter IV
PRACTICAL MICROSCOPY--MANIPULATION--MODE OF EMPLOYING THE MICROSCOPE--WORKING ACCESSORIES--METHODS OF PREPARING, HARDENING, STAINING, AND SECTION CUTTING--CUTTING HARD STRUCTURES--INJECTING APPARATUS, MATERIAL, ETC., EMPLOYED IN BACTERIOLOGICAL INVESTIGATIONS--WARM CHAMBERS AND INCUBATORS--PREPARING, MOUNTING, CEMENTING, AND COLLECTING OBJECTS 258
Chapter I
MICROSCOPIC FORMS OF LIFE--THALLOPHYTES, PTERIDOPHYTA, PHANEROGAMÆ--STRUCTURE AND PROPERTIES OF THE CELL--PATHOGENIC FUNGI AND MOULDS--PARASITIC DISEASES OF PLANTS, MAN, AND ANIMALS--INDUSTRIAL USES OF FUNGI AND SACCHAROMYCETES--DESMIDIACEÆ AND DIATOMACEÆ--LICHENS, MOSSES, FERNS, FLOWERING PLANTS 353
Chapter II
SUB-KINGDOM PROTOZOA--RHIZOPODA--GROMIA AND FORAMINIFERA--INFUSORIA--CILIATA--ROTIFERA--PORIFERA--SPONGES 478
Chapter III
ZOOPHYTES--CŒLENTERATA--MEDUSÆ--CORALS--HYDROZOA--MOLLUSCA-- ANNULOSA--WORMS--ENTOZOA--ANNELIDA--CRUSTACEA 515
Chapter IV
ARTHROPODA--INSECTA--ARACHNIDA--ACARINA--IXODIDÆ--MITES AND TICKS 583
Chapter V
VERTEBRATA--INTERNAL AND EXTERNAL STRUCTURES 633
Chapter VI
THE MINERAL AND GEOLOGICAL KINGDOMS 670
Appendix
DR. MERCER ON ILLUMINATION, AND ABBÉ’S THEORY--MICRO-SPECTROSCOPE--FORMULÆ, METHODS, CEMENTING, CLEARING, HARDENING, AND MOUNTING--TABLES, METRIC AND THERMOMETRIC 672
INDEX 691
DESCRIPTION OF PLATES,
COLOURED AND PLAIN.
FRONTISPIECE.
RADIOLARIA.
In this Plate Fig. 1 shows the elegant lattice-sphere of Rhizosphæra; Fig. 2 represents Sphærozoum, whose skeleton consists of loose spicules, arranged tangentially; Actinomma, Fig. 3, possesses three concentric lattice-spheres, joined by radiating spines; Figs. 4, 5, and 6, represent Lithomespilus, Ommatocampe, and Carpocanium; Fig. 7 represents a deep-sea form (Challengeria), whose oval case is formed of a regular, very fine-meshed, network; Fig. 8 depicts the elegant lattice-sphere of Heliosphæra; Figs. 9 and 10, Clathrocyclas and Dictyophimus.
PLATE I.--Page 400.
PROTOPHYTA. THALLOPHYTES.
Fig. 1. Peziza bicolor--2. Truffle: a. ascus of spores; b. mycelium--3. Sphæria herbarum: a. piece of dead plant, with S. herbarum natural size; b. section of same, slightly magnified; d. Ascus with spores, and paraphyses more magnified--4. Peziza pygmæa--5. Apical form of same--6. P. corpulasis: Ascus with spores and paraphyses, merely given as a further illustration of structure in Peziza--7. Yeast healthy--8. Yeast exhausted--9. Phyllactinia guttata--10. Yeast with favus spores and mycelium of fungus--11. Favus ferment, with oïdium and bacteria--12. Puccinia spores, growing in a saccharine solution--13. Aerobic bacteria--14. Spores and mycelia from eczema produced by yeast--15. Volvox globator--16. Amœboid condition of portion of volvox--17. Puccinia buxi--18. Ditto, more enlarged--(17 to 20 illustrate Ascomycetes.)--19. Æcidium grossulariæ from transverse section of leaf of currant: a. spermogones on upper surface; b. perithecia with spores--20. Phragmidium bulbosum, development of--21. Palmella parietina, trans. section through a spermogone, showing green gonidia and spermatia escaping--22. Æcidium berberida, from leaf of berberry--23. Vaucheria sessilis--24. Stephanosphæra pluvialis: a. Full-grown example, germ cells spindle-shaped with flagella; b. Resting-cell; c. division into four; d. Free-swimming ciliated young specimen; e. Amœboid condition--25. a, b, c, d, e, f and g, Development of lichen gonidia--26. Palmella stellaris (lichen), vertical section through apothecium, showing asci, spores, and paraphyses, with gonidia and filamentous medulla: a. Spermatophore with spermatia--27. Moss gonidia assuming amœboid form.
Typical forms of Protophyta; 7 to 14, modes of development or rudimentary conditions; Confervoideæ, 23; Vaucheria, Stephanosphæra, 24; Volvox, 15, &c.
PLATE II.--Page 412.
PROTOPHYTA. ALGÆ.
Fig. 27. Ceramium acanthonotum--28. Closterium, Triploceras gracilis--29. Cosmarium radiatum--30. Micrasterias denticulata--31. Docidium pristidæ--32. Callithamnion plumula--33. Diatoma, living: a. Licmophora splendida; b. Achnanthes longipes; c. Grammatophora marina. These figures are intended to show the general character of the endochrome and growth of frustule--34. Callithamnion refractum--35. Jungermannia albicans; b. representing elater and spores--36. Leaf with antheridia, or male elements, represented more magnified at a to the left of the figure--37. Ceramium echinotum--38. Pleurosigma angulatum, side view--39. Delesseria hypoglossum--40. Pleurosigma angulatum, front view, endochrome not represented--41. Ceramium flabelligerum.
PLATE III.--Page 479.
PROTOZOA.
Figs. 43, 44, 45, 46, 47, 48, 49, 50, 51, 52. These figures are from drawings made by Major Owen, to illustrate forms of living Polycystina, sketched from life; these convey a faint idea of the richly coloured appearance of the natural structure; Figs. 48 to 52--53. Gregarina lumbricorum, round form--54. Gregarina lumbricorum, the usual elongated form--55. Gregarina serpulæ--56. Gregarina Sieboldii; illustration of septate form, with reflexed hook-like processes--57. Gregarina lumbricorum, encysted--58. Gregarina lumbricorum, more advanced and pseudo-navicellæ forming--59. Gregarina lumbricorum, free pseudo-navicella of--60, 61. Gregarina lumbricorum, amœboid forms of--62. Cruciate sponge-spicule--63. Astromma Humboldtii--64. Eözoon Canadense, represents appearance of a portion of the natural size--65. Eözoon Canadense, magnified, showing portions of cell-walls left uncoloured, the animal sarcode inhabiting it coloured dark green as in nature, and converted by fossilisation into a silicious mineral; the narrow bands passing between these are processes (stolons) of the same substance--66. Actinophrys sol, budding--67. Euglena viridis: a. contracted; b. elongated form--68. Acineta tuberosa--69. Œcistes longicornis (Davis)--70. Oxytricha gibba (side view)--71. Oxytricha pellionella--72. Thuricola valvata, expanded--73. Cyclidium (glaucoma)--74. Oxytricha scintillans--75 to 79, 80 to 85, illustrate types of Foraminifera discovered by Major Owen, living--75. Globigerina acerosa, n. sp., broken open to show interior--76. Globigerina, n. sp., broken open to show interior--77. Globigerina hirsuta--78. Globigerina universa--79 and 81. G. Bulloides--80. Conochilus vorticella--82. Globigerina inflata, sinistral shell--83. Pulvinulina Micheliniana--84. P. Canariensis--85. P. Menardii.
PLATE IV.--Page 514.
METAZOA. BRYOZOA.
Fig. 86. Hartea elegans--87. Side view of Synapta spicula--88. Ophioglypha rosula (very immature specimen): a. Claw hooks; b. palmate spicula. The development of this species is described by G. Hodge, in “Transactions of Tyneside Naturalists’ Field-Club”--89. Spine of a star-fish, particularly interesting as showing the reticular calcareous network obtaining in this as in all other hard parts of the Echinodermata--90. Very minute Spatangus, obtained from stomach of a bream: many of the spines are gone, but the structure of the shell is intact and forms a beautiful object, interesting in connection with the source whence obtained--91. Ophioglypha neglecta: wriggling or brittle starfish. The plate does not admit of a figure on a scale sufficient to show the full beauty of this object--92. Tubularia Dumortierii--93. Pedicellaria mandibulata from Uraster glacialis--94. Pedicellaria forcepiforma, from the same--95. Cristatella mucedo; 96. Edge-view of statoblast; 97. early stage in development of same--98. Lophopus crystallinus--99. Plumatella repens with ova, on submerged stem--100. Tænia echinococcus--101. Hydatids from human liver--102. Bilharzia hæmatobia--103. Amphistoma conicum--104. Trichina spiralis from fleshy part of Hambrc’ pork--105. Trichina spiralis male, separated from muscle.--106, 107. Fasciola gigantea.
PLATE V.--Page 556.
MOLLUSCA.
Fig. 108. Velutina lævigata, portion of lingual membrane--109. Velutina lævigata, part of mandible--110. Hybocystis blennius, portion of palate--111. Sepia officinalis, portion of palate--112. Aplysia hybrida, part of mandible--113. Loligo vulgaris, part of palate--114. Haliotis tuberculatus, part of palate--115. Cistula catenata, part of palate--116. Patella radiata, part of palate--117. Acmæa virginea, part of palate--118. Cymba olla, part of palate--119. Scapander ligniarius--120. Oneidoris bilamellata, part of palate--121. Testacella Maugei, part of palate--122. Pleurobranchus plumula, part of mandible--123. Turbo marmoratus, part of palate.
Lingual membranes of Mollusca; drawings made from specimens in the collection formed by F. E. Edwards, Esq., now in the British Museum. Typical examples of the numerous forms of Odontophors met with in Gasteropod and Cephalopod Mollusca.
PLATE VI.--Page 582.
INSECTA.
Fig. 124. Egg of Caradrina morpheus, mottled rustic moth--125. Egg of tortoise-shell butterfly, Vanessa urticæ--126. Egg of common footman, Lithosia complanula--127. Egg of shark moth, Cucullia umbratica--128. Maple-aphis--129. Egg shell of acarus, empty--130. Egg of house-fly--131. Mouth of Tsetse-fly, Glossina morsitans--132. Vapourer moth, Orgyia antiqua: antenna of male--133. Vapourer moth: antenna of female; a. branch more magnified to show rudimentary condition of the parts--134. Tortoise-shell butterfly; head in profile, showing large compound eye, one of the palpi, and spiral tongue--135. Tortoise-beetle, Cassida viridis; under surface of left fore-foot, to show the bifurcate tenent appendages, one of which is given at a more magnified. This form of appendage is characteristic of the family. “West on Feet of Insects,” Linn. Trans. vol. xxiii. tab. 43-136. Egg of blue argus butterfly, Polyommatus argus--137. Egg of mottled umber, Erannis defoliaria--138. Egg of Ennomos erosaria, thorn-moth--139. Egg of Aspilates gilvaria, straw-belle--140. Blow-fly, Musca vomitoria: left fore-loot, under-surface, to show tenent hairs; a b more magnified; a from below, b from the side--141. House-fly larva--142. Amara communis: left fore-foot, under-surface, to show form of tenent appendages, of which one is given more magnified at a. These, in ground beetles, are met with only in the males, believed to be used for sexual purposes. These appendages are carefully protected when not in use, as explained by West--143. Ephydra riparia: left fore-foot, under-surface. This fly is met with sometimes in immense numbers on the water in salt-marshes; it has no power of climbing on glass, as seen by the structure of the tenent hairs; the central tactile organ also is peculiar, the whole acting as a float, one attached to each foot, enabling the fly to rest on the surface of the water; a. an enlarged external hair--144. Egg of bot-fly, the larva just escaping--145. Egg of parasite of pheasant--146. Egg of Scatophaga--147. Egg of parasite of magpie--148. Egg of Jodis vernaria, small emerald moth.
PLATE VII.--Page 633.
VERTEBRATA.
Fig. 149. Toe of mouse, integuments, bone of foot, and vessels--150. Tongue of mouse, showing erectile papillæ and muscular layer--151. Brain of rat, showing vascular supply--152. Vertical section of tongue of cat, fungi-form papillæ and capillary loops passing into them, vessels--153. Kidney of cat, showing Malpighian turfts and arteries--154. Small intestine of rat, with villi and layer of mucous membrane exposed--155. Nose of mouse, showing vascular supply to roots of whiskers--156. Vascular supply to internal gill of tadpole, during one phase of development--157. Section through sclerotic coat and retina of cat’s eye, showing vascular supply of choroid vessels cut cross-ways--158. Interior of fully-developed tadpole, exhibiting heart, vascular arrangement and vascular system throughout body and tail.
This plate is designed to show the value, in certain cases, of injected preparations in the delineation of animal structures. By thus artificially restoring the blood and distending the tissues, a better idea is obtained of the relative condition of parts during life.
PLATE VIII.--Page 220.
POLARISCOPE OBJECTS.
Fig. 158. New Red Sandstone--159. Quartz--163. Granite--161. Sulph. Copper--162. Saliginine--163. Sulph. Iron and Cobalt, crystallized in the way described by Thomas--164. Borax--165. Sulph. Nickel and Potash--166. Kreatine--167. Starch granules--168. Aspartic Acid--169. Fibro-cells, orchid.--170. Equisetum cuticle--171. Holothuria spicula, Australia--172. Holothuria spicula, Port Essington--173. Deutzia scabra; upper and under surface--174. Cat’s tongue, process--175. Prawn shell, exuvia with crystals of lime--176. Grayling scale--177. Scyllium caniculum scale--178. Rhinoceros horn, transverse section--179. Horse hoof--180. Dytiscus, elytra with crystals of lime.
PLATE IX.--Page 362.
TYPICAL PLATE OF BACTERIA AND SCHIZOMYCETES.
Fig. 1. Cocci, singly, and varying in size--2. Cocci in chains or rosaries (streptococcus)--3. Cocci in a mass (staphylococcus)--4 and 5. Cocci in pairs (diplococcus)--6. Cocci in groups of four (merismopedia)--7. Cocci in packets (sarcina)--8. Bacterium termo--9. Bacterium termo × 4000 (Dallinger and Drysdale)--10. Bacterium septicæmiæ hæmorrhagicæ--11. Bacterium pneumoniæ crouposæ--12. Bacillus subtilis--13. Bacillus murisepticus--14. Bacillus diphtheriæ--15. Bacillus typhosus (Eberth)--16. Spirillum undula (Cohn)--17. Spirillum volutans (Cohn)--18. Spirillum choleræ Asiaticæ--19. Spirillum Obermeieri (Koch)--20. Spirochæta plicatilis (Flügge)--21. Vibrio rugula (Prazmowski)--22. Cladothrix Försteri (Cohn)--23. Cladothrix dichotoma (Cohn)--24. Monas Okenii (Cohn)--25. Monas Warmingii (Cohn)--26. Rhabdomonas rosea (Cohn)--27. Spore-formation of Bacillus alvei--28. Spore-formation (Bacillus anthracis)--29. Spore-formation in bacilli cultivated from rotten melon (Fränkel and Pfeiffer)--30. Spore-formation in bacilli cultivated from earth (Fränkel and Pfeiffer)--31. Involution-form of Crenothrix (Zopf)--32. Involution-forms of Vibrio serpens (Warming)--33. Involution-forms of Vibrio rugula (Warming)--34. Involution-forms of Clostridium polymyxa (Prazmowski)--35. Involution-forms of Spirillum choleræ Asiaticæ--36. Involution-forms of Bacterium aceti (Zopf and Hansen)--37. Spirulina-form of Beggiatoa alba (Zopf)--38. Various thread-forms of Bacterium merismopedioides (Zopf)--39. False-branching of Cladothrix (Zopf).
PLATE X.--Page 420.
DESMIDIACEÆ.
Fig. 1. Euastrum oblongum--2. Micrasterias rotata--3. Desmidium quadrangulatum--4. Didymoprium Grevillii--5. Micrasterias, sporangium of--6. Didymoprium Borreri--7. Cosmarium Ralfsii--8, 9. Xanthidiæ--10. X. armatum--11. Cosmarium crenatum--12. C. Sphærozosma vertebratum--13, 17. Sporangia of Cosmarium--14. X. fasiculatum--18. Staurastrum hirsutum--19. Arthrodesmus convergens--15. Staurastrum tumidum--16. Staurastrum dilitatum--21. Penium--22. Euastrum Didelta--23. Docidium clavatum--24. Pediastrum biradiatum--25. Closterium, showing conjugation or self-division--26. Volvox, parent cell about to break up--27. Penium Jennerii--28. Aptogonum desmidium--29. Pediastrum pertusum--30. Ankistrodesmus falcatus--31. Parent cell of Closterium--32. Staurastrum gracilis.--33. Conjugation of Penium margaritaceum--34. Spirotænia--35. Closterium
PLATE XI.--Page 428.
DIATOMACEÆ.
Fig. 1. Arachnoidiscus--2. Actinocyclus (Bermuda)--3. Cocconeis (Algoa Bay)--4. Coccinodiscus (Bermuda)--5. Isthmia enervis--6. Zygoceros rhombus--7. Campilodiscus clypeus--8. Biddulphia--9. Gallionella sulcata--10. Triceratium, found in Thames mud--11. Gomphonema geminatum, with their stalk-like attachments--12. Dictyocha fibula--13. Eunotia--14. Cocconema--15. Fragilaria pectinalis--16. Meridion circulare--17. Diatoma flocculosum.
PLATE XII.--Page 438.
MICRO-PHOTOGRAPH OF TEST DIATOMS.
Taken with Zeiss’s 3 mm. N.A. 1·40 by Mr. A. A. Carvell for the Author.
Fig. 1. Portion of Surirella gemma, magnified × 1,000--2. Broken Frustule of Pleurosigma angulatum, × 750--3 and 5. Triceratium favus ×--1,000--4. Navicula rhomboides × 1,300--6. Pleurosigma formosum, showing black dots--7. P. formosum, showing white dots, × 750.
PLATE XIII.--Page 454.
PHANEROGAMIÆ--ELEMENTARY TISSUE OF PLANTS.
Fig. 1. Elementary ovid cells--2. Branching tissue--2A and 3. Spiral vessels from Opuntia vulgaris--4. Stellate tissue, section of rush--5. Mushroom spawn--6. Starch from Tous-les-mois--7. Starch from sago--8. Starch from rice--9. Wheat-starch--10. Rhubarb starch in isolated cells--11. Maize-starch--12. Oat-starch--13. Barley-starch--14. Section of Potato cells, filled with healthy starch--15. Potato starch more highly magnified--16. Section of Potato with nearly all starch absent--17. Potato with starch destroyed by fungoid disease--18. Ciliated spermagones--19. Hairs of stinging-nettle--20. Section of cellular parenchyma of ripe strawberry.
PLATE XIV.--Page 472.
STELLATE AND CRYSTALLINE TISSUE.
Fig. 1. Epidermis of husk of wheat, spiral vessels and silicious crystals--2. Section of cane, silicious cell walls, internal portion filled with granular bodies--3. Cuticular layer of the onion, showing crystals of calcium carbonate and oxalate--4. Cells of garden rhubarb, with crystalline bodies and raphides--4_a_. Another layer filled with starch grains--5. Section of pear, testa, sclerogenous and granular tissue--6. Stellate hairs, sinuous cells and silicious parenchyma of leaf of Deutzia scabra, under surface--7. Silicious cuticle layer of grass, Pharus cristatus.
PLATE XV.--Page 482.
RHIZOPODA.--GROMIA.--FORAMINIFERA.
Fig. 1. Astrorhiza limicola--2. Lieberkühnia paludosa--3. Micro-gromia socialis undergoing fission--4. A colony of Hertwig’s Micro-gromia socialis--5. G. Lieberkühnia--6. Egg-shaped Gromia, G. oviformis, with pseudopodia extended, magnified 500 diameters. “Hertwig Ueber Micro-gromia, archiv. für Mickr. Anat. bdx.”
PLATE XVI.--Page 510.
SPONGE SPICULES.
Fig. 1. A portion of sponge, Halichondria simulans, showing silicious spicula imbedded in the sarcode matrix--2. Spicula divested of its matrix by acid--3. Gemmule Spongilla fluviatallis enclosed in spicula--4. Birotulate spicula from same--5. Gemmule after being steeped in acid showing reticulated coating of birotulate spicula--6. Gemmules of Geodia--7. Gemmule in more advanced stage of growth--8. Skeleton of the acerate form covered by rows of spines--9. Showing rings of growth and horny covering, and bundles of spicula of the genus Verongia--10. Sphero-stellate spicula of Tethya--11. Tricuspidanchorate and sphero-stellate spicula--12. Acuate-bi-clavate and other forms of spicula from Geodia--13. Clavate spicula covered with short spines.
PLATE XVII.--Page 518.
ZOOPHYTES, ASTEROIDS, NUDIBRANCHS, AND ECHINOIDS.
Fig. 1. a. Astrophyton scutatum--b. Doris pinnatifida, back and side view--c. Æquorea Forbesina--d. Medusæ bud--e. Thaumantias corynetes--f. Echinus in an early free stage--g. Echinus sphæra--h. Cydippe pyleus--i. Ascidiæ--k. Botryllus violaceus, on a Fucus--l. Corystes cassivelaunus--m. Eurynome aspera--n. Ophiocoma rosula--o. Pagurus Prideauxii--p. Ebalia Permantii.
PLATE XVIII.--Page 558.
SHELLS OF MOLLUSCA.
Fig. 1. Transverse section of spine of Echinus--2. Another section of Echinus, showing reticulated structure, the calcareous portion dissolved out by acid--3. Horizontal section of shell of Haliotis splendens, showing stellate pigment--4. Shell of crab with granules in articular layer--5. Another section of same shell, showing hexagonal structure--6. Horizontal section of coach-spring shell, Terebratulata rubicunda, showing radiating perforations--7. Transverse section of shell of the Pinna ingens--8. Crystals of carbonate of lime, from oyster shell.
PLATE XIX.--Page 636.
VERTEBRATA.
Fig. 1. a. Spheroidal epithelium cells, filled with central nuclei and granular matter; b. mucous membrane of stomach, showing cells, with open mouths of tubes at the bottom of each, magnified 50 diameters--2. a. Diagram of a portion of the involuted mucous membrane, showing continuation of its elements in the follicles and villi, with a nerve entering the submucous tissue. The upper surface of one villus is covered with cylindrical epithelium; the other denuded, and with dark line of basement membrane running around it; b. epithelium cells, separated and magnified 200 diameters, a central nucleus, with a nucleolus, seen in centre; c. pavement epithelium cells, from the mucous membrane of bronchial or air tubes with nuclei, and nucleoli in some; d. vibratile or ciliated epithelium, nuclei visible, and cilia at the upper free surface, magnified 200 diameters--3. a. is one of the tubular follicles from a pig’s stomach, cut obliquely to display upper part of cavity, and the cylindrical epithelium forming its walls, a few cells detached; b. shows a section of a lymphatic, with capillary blood-vessels, distributed beneath the mucous surfaces--4. Cells of adipose tissue, or fat, magnified 100 diameters--5. a single fat-cell separated, and magnified 250 diameters--6. A capillary of blood-vessels distributed through tissue--7. Section of the Tendo-Achillis as it joins the cartilage, showing stellate cells of tendon, seen to be gradually coalescing to form round or oval cells of cartilage--8. A vertical section of cartilage, with clusters of cells arranged in columns previous to their conversion into bone--9. A small transverse section of the same, showing the gradual change of the cartilage cells at a. into the true bone cells, lacunæ, at b. with characteristic canaliculi--10. A stellate nerve corpuscle, with tubular processes issuing forth, at a. filled with corpuscles containing black pigment, above which is a corpuscle the nucleus of which is seen to have nucleoli; at b. a corpuscle enclosed within sheath, and filled with granular matter taken from the root of a spinal nerve--11. The continuity of muscle, the upper portion, with connective tissue of the lower portion, from the tongue of a lamb--12. Branched muscle, ending in stellate connective cells, from the upper lip of the rat--13. Choroidal black pigment-cells from the human eye.
PLATE XX.--Page 658.
BONE STRUCTURE.
Figs. 1. and 2. Transverse section of the human clavicle (collar bone), showing Haversian canals, concentric laminæ, and concentric arrangement of bone cells--3. Transverse section of the femur of an ostrich--4. Transverse section of humerus (fore-arm) bone of a turtle, Chelonia mydas--5. Horizontal section of the lower jaw-bone of a conger eel, in which no Haversian canals are present--6. A portion of the cranium of a siren, Siren lacertina--7. Portion of bone taken from the shaft of humerus of a Pterodactyle, showing elongated bone-cells characteristic of the order Reptilia--8. Horizontal section of a scale, or flattened spine, from the skin of a Trygon (sting-ray), showing large Haversian canals, numerous wavy parallel tubes, also bone-cells with canaliculi communicating as in dentine.
ERRATA.
Prefaces, page vi., line 22 Insert “a” into “admitted.” " " x., line 13 Insert “the” before “assistance.” " " xii. Insert “for” at commencement of line 24. Page 33, line 13 For “Rabbit” read “Kitten.” " 486, 4th line from bottom Strike out “The late.” " 511, two lines from bottom For “Plate XIII.” read “Plate XVI.” " 584, 5th line from bottom Insert “Stalk-Eyed” before “crustaceans.” " 624, line 12 For “or” read “and.” " 633, Plate VII. Numbering of figures-- For “152” read “158.” For “152a” read “152.”
(Professor Abbe, erroneously referred to more than once as “the late” is, the author is happy to say, in excellent health).
THE MICROSCOPE.
I. Early History of the Microscope
The instrument known as the Microscope derives its designation from two Greek words, μικρὸς (mikros), small, and σκοπέω (skopeo), to see or observe; and is an optical instrument by means of which objects are so magnified that details invisible or indistinct to the naked eye are clearly seen. Its origin, so far as yet can be traced back, seems to be of a doubtful nature. It is tolerably certain the ancients had little or no conception of the magnifying power of lenses; this may be surmised from their writings. The elder Pliny incidentally states that the physicians of his day cauterised by means of “a globe of crystal.” The learned Greek physician, Galen, however, demonstrates conclusively that in the first and second centuries of our era the use of magnifying lenses was quite unknown either to Greek or Roman. Moreover, the writings of Archimedes, Ptolemy, and other learned men, show that, although they had some idea of the action of refraction at plane surfaces, as of water, yet of the refraction at curved surfaces they had formed no conception. Indeed, they refer quite indiscriminately to the spherical form, or the disc, or the plane surface of the water, but not one of them speaks of the lenticular form, or the curvature of their surfaces.
As to the more powerful optical instruments, the telescope and microscope, although it would appear that Alhazen in the 10th or 11th century, Roger Bacon in the 13th, and Fracastoro and Baptist Porta in the 16th, had formed some idea that lenses might be made and combined so that distant objects might be seen clearer, or near ones magnified beyond the power of normal vision; yet we hold with Kepler, that no instrument analogous to our telescope was known before the early part of the 17th century.
The combination of lenses associated with the name of Galileo, was, he tells us, of Dutch origin, and of a date anterior to that of his telescope, constructed by him in 1609; and this would appear to be the probable origin of the microscope consisting of a combination of a convex object lens with a concave eye lens.[3]
It now appears almost impossible to assign the exact date of the first production of the microscope (as distinguished from the simple magnifying lens), but those who have made a special investigation, agree that it must have been invented between 1590 and 1609, and that either of the three spectacle-makers of Middelburg, Holland, Hans Janssen, his son Zacharias Janssen, and Hans Lippershey, may have been the inventor, the probabilities being in favour of the Janssens, and there the question must remain.
The history of the modern microscope, like that of nations and arts, has had its brilliant periods, in which it shone with uncommon splendour, and was cultivated with extraordinary ardour; these periods have been succeeded by intervals marked with no discovery, and in which the science seemed to fade away, or at least to lie dormant, till some favourable circumstance--the discovery of a new object, or some new improvement in the instruments of observation--awakened the attention of the curious, and reanimated the spirit of research. Thus, soon after the invention of the microscope, the field it presented to observation was cultivated by men of the first rank in science, and who enriched almost every branch of natural history by the discoveries made by means of this instrument.
The Modern Microscope.
To the celebrated Dr. Hooke belongs the honour of publishing an account of the compound instrument in 1665 in his “Micrographia.” His first claim, however, is founded on the application of a lamp adjustable on a pillar, together with a glass globe of water and a deep plano-convex condensing lens. By means of this arrangement, he says, “The light can be directed more directly on the object under examination.” In the further description given of his microscope, he explains: “It has four draw-tubes for lengthening the body, and a third lens to the optical combination.” This, it would appear, was only brought into use when he wished to see the whole object at once: “The middle-glass lens, conveying a very great company of radiating pencils (of light) which would stray away; but when I had occasion to examine the small parts of a body, I took out the middle glass and made use of one eye-glass with the object-glass.”
From Hooke’s description I gather that he also introduced the ball-and-socket movement into the construction of the body of his instrument. This has found many imitators since his day; some of them have gone so far as to claim the invention as one quite new. For small accessories, where the leverage need not be considered, the ball-and-socket has proved convenient enough; but not, however, if applied to the stand of the microscope. Hooke, in his early work, expressed dissatisfaction with the English-made lenses he had in use. He complains of the “apertures of the object-glasses, which are so small that very few rays are admitted; none will admit a sufficient number of rays to magnifie the object beyond a determinate bigness.” So we may take it that he thus early discovered the great importance of an increase in the aperture of his microscope. Other improvements of importance were made, and he was the first to describe a useful method of estimating the magnifying power of his lenses, and the difficulty of distinguishing between a prominence and a depression in the object under investigation, which he was made more fully aware of when preparing drawings for the illustration of his “Micrographia Illustrata”; this would be in 1664, if not earlier. His book created no little sensation on its first appearance, and it soon became scarce. Hooke (says Mr. Mayall) “must undoubtedly be credited with the first suggestion of immersion lenses.” Nevertheless, in his “Lectures and Collections,” published in 1676, he appears to be no longer enthusiastic over his double microscope, and once more he reverts to the simpler instrument of his earlier days. Whether this change of opinion was due to the publication of Leeuwenhoek’s observations with his simple microscopes it is impossible to say.
As early as 1673 Leeuwenhoek communicated some important discoveries made by a simple microscope of his own construction to the Royal Society; he, however, gave no particulars of the construction of the instrument. Dr. Adams, writing to his friend (Sir) Hans Sloane, says: “They appear to be spherules lodged between two plates of gold or brass, in a hole whose diameter appears to be no bigger than that of a small pin’s head.” At his death he bequeathed to the Royal Society a cabinet containing twenty-six of these microscopes; the cabinet and the microscopes long ago disappeared, but not before they were carefully examined and described by Mr. Henry Baker, F.R.S. In his report to the Royal Society, he says: “They consisted of a series of convex-lenses, ranging in power from 1·20 to 1·5, and magnifying from 160 to 40 diameters.” This must now be regarded as an eventful period in the history of the microscope, since Leeuwenhoek’s discoveries created a great sensation throughout Europe. And all further improvements in compound instruments appear to have been laid aside for some considerable period in consequence: and the pocket instrument of Wilson, together with that of his scroll standard (seen on the cover of this book), and which was one of the first simple microscopes with a mirror mounted on the base in a line with the optic axis.
The discoveries once more made, and at a much later period (1738), by Dr. Nathaniel Lieberkuhn with his simple microscopes, and by means of which he discovered the minute structure of the mucous membrane of the alimentary canal, and which alone would have immortalised his name had we not preserved in use to this day an important adjunct of every modern instrument, the Lieberkuhn reflector.
In the Museum of the Royal College of Surgeons of England, there is a small cabinet of two drawers, containing a set of twelve of his simple microscopes, each being provided with an original injection. The form of the instrument is shown in Figs. 1 and 2. a b represents a piece of brass tubing about an inch long and an inch in diameter and provided with a cap at each extremity. The one at a carries a small double-convex lens of half an inch focal length; while at b there is fixed a condensing lens three-quarters of an inch in diameter. In Fig. 2 the instrument is seen in section, and explains itself. It is held by the handle in such a position that the rays of light, from a lamp or a white cloud, may fall on the condenser b, and concentrate on the speculum l. This again further condenses the rays on the disc c, where the object is held, and its adjustment made by the milled-head screw d, so as to bring it within the focus of the lens a.
From this digression I pass on to the evolution of the compound microscope. The earliest workable form known was that designed by Eustachio Divini, who brought it to the notice of the Royal Society in 1668. It consisted of two plano-convex lenses, combined with their convex surfaces retained in apposition. His idea was subsequently improved upon by a London optician. Not long afterwards, Philip Bonnani published an account of his improved compound microscope; and we are certainly indebted to him for two or more forms of the movable horizontal microscopes, and for the compound condenser fitted with focussing gear for illuminating transparent objects by transmitted light. I must, however, pass by the many changes made in the structure and form of the instrument by the celebrated Dr. Culpeper, Scarlet, Cuff, and many other inventors.
=Benjamin Martin’s Microscope.=--Benjamin Martin, about 1742, was busily engaged in making improvements in the microscope, and I may say he was certainly the first to provide accurate results for determining the exact magnifying power of any object-lens, so that the observer might state the exact amplification in a certain number of diameters. He devised numerous improvements in the mechanism and optical arrangements of the instrument; the rack and pinion focussing adjustments; the inclining movements to the pillar carrying the stage; and the rectangular mechanical motions to the stage itself. He was familiar with the principles of achromatism, since it appears he produced an achromatic objective about 1759, and he is said to have sent an achromatic objective to the Royal Society about that date. But an ingeniously constructed microscope by Martin found its way to George the Third, the grandfather of our Queen, and afterwards came into the possession of the late Professor John Quekett, of the Royal College of Surgeons, who presented it to the Royal Microscopical Society of London. This microscope will ever associate Martin’s name with the earliest and best form of the instrument, even should he not receive full recognition as the inventor of the achromatic microscope. On this account I introduce a carefully made drawing of so singularly perfect a form of the early English microscope to the notice of my readers. (Fig. 3.) The description given of it by the late Professor Quekett is as follows:--“It stands about two feet in height, and is supported on a tripod base, A; the central part of the stem, B, is of triangular figure, having a rack at the back, upon which the stage, O, and frame, D, supporting the mirror, E, are capable of being moved up or down. The compound body, F, is three inches in diameter; it is composed of two tubes, the inner of which contains the eye-piece, and can be raised or depressed by rack and pinion, so as to increase or diminish the magnifying power. At the base of the triangular bar is a cradle joint, G, by which the instrument can be inclined by turning the screw-head, H (connected with an endless screw acting upon a worm-wheel). The arm, I, supporting the compound body, is supplied with a rack and pinion, K, by which it can be moved backwards and forwards, and a joint is placed below it, upon which the body can be turned into the horizontal position; another bar, carrying a stage and mirror, can be attached by a screw, L N, so as to convert it into a horizontal microscope. The stage, O, is provided with all the usual apparatus for clamping objects, and a condenser can be applied to its under surface; the stage itself may be removed, the arm, P, supporting it, turned round on the pivot, C, and another stage of exquisite workmanship placed in its stead, the under surface of which is shown at Q.”
This stage is strictly a micrometer one, having rectangular movements and a fine adjustment, the movements being accomplished by the fine-threaded screws, the milled heads of which are graduated. The mirror, E, is a double one, and can be raised or depressed by rack and pinion; it is also capable of removal, and an apparatus for holding large opaque objects, such as minerals, can be substituted for it. The accessory instruments are very numerous, and amongst the more remarkable may be mentioned a tube, M, containing a speculum, which can take the place of the tube, R, and so form a reflecting microscope. The apparatus for holding animalcules or other live objects, which is represented at S, as well as a plate of glass six inches in diameter, with four concave wells ground in it, can be applied to the stage, so that each well may be brought in succession under the magnifying power. The lenses belonging to this microscope are twenty-four in number; they vary in focal length from four inches to one-tenth of an inch; ten of them are supplied with Lieberkuhns. A small arm, capable of carrying single lenses, can be supplied at T, and when turned over, the stage of the instrument becomes a single microscope; there are four lenses suitable for this purpose, their focal length varying from one-tenth to one-fortieth of an inch. The performance of all the lenses is excellent, and no pains appear to have been spared in their construction. There are numerous other pieces of accessory apparatus, all remarkable for the beauty of their workmanship.[4]
In addition to the movements described by Quekett, the body-tube with its support can be moved in an arc concentrically with the axis of the triangular pillar, on the top of which it is fitted with a worm-wheel and endless-screw mechanism, actuated by the screw-head, T, below. It must therefore be admitted that Martin led the way far beyond his contemporaries, both in the design and the evolution of the microscope. Furthermore, in his “New Elements of Optics,” 1759, he dealt with the principle of achromatism, by the construction of an achromatic telescope.
At a somewhat later period there lived in London a philosophical instrument maker of some repute, George Adams, who published in 1746 a quarto book, entitled “Micrographia Illustrata, or the Knowledge of the Microscope Explained.” This work fairly well describes “the nature, uses, and magnifying powers of microscopes in general, together with full directions how to prepare, apply, examine, and preserve minute objects.” Adams’ book was the first of the kind published in this country, and it contributed in no small degree to the advancement of microscopical science. Adams writes: “We owe the construction of the variable microscope to the ingenuity and generosity of a noble person. The apparatus belonging to it is more convenient, more certain, and more extensive than that of any other at present extant; consequently, the advantage and pleasure attending the observations in viewing objects through it must be as extensive in proportion.” This is believed to apply to Martin’s several microscopes, and that especially constructed for the king, afterwards improved upon by Adams. Another early form of microscope, Wilson Simple Scroll (1746), stamped on the cover of this book, and has thus become familiar to microscopists, was also made by Adams.
We now closely approach a period fertile in the improvement of the microscope, and in the discoveries made by its agency. The chief of those among the honoured names of the time we find Trembley, Ellis, Baker, Adams, Hill, Swammerdam, Lyonet, Needham, and a few others. Adams somewhat sarcastically observes “that every optician exercises his talents in improving (as he calls it) the microscope, in other words, in varying its construction and rendering it different in form from that sold by his neighbour; or at the best rendering it more complex and troublesome to manage.” There were no doubt good reasons for these and other strictures upon inventors as well as makers of microscopes, even in the Adams’ day. In the year 1787 the “Microscopical Essays” of his son were published, in which he described all the instruments in use up to that period.
Looking back, and taking a general survey of the work of nearly two centuries in the history of the microscope, it cannot be said that either in its optical or mechanical construction any great amount of progress was made. This in part may have arisen from the fact that no pressing need was felt for either delicate focussing or higher magnification. At all events, it was not until the application of achromatism to the instrument that new life was infused into its use, and a great impetus was given to its development, both optically and mechanically.
In the year 1823 a strong desire became manifest for improved forms of the instrument, in France by M. Selligue, by Frauenhofer in Munich, by Amici in Modena, by M. Chevalier in Paris, and by Dr. Goring, Mr. Pritchard, and Mr. Tully in London. The result was that in 1824 a new form of achromatic object-glass was constructed of nine-tenths of an inch focal length, composed of three lenses, and transmitting a pencil of eighteen degrees; and which, as regards accurate correction throughout the field, was for some years regarded as perfect.
Sir David Brewster was the first to suggest the great importance of introducing materials of a more highly refracting nature into the construction of lenses. He wrote: “There can be no essential improvement expected in the microscope unless from the discovery of some transparent substance which, like the diamond, combines a high refractive with a low dispersive power.” Having experienced the greatest difficulty in getting a small diamond cut into a prism in London, he did not conceive it practicable to grind, polish, and form it into a lens.
Mr. Pritchard, however, was led to make the experiment, and on the 1st of December, 1824, “he had the pleasure of first looking through a diamond microscope.” Dr. Goring also tried its performance on various objects, both as a single microscope and as an objective of a compound instrument, and satisfied himself of its superiority over other kinds of lenses. But here Mr. Pritchard’s labours did not end. He subsequently found that the diamond used had many flaws in it, which led him to abandon the idea of finishing it. Having been prevented from resuming his operations on this refractory material for a time he made a third attempt, and met with another unexpected defect; he found that some lenses, unlike the first, gave a double or triple image instead of a single one, in consequence of some of their parts being either harder or softer than others. These defects were found to be due to polarisation. Mr. Pritchard having learned how to decide whether a diamond is fit for a magnifier or not, subsequently succeeded in making two planoconvex lenses of adamant; these proved to be perfect for microscopic purposes. “One of these, of one-twentieth of an inch in focal length, is now in the possession of his Grace the Duke of Buckingham; the other, of one-thirtieth of an inch focus, is in his own hands.”
“In consequence of the high refracting power of a diamond lens over a glass lens, the former material may be at least one-third as thin as that of the latter, and if the focal length of both be equal, say, one-eightieth of an inch, the magnifying power of the diamond lens will be 2,133 diameters, whereas that of glass will be only 800.” At a date (1812) before Brewster proposed diamond lenses he demonstrated a simple method of rendering both single and compound microscopes achromatic. “Starting,” he says, “with the principle that all objects, however delicate, are best seen when immersed in fluid, he placed an object on a slip of glass, and put above a drop of oil, having a greater dispersive power than the single concave lens, which formed the object-glass of the microscope. The lens was then made to touch the fluid, so that the surface of the fluid was formed into a concave lens, and if the radius of the outward surface was such as to correct the dispersion, we should have a perfect achromatic microscope.” Here we have the immersion system foreshadowed. Shortly after these experiments of Brewster’s were in progress, Dr. Goring is said to have discovered that the structure of certain bodies could be readily seen in some microscopes and not in others. These bodies he named test objects. He then examined these tests with the achromatic combinations of the Tullys, and was led to the discovery that “the penetrating power of the microscope depends upon its angle of aperture.”
“While these practical investigations were in progress,” writes Andrew Ross, “the subject of achromatism engaged the attention of some of the most profound mathematicians in England, Sir John Herschel, and Professors Airy and Barlow. Mr. Coddington and others contributed largely to the theoretical examination of the subject; and although the results of their labours were not applicable to the microscope, they essentially promoted its improvement.”
About this period (1812) Professor Amici, of Modena, was experimentally engaged in the improvement of the achromatic object-glass, and he invented a reflecting microscope superior to those of Newton, Baker, or Smith, made as early as 1738, and long ago abandoned. In 1815 Amici made further experiments, and introduced the immersion system; while Frauenhofer, of Munich, about the same time constructed object-glasses for the microscope of a single achromatic lens, in which the two glasses, although placed in juxtaposition, were not cemented together.
Dolland, it has been said, introduced achromatic lenses; but although he constructed many achromatic telescopes, he did not apply the same principle to microscopes, and those which he sold were only modifications of the compound microscope of Cuff.
Dr. Wollaston employed a new form of combination in a microscope constructed for his own use, and by which “he was able to see distinctly the finest markings upon the scales of the Lepisma and Podura, and upon those of the gnat’s wing.” His doublet is still employed, and to which I shall refer under “Simple Microscopes.”
I. Elementary Optics
Value of Inductive Science--Light: Its Propagation, Refraction, Reflection--Spherical and Chromatic Aberrations--Human Eye, formation of Images of External Objects in--Visual Angle increased--Abbe’s Theory of Microscopic Vision.
The advances made in physics and mechanics during the 17th and 18th centuries fairly opened the way to the attainment of greater perfection in all optical instruments. This has been particularly exemplified with reference to the invention of the microscope, as briefly sketched out in the previous chapter. Indeed, in the first half of the present century the microscope can scarcely be said to have held a position of importance among the scientific instruments in frequent use. Since then, however, the zoologist and botanist by its aid have laid bare the intimate structure of plants and animals, and thereby have opened up a vast kingdom of minute forms of life previously undreamt of; and in connection with chemistry a new science has been founded, that of bacteriology.
For these reasons it will be of importance to the student of microscopy to begin at the beginning, and it will be my endeavour to introduce to his notice such facts in physical optics as are closely associated with the formation of images, and, so to speak, systematise such stepping stones for work hereafter to be accomplished. Elementary principles only will be adduced, and without attempting to involve my readers in intricate mathematical problems, and which for the most part are unnecessary for the attainment of the object in view. I therefore pass at once to the consideration of the propagation of light through certain bodies.
The microscope, whether simple or compound, depends for its magnifying power on the influence exerted by lenses in altering the course of the rays of light passing through them being REFRACTED. Refraction takes place in accordance with two well-known laws of optics. When a ray of light passes from one transparent medium to another it undergoes a change of direction at the surface of separation, so that its course in the second medium makes an angle with its course in the first. This change of direction is a resultant of refraction. The broken appearance presented by a stick partly immersed in water, and viewed in an oblique position, is an illustration of the law of refraction. Liquids have a greater refractive power than air or gases. As a rule, with some few exceptions, the denser of the two substances has the greater refractive power; hence it is customary in enumerating some of the laws of optics to speak of the denser medium and the rarer medium. The more correct designation would be the more refractive and the less refractive.[5]
Let R I (Fig. 4) be a ray incident at I on the surface of separation of two media, and let I S′ be the course of the ray after refraction. Then the angles which R I and I S make with the normal are the angle of incidence and the angle of refraction respectively, and the first law of refraction is that these angles lie in the same plane, or the plane of refraction is the same as the plane of incidence. The law which connects the magnitudes of these angles, and which was discovered by Snell, a Dutch philosopher, can only be stated either by reference to a geometrical construction, or by using the language of trigonometry. Describe a circle about the point of incidence, I as a centre, and drop perpendiculars from the points where it cuts the rays on the normal. The law is that these perpendiculars, R′ P′, S′ P, will have a constant ratio, or the sines of the angles of incidence and refraction are in a constant ratio; that is, so long as the media through which the ray first passes, and by which it is afterwards refracted, remain the same, and the light also of the same kind, then it is referred to as the law of sines.
Indices of Refraction.
The ratio of the sine of the angle of incidence to the sine of the angle of refraction, when a ray passes from one medium to another is termed the relative index of refraction. When a ray passes from vacuum into any medium, this ratio is always greater than unity, and is called the absolute index of refraction, or simply the index of refraction for the medium in question.
The absolute index of air is so small that it may be neglected in comparison with those of solids and liquids; but strictly speaking, the relative index for a ray passing from air into a given substance must be multiplied by the absolute index of the air, in order to obtain the true index of refraction.
=Critical Angle.=--It will be seen from the law of sines that, when the incident ray is in the less refractive of the two media, to every possible angle of incidence there is a corresponding angle of refraction. The angle referred to is termed the critical angle, and is readily computed if the relative index of refraction be given. When the media are air and water, this angle is about 48° 30′. For air and ordinary kinds of glass its value varies from 38° to 41°.
The phenomenon of total reflection may be observed in several familiar instances. For example, if a glass of water, with a spoon in it, is held above the level of the eye, the under side of the surface is seen to shine like a mirror, and the lower part of the spoon is seen reflected in it. Effects of the same kind are observed when a ray of sunlight passes into an aquarium--on the other hand rays falling normally on a uniform transparent plate of glass with parallel faces keep their course; but objects viewed obliquely through the same are displaced from their true position. Let S (Fig. 5) be a luminous point which sends light to an eye not directly opposite to it, on the other side of a parallel plate. The emergent rays which enter the eye are parallel to the incident rays; but as they have undergone lateral displacement, their point of concourse is changed from S to S′, and this is accordingly the image of S. The rays in such a case which compose the pencil that enters the eye will not exactly meet in any one point; there will be two focal lines, just as in the case of spherical mirrors. The displacement produced, as seen in the figure referred to above, increases with the thickness of the plate, its index of refraction, and the obliquity of incidence. This furnishes one of the simplest means of measuring the index of refraction of a glass substance, and is thus employed in Pichot’s refractometer (“Deschanel”).
=Refraction through a Prism.=--A prism is a portion of a refracting medium bounded by two plane surfaces, inclined at a definite angle to one another. The two plane surfaces are termed the faces of the prism, and their inclination to one another is the refracting angle of the prism. A prism preserves the property of bending rays of light from their original course by refraction. A cylinder may be regarded as the limit of a prism whose sides increase in number and diminish in size indefinitely: it may also be regarded as a pyramid whose apex is removed to an indefinite distance.
Let S I (Fig. 6) be an incident ray in the plane of the principal section of the prism. If the external medium be air, or other substance of less refractive power than the prism, the ray on entering the same will be bent nearer to the normal, taking such a course as I E, and on leaving the prism will be bent away from the normal, taking the course E B. The effect of these two refractions is, therefore, to turn the ray away from the edge (or refracting angle) of the prism. In practice, the prism is usually so placed that I E, the path of the ray through the prism, makes equal angles with the two faces at which refraction occurs. If the prism is turned very far from this position, the course of the ray may be altogether different from that represented in the figure; it may enter at one face, be internally reflected at another, and come out at the third.
It is evident, therefore, that the minimum number of sides, i.e., the bounding faces, exclusive of the ends, which a prism can have is three. In this form, it constitutes a most valuable instrument of research in physical optics. A convex lens is practically merely a curved form of two prisms combined, their bases being brought into contact; on the other hand the concave lens is simply a reversal of the position of the apices brought into contact, as shown in Fig. 11. Both convex and concave lenses are therefore closely related to the prism.
=Reflection.=--The laws that govern the change of direction which a ray of light experiences when it strikes upon the surfaces of separation of two media and is thrown back into the same medium from which it approached is as follows:--When the reflecting surface is plain the direction of the reflected ray makes with the normal to the surface the same angle which the incident ray makes with the same normal; or, as it is usually expressed, the angles of reflection and incidence are equal. When the surfaces are curved the same law holds good. In all cases of reflection the energy of the ray is diminished, so that reflection must always be accompanied by absorption. The latter probably precedes the former. Most bodies are visible by light reflected from their surfaces, but before this takes place the light has undergone a modification, namely, that which imparts colour peculiar to the bodies viewed. When light impinges upon the surface of a denser medium part is reflected, part absorbed, and part refracted. But for a certain angle depending upon the refractive index of the refracting medium no refraction takes place. This angle is termed the angle of total reflection, since all the light which is not absorbed is wholly reflected.
Multiple images are produced by a transparent parallel plate of glass. If the glass be silvered at the back, as it usually is in the microscope-mirror, the second image is brighter than the first, but as the angle of incidence increases the first image gains upon the second; and if the luminous object be a lamp or candle, a number of images, one behind the other, will be visible to an eye properly placed in front. This is due to the fact that the reflecting power of a surface of glass increases with the angle of incidence.
=Concave Surfaces.=--Rays of light proceeding from any given point in front of a concave spherical mirror, are reflected so as to meet in another point, and the line joining the two points passes through the centre of the sphere. The relation between them is or should be mutual, hence they are termed conjugate foci. By a focus in general is meant a point in which a number of rays of light meet, and the rays which thus meet, taken collectively, are termed a pencil. Fig. 7 represents two pencils of rays whose foci, S s, are conjugate, so that, if either of them be regarded as an incident pencil, the other will be the corresponding reflected pencil. Each point, in fact, sends a pencil of rays which converge, after reflection, to the conjugate focus. The principal focal distance is half the radius of curvature. But it will not escape attention that concave mirrors have two reflecting surfaces, a front and a back. This, however, does not practically disturb its virtual focus, since the achromatic condenser when brought into use collects and concentrates the light received from the mirror upon an object for the purpose of rendering it more distinctly visible to the eye when viewing an object placed on the stage of the microscope. The images seen in a plane mirror are always virtual, and any spherical mirror, whether concave or convex, is nearly equivalent to a plane mirror when the distance of the object from its surface is small in comparison with the radius of curvature.
Lenses.
=Forms of Lenses.=--A lens is a portion of a refracting medium bounded by two surfaces which are portions of spheres, having a common axis, termed the axis of the lens. Lenses are distinguished by different names, according to the nature of their surfaces.
Lenses with sharp edges (thicker at the centre) are convergent or positive lenses. Lenses with blunt edges (thinner at the centre) are divergent or negative lenses. The first group comprises:--(1) The bi-convex lens; (2) the plano-convex lens; (3) the convergent meniscus. The second group:--(4) The concave lens; (5) the plano-concave lens; (6) the divergent meniscus (Fig. 8).
=Principal Focus.=--A lens is usually a solid of revolution, and the axis of revolution is termed the principal axis of the lens. When the surfaces are spherical it is the line joining the centre of curvature.
From the great importance of lenses, especially convex lenses, in practical optics, it will be necessary to explain their properties somewhat at length.
=Principal Focus of Convex Lens.=--When rays which were originally parallel to the principal axis pass through a convex lens (Fig. 9), the effect of the two refractions which they undergo, one on entering and the other on leaving the lens, is to make them all converge approximately to one point F, which is called the principal focus. The distance A F of the principal focus from the lens is called the principal focal distance, or more briefly and usually, the focal length of the lens. The radiant point and its image after refraction are known as the conjugate foci. In every lens the right line perpendicular to the two surfaces is the axis of the lens. This is indicated by the line drawn through the several lenses, as seen in the diagram (Fig. 8). The point where the axis cuts the surface of the lens is termed the verte.
Parallel rays falling on a double-convex lens are brought to a focus in the centre of its diameter; conversely, rays diverging from that point are rendered parallel. Hence the focus of a double-convex lens will be at just half the distance, or half the length, of the focus of a plano-convex lens having the same curvature on one side. The distance of the focus from the lens will depend as much on the degree of curvature as upon the refracting power (termed the index of refraction) of the glass of which it may be formed. A lens of crown-glass will have a longer focus than a similar one of flint-glass; since the latter has a greater refracting power than the former. For all ordinary practical purposes we may consider the principal focus--as the focus for parallel rays is termed--of a double-convex lens to be at the distance of its radius, that is, in its centre of curvature; and that of a plano-convex lens to be at the distance of twice its radius, that is, at the other end of the diameter of its sphere of curvature. The converse of all this occurs when divergent rays are made to fall on a convex lens. Rays already converging are brought together at a point nearer than the principal focus; whereas rays diverging from a point within the principal focus are rendered still more diverging, though in a diminished degree. Rays diverging from points more distant than the principal focus on either side, are brought to a focus beyond it: if the point of divergence be within the circle of curvature, the focus of convergence will be beyond it; and vice-versâ. The same principles apply equally to a plano-convex lens; allowance being made for the double distance of its principal focus; and also to a lens whose surfaces have different curvatures; the principal focus of such a lens is found by multiplying the radius of one surface by the radius of the other, and dividing this product by half the sum of the radii.
In the case of a concave lens (Fig. 10), rays incident parallel to the principal axis diverge after passing through; and their directions, if produced backwards, would approximately meet in a point F; this is its principal focus. It is, however, only a virtual focus, inasmuch as the emergent rays do not actually pass through it, whereas the principal focus of a converging lens is real.
=Optical Centre of a Lens.=--Secondary Axes.--Let O and O′ (Fig. 11) be the centres of the two spherical surfaces of a lens. Draw any two parallel radii, O I, O′ E, to meet these surfaces, and let the joining line I E represent a ray passing through the lens. This ray makes equal angles with the normals at I and E, since these latter are parallel by construction; hence the incident and emergent rays S I, E R also make equal angles with the normals, and are therefore parallel. In fact, if tangent planes (indicated by the dotted lines in the figure) are drawn at I and E, the whole course of the ray S I E R will be the same as if it had passed through a plate bounded by these planes.
Let C be the point in which the line I E cuts the principal axis, and let R, R′ denote the radii of the two spherical surfaces. Then from the similarity of the triangles O C I, O′ C E, we have (O C)/(C O′) = R′/R; which shows that the point C divides the line of centres O O′ in a definite ratio depending only on the radii. Every ray whose direction on emergence is parallel to its direction before entering the lens, must pass through the point C in traversing the lens; and conversely, every ray which in its course through the lens traverses the point C, has parallel directions at incidence and emergence. The point C which possesses this remarkable property is called the centre, or optical centre, of the lens.
This diagram may also be taken to prove my former proposition, that the convex lens is practically a form of two prisms combined.
=Conjugate Foci, one Real, one Virtual.=--When two foci are on the same side of the lens, one (the most distant of the two) must be virtual. For example, in Fig. 12, if S, S′ are a pair of conjugate foci, one of them S being between the principal focus F and the lens, rays sent to the lens at a luminous point at S, will, after emergence, diverge as if from S′; and rays coming from the other side of the lens, if they converge to S′ before incidence, will in reality be made to meet in S. As S moves towards the lens, S′ moves in the same direction more rapidly; and they become coincident at the surface of the lens.
=Formation of Real Images.=--Let A B (Fig. 13) be an object in front of a lens, at a distance less than the principal focal length. It will have a real image on the other side of the lens. To determine the position of the image by construction, draw through any point A of the object a line parallel to the principal axis, meeting the lens in A′. The ray represented by this line will, after refraction, pass through the principal focus, F, and its intersection with the secondary axis, A O, determines the position of a, the focus conjugate to A. We can in like manner determine the position of b, the focus conjugate to B, another point of the object; and the joining line a b will then be the magnified image of the line A B. It is evident that if a b were the object, A B would be the image.
The figures 12 and 13 represent the cases in which the distance of the object is respectively greater and less than twice the focal length of the lens.
The focal length of a lens is determined by the convexity of its surfaces and the refractive power of the material of which it is composed, being shortened either by an increase of refractive power, or diminution of the radii of curvature of the faces of the lens. The increase or decrease of spherical aberration is determined by the shape or curvature of the lens; it is less in the bi-convex than in other forms. When a lamp or other source of light is placed at the focus of the rays constituting that portion of its light which falls upon the lens, the light is so refracted as to become parallel. Should the source of light be brought nearer to the lens than the focus the refracted rays are still divergent, though not to the same extent; on the other hand, if the source be beyond the focus, the refracted rays are rendered convergent so as to meet at a point which is mathematically related to the distance of the luminous source from the focus. The former arrangement is that with which we are most familiar, since it is the ordinary magnifying glass.
Concave Lenses.
The refracting influence of a concave lens (Fig. 14) will be precisely the opposite of that of a convex. Rays which fall upon it in a parallel direction will be made to diverge as if from the principal focus, which is here called the negative focus. This will be, for a plano-concave lens, at the distance of the diameter of the sphere of curvature; and for a double-concave, in the centre of that sphere.
In Fig. 14 A B is the object and a b the image. Rays incident from A and B parallel to the principal axis will emerge as if they came from the principal focus F; hence, the points a b are determined by the intersections of the dotted lines in the figure with the secondary axis, O A, O B. An eye on the other side of the lens sees the image a b, which is always virtual, erect and diminished.
In the construction of the microscope, either simple or compound, the curvature of the lenses employed is usually spherical. Convergent lenses, with spherical curvatures, have the defect of not bringing all the rays of light which pass through them to one and the same focus. Each circle of rays from the axis of the lens to its circumference has a different focus, as shown in Fig. 15. The rays a a, which pass through the lens near its circumference, are seen to be more refracted, or come to a focus at a shorter distance behind it than the rays b b, which pass through near its centre or axis, and are less refracted. The consequence of this defect of lenses with spherical curvatures, which is called spherical aberration, is that a well-defined image or picture is not formed by them, for when the object is focussed, for the circumferential rays, the picture projected to the eye is rendered indistinct by a halo or confusion produced by the central rays falling in a circle of dissipation, before they have come to a focus. On the other hand, when placed in the focus of the central rays, the picture formed by them is rendered indistinct by the halo produced by the circumferential rays, which have already come to a focus and crossed, and now fall in a state of divergence, forming a circle of dissipation. The grosser defects of spherical aberration are corrected by cutting off the passage of the rays a a, through the circumferences of the lens, by means of a stop diaphragm, so that the central rays, b b, only are concerned in the formation of the image. This defect is reduced to a minimum, by using the meniscus form of lens, which is the segment of an ellipsoid instead of a sphere.
The ellipse and the hyperbola are forms of lenses in which the curvature diminishes from the central ray, or axis, to the circumference b; and mathematicians have shown that spherical aberration may be practically got rid of by employing lenses whose sections are ellipses or hyperbolas. The remarkable discovery of these forms of lenses is attributed to Descartes, who mathematically demonstrated the fact.
If a l, a l′, for example (Fig. 16) be part of an ellipse whose greater axis is to the distance between its foci f f as the index of refraction is to unity, then parallel rays r l′, r′′ l incident upon the elliptical surface l′ a l, will be refracted by the single action of that surface into lines which would meet exactly in the farther focus f, if there were no second surface intervening between l a l′ and f. But as every useful lens must have two surfaces, we have only to describe a circle l a′ l′ round f as a centre, for the second surface of the lens l′ l.
As all the rays refracted at the surface l a l′ converge accurately to f, and as the circular surface l a′ l′ is perpendicular to every one of the refracted rays, all these rays will go on to f without suffering any refraction at the circular surface. Hence it should follow, that a meniscus whose convex surface is part of an ellipsoid, and whose concave surface is part of any spherical surface whose centre is in the farther focus, will have no appreciable spherical aberration, and will refract parallel rays incident on its convex surface to the farther focus.
The spherical form of lens is that most generally used in the construction of the microscope. If a true elliptical or hyperbolic curve could be ground, lenses would very nearly approach perfection, and spherical aberration would be considerably reduced. Even this defect can be further reduced in practice by observing a certain ratio between the radii of the anterior and posterior surfaces of lenses; thus the spherical aberration of a lens, the radius of one surface of which is six or seven times greater than that of the other, will be much reduced when its more convex surface is turned forward to receive parallel rays, than when its less convex surface is turned forwards. It should be borne in mind that in lenses having curvatures of the kind the object would only be correctly seen in focus at one point--the mathematical or geometrical axis of the lens.
=Chromatic Aberration.=--We have yet to deal with one of the most important of the phenomena of light, CHROMATIC ABERRATION, upon the correction of which, in convex lenses in particular, the perfection of the objective of the microscope so much depends. Chromatism arises from the unequal refrangibility and length of the different coloured rays of light that together go to make up white light; but which, when treated of in optics, is always associated with achromatism, so that a combination of prisms, or lenses, is said to be achromatic when the coloured rays arising from the dispersion of the pencil of light refracted through them are combined in due proportions as they are in perfectly white light.
A lens, however, of uniform material will not form a single white image, but a series of images of all colours of the spectrum, arranged at different distances, the violet being nearest, and the red the most remote, every other colour giving a blurred image; the superposition of these and the blending of the different elementary rays furnishing a complete explanation of the beautiful phenomenon of the rainbow. Sharpness of outline is rendered quite impossible in such a case, and this source of confusion is known as chromatic aberration.
In order to ascertain whether it is possible to remedy this evil by combining lenses of two different materials, Newton made some trials with a compound prism composed of glass and water (the latter containing a little sugar of lead), and he found it impossible by any arrangement of these two, or by other substances, to produce deviation of the transmitted light without separation into its component colours. If this ratio were the same for all substances, as Newton supposed, achromatism would be impossible; but, in fact, its value varies greatly, and is far greater for flint than for crown glass. If two prisms of these substances, of small refracting angles, be combined into one, with their edges turned in opposite directions, they will achromatise each other.
The chromatism of lenses may, however, be somewhat further reduced by stopping out the marginal rays, but as the most perfect correction possible is required when lenses are combined for microscopic uses, other means of correction are resorted to, as will be seen hereafter. I shall first proceed to show the deviations which rays of white light undergo in traversing a lens.
If parallel rays of light pass through a double-convex lens the violet rays, the most refrangible of them, will come to a focus at a point much nearer to the lens than the focus of the red rays, which are the least refrangible; and the intermediate rays of the spectrum will be focussed at points between the red and the violet. A screen held at either of these foci will show an image with prismatic fringes. The white light, A A′′ (Fig. 18), falling on the marginal portion of the lens is so far decomposed that the violet rays are brought to a focus at C, and crossing there, diverge again and pass on to F F′, while the red rays, B B′′, do not come to a focus until they reach the point D, and cross the divergent violet rays, E E′. The foci of the intermediary rays of the spectrum (red, green, and blue) are intermediate between these extremes. The distance, C D, limiting the blue or violet, and the red is termed the longitudinal chromatic aberration of the lens. If the image be received upon a screen placed at C, violet will predominate and appear surrounded by a prismatic fringe, in which violet will predominate. If the screen be now shifted to D, the image will have a predominant red tint, surrounded by a series of coloured fringes in an inverted order to those seen in the former experiment. The line E E′ joins the points of intersection between the violet and red rays, and this marks the mean focus, the point where the coloured rays will be least apparent.
In the early part of this century the optical correction of chromatic aberration was partially brought about by combining a convex lens of crown-glass with a concave lens of flint-glass, in the proportion of which these two kinds of glass respectively refract and disperse rays of light; so that the one medium may by equal and contrary dispersion neutralise the dispersion caused by the other, without at the same time wholly neutralising its refraction. It is a curious fact that the media found most available for the purpose should be a combination of crown and flint-glass, of crown-glass whose index of refraction is 1·519, and dispersive power 0·036, and of flint-glass whose index of refraction is 1·589, and dispersive power 0·0393. The focal length of the convex crown-glass lens must be 4-1/3 inches, and that of the concave flint-glass lens 7-2/3 inches, and the combined focal length 10 inches. The diagram (Fig. 19) shows how rays of light are brought to a focus, nearly free from colour. The small amount of residual colour in such a combination is termed the secondary spectrum; the violet ray F Y, crossing the axis of the lens at V, and going to the upper end P of the spectrum, the red ray F B going to the lower end T. But as the flint-glass lens l l, on the prism A a C, which receives the rays F V, F R, at the same points, is interposed, these rays will unite at f, and form a small circle of white light, the ray S F being now refracted without colour from its primitive direction S F Y into the direction F f. In like manner, the corresponding ray S F′ will be refracted to f, and a white colourless image be the result.
The achromatic aplanatic objective constructed on the optical formula enunciated, did not meet all the difficulties experienced by the skilled microscopist, in obtaining resolution of the finest test objects, and whereby the intrinsic value of the objective (in his estimation) must stand or fall. There were other disturbing residuary elements besides those of the secondary spectrum, and which at a later period were met by the practical skill of the optician, who applied the screw-collar, and by means of which the back lens of the objective is made to approach the front lens, thus more accurately shortening the distance between the eye-piece, where the image is eventually formed, and the back lens of the objective.
In this diagram L L is a convex lens of crown-glass, and l l a concave one of flint-glass. A convex lens will refract a ray of light (S) falling at F on it exactly in the same manner as the prism A B C, whose faces touch the two surfaces of the lens at the points where the ray enters, and quits. The ray S F, thus refracted by the lens L L, or prism A B C, would have formed a spectrum (P T) on a screen or wall, had there been no other lens.
=Formation of Virtual Images.=--The normal eye possesses a considerable power of adjusting itself to form a distinct image of objects placed at varying distances; the nearer, within a certain limit, the larger it appears, and the more distinctly the details are brought out. When brought within a distance of two or three inches, the images become blurred or quite indistinct, and when brought closer to the eye, cannot be seen at all, and it simply obstructs the light. Now the utility of a convex lens, when interposed between the object and the eye, consists in reducing the divergence of the rays forming the several pencils which issue from it, and send images to the retina in a state of moderate divergence, that is, as if they had issued from an object beyond the nearest point of distinct vision, and so that a more clearly defined image may reach the sensitive membrane of the eye. But, not only is the course of the several rays in each pencil altered as regards the rest, but the course of the pencils themselves is changed, so that they enter the eye under an angle corresponding with that under which they would have arrived from a larger object situated at a greater distance, and thus the picture formed by any object corresponds in all respects with one which would have been made by the same object increased in its dimensions and viewed at the smallest ordinary distance of distinct vision. For instance, let an object A B (Fig. 20) be placed between a convex lens and its principal focus. Then the foci conjugate to the points A B are virtual, and their positions can be found by construction from the consideration that rays through A, B, parallel to the principal axis, will be refracted to F, the principal focus on the other side. The refracted rays, if produced backwards, must meet the secondary axis O A, O B in the required points. An eye placed on the other side of the lens will accordingly see a virtual image erect, magnified, and at a greater distance from the lens than the object. This is the principle of the simple microscope.
The Human Eye.
To gain a clear insight into the mode in which a single lens serves to magnify objects, it will be necessary to revert to the phenomena of ordinary vision. An eye free from any defect has a considerable power of adjusting itself to very considerable distances. One of the special functions of the eye is bringing the rays of light, by a series of dioptric mechanisms, to a perfect focus on its nervous sensitive layer, the retina. The eye in this respect has been compared to a photographic camera. But this is not quite correct. The retina is destined simply to receive the images furnished by the dioptric apparatus, and has no influence upon the formation of these images. The luminous rays are refracted by the dioptric apparatus; the images would be formed quite as well--indeed, even better in certain cases--if the retina were not there. The dioptric apparatus and its action are absolutely independent of the retina.
The same laws with regard to the passage of the rays of light into the human eye hold good, as those already enunciated in the previous pages. As to change of direction when rays are passing obliquely from a medium of low density to that of a higher density, i.e., it changes its course, and is bent towards the perpendicular. On leaving the denser for the rarer medium it is bent once more from the perpendicular. Again, by means of a convex lens, the rays of light from one source will be refracted so as to meet at a point termed the principal focus of vision.
In the eye there are several surfaces separating the different media where refraction takes place. The refractive index of the aqueous humour and the tears poured out by the lachrymal gland is almost equal to that of the cornea. We may, therefore, speak of the refracting surfaces as three, viz.: Anterior surface of cornea, anterior surface of lens, and posterior surface of lens; and also of the refracting media as three--the aqueous humour, the lens, and vitreous humour. These several bodies are so adapted in the normal eye that parallel rays falling on the cornea are converged to a focus at the most sensitive spot (the yellow spot, or fovea centralis) in the retina, a point representing to the principal focus of the eye. A line drawn from this point through the centre of the cornea is called the optic axis of the eye-ball.
But as we are able to form a distinct image of near objects, and as we notice when we turn our gaze from far to near objects there is a distinct feeling of muscular effort in the eyes, there must be some means whereby the eye can readily adapt itself for focussing near and distant objects. In a photographic camera the focus can be readily altered, either by changing the lenses, employing a lens of greater or less curvature, or by altering the distance of the screen from the lens. The last method is obviously impossible in the rigid eye-ball, and therefore the act of focussing for near and distant objects is associated with a change in the curvature of the lens, a faculty of the eye termed accommodation (Fig. 22), a change chiefly accomplished by the ciliary (muscle) processes, which pull the lens forwards and inwards by virtual contracting power of the ciliary muscle, and by which its suspensory ligament is relaxed, and the front of the lens allowed to bulge forward. In every case, however, accommodation is associated with contraction of the iris, the special function of which is that of a limiting diaphragm (an iris-diaphragm), Fig. 23.
In an ordinary spherical bi-convex lens, as already pointed out, the rays of light passing through the periphery of the lens come to a focus at a nearer point than the rays passing through the central portion. In this way a certain amount of blurring of the image takes place, and which, in optical language, is termed spherical aberration. This defect of the eye is capable of correction in three possible ways, and which it may be well to repeat: 1. By making the refractive index of the lens higher at its centre than at its circumference; (2) By making the curvature of the lens less near the circumference than at the centre; (3) By stopping out the peripheral rays of light by a diaphragm. The two latter methods are those resorted to in most optical instruments.
In the human eye an attempt is made to apply all these methods, but the most important is the third, that of applying the diaphragm formed by the iris, a circular semi-muscular curtain lying just in front of the anterior surface of the lens. The iris is also furnished with a layer of pigmental cells which effectually stop out all peripheral rays of light that otherwise would pass into the eye, creating circles of diffusion of a disturbing nature to perfect vision. This delicate membrane, then, is kept in constant action by a two-fold nerve supply, derived from five or six sources, which it is unnecessary to describe at length. But the eye, with all its marvellous adaptations, has an obvious defect, that of secondary or uncorrected chromatic aberration.
=Chromatic Aberration of the Eye.=--White light, as previously explained, is composed of different wave lengths; and accordingly as these undulations are either longer or shorter, so do they produce on the eye the impression of different colours. We have seen how a pencil of white light may, by means of a prism, be decomposed into a multi-coloured band. In an ordinary magnifying reading-glass these coloured fringes are always seen around the margins. In practical optics chromatic aberration is partially corrected by employing two different kinds of glass in the construction of certain combined lenses. In the human eye chromatism cannot be corrected in this way; hence a blue light and a red light placed at the same distance from the eye appears to be unequally distant: the red light requiring greater accommodation in the eye than the blue, and this accordingly appears to be the nearer of the two.
This visual error may be experimentally shown and explained. There is a kind of glass which at first sight appears dark blue or violet, but which really contains a great deal of red. Take an ordinary microscope lamp, having a metal or opaque chimney, and drill a circular hole in it, about 3 mm. in diameter. This opening should be just at the height of the flame; cover it over with a piece of ground glass and a piece of the red-blue glass. Thus will be formed a luminous point whose light is composed of red and blue, i.e., of colours far apart from each other in the spectrum.
If rays coming from this point enter the eye, the blue rays (Fig. 24), being more strongly reflected than the red, will come to a focus sooner than the latter. The red rays, on the contrary, will be brought to a focus later than the blue, while the latter, past their focus, are diverging. Let A B C D (Fig. 24) be the section of a pencil of rays given off from a red-blue point sufficiently distant so that these rays may be regarded as parallel. The focus of the blue is at b, that of the red at r.
An eye is adapted to the distance of the luminous point when the circle of diffusion, received upon the retina, is at its minimum. This is the case when the sentient layer of the retina lies between the two foci E. In this case the point will appear as a small circle, composed of the two colours, that is to say--violet. If the retina be in front of this point, at the focus of the blue rays for instance, the eye will perceive a blue point surrounded by a red circle, the latter being formed by the periphery of the luminous cone of red rays, which are focussed only after having passed the retina. The blue point will become a circle of diffusion larger in proportion as the retina is nearer the dioptric system, or as the focus for blue is farther behind it. But the blue circle will always be surrounded by a red ring. If, on the contrary, the retina is behind the focus for red, the blue cone will be greater in diameter than the red, and we shall have a red circle of diffusion, larger in proportion as the retina is farther from the focus, but always surrounded by a blue ring M. If the blue-red point is five metres, or more, distant, the emmetropic[7] eye will evidently see it more distinctly, i.e., as a small violet point; the hyperopic eye, whose retina is situated in front of the focus of its dioptric system, will see a blue circle, surrounded by red; the myopic eye, whose retina is behind its focus, will see a red circle, surrounded by blue. The size of these circles will be either larger or smaller when the principal focus of the eye is either in front of or behind the retina.[8]
The refractive surfaces of a perfectly formed eye are very like an ellipsoid of revolution with two axes, one of which, the major axis of the ellipse, is at the same time the optic axis and that of rotation; the other is perpendicular to it, and is equal in all meridians. Eyes, however, perfectly constructed are rarely met with. The curvature of the cornea is nearly always greater in one meridian than in another. Its surfaces then cannot be regarded as entirely belonging to an ellipsoid of revolution, since the solid figure, of which the former would constitute a part, has not only two axes, but three, and these unequal. This irregularity is not, however, always great enough to produce discomfort and it is therefore disregarded. But in other cases the difference of curvature in the different meridians of the eye attain to a higher degree, and vision falls far below the average.
The refractive anomaly alluded to is termed astigmatism (from the Greek, α privative, στιγμα, a point--inability to see a point). The way in which objects appear to such a person will mainly result from the way in which he sees a point. Take, for example, the vertical to be the most, and the horizontal to be the least, refractive meridian: place a vertical line (Fig. 25, I) at a stated distance before the eye, and the line will appear elongated, owing to the diffusion image of each of the points composing it. It will also seem to be somewhat broadened, as at II. If the vertical meridian is adapted to the distance of the vertical, the line will appear very diffuse and broadened, as at III. All these little diffusion lines overlap each other, and give the line an elongated appearance. Hence a straight line is seen distinctly by an astigmatic eye only when the meridian to which it is perpendicular is perfectly adapted to its distance. A vertical line is seen distinctly when the horizontal meridian is adapted to its distance. It appears indistinct when its image is formed by the vertical meridian. The way in which an astigmatic person sees points and lines led to the discovery of this remarkable irregularity in the refraction of the eye. The late Astronomer Royal, Sir George Airy, suffered for some years until, indeed, he discovered how it could be corrected. This anomaly of curvature of the refractive surfaces of the eye is now known to prevail largely among the more civilised races of mankind. It is, then, of very great importance when using high powers of the microscope. In most persons the visual power of both eyes is rarely quite equal; on the other hand, the mind exerts an important influence, dominates, as it were, the eye in the interpretation of visual sensations and images. An example of this is presented in Wheatstone’s pseudoscope, known to produce precisely the opposite effect of his stereoscope--conveys, in fact, the converse of relief produced by the latter and better known instrument.
=Visual Judgment.=--The apparent size of an object is determined by the magnitude of the image formed on the retina, and this is inversely proportional to the distance. Thus the size of an image on the retina of an object two inches long at a distance of a foot, is equal to the image of an object four inches long at a distance of two feet. An object can be seen if the visual angle subtended by it is not less than sixty seconds. This is equivalent to an image on the fovea centralis of the retina of about 4 µ[9] across, and which corresponds to the diameter of a cone: so that while we have had under consideration the optical and physical conditions of human vision, we have likewise taken a lesson on the action of lenses used in the construction of the microscope.
The Theory of Microscopical Vision.
It has been said that no comparison can be instituted between microscopic vision and macroscopic; that the images formed by minute objects are not delineated microscopically under ordinary laws of diffraction, and that the results are dioptrical. This assertion, however, cannot be accepted unconditionally, as will be seen on more careful examination of the late Professor Abbe’s masterly exposition of “The Microscopical Theory of Vision,” and also his subsequent investigations on the estimation of aperture and the value of wide-angled immersion objectives, published in the “Journal of the Royal Microscopical Society.”
The essential point in Abbe’s theory of microscopical vision is that the images of minute objects in the microscope are not formed exclusively on the ordinary dioptric method (that is, in the same way in which they are formed in the camera or telescope), but that they are largely affected by the peculiar manner in which the minute construction of the object breaks up the incident rays, giving rise to diffraction.
The phenomena of diffraction in general may be observed experimentally by plates of glass ruled with fine lines. Fig. 26 shows the appearance presented by a single candle-flame seen through such a plate, an uncoloured image of the flame occupying the centre, flanked on either side by a row of coloured spectra of the flame, which become dimmer as they recede from the centre. A similar phenomenon may be produced by dust scattered over a glass plate, and by other objects whose structure contains very minute particles, or the meshes of very fine gauze wire, the rays suffering a characteristic change in passing through such objects; that change consisting in the breaking up of a parallel beam of light into a group of rays, diverging with wide angle and forming a regular series of maxima and minima of intensity of light, due to difference of phase of vibration.[10]
In the same way, in the microscope, the diffraction pencil originating from a beam incident upon, for instance, a diatom, appears as a fan of isolated rays, decreasing in intensity as they are further removed from the direction of the incident beam transmitted through the structure, the interference of the primary waves giving a number of successive maxima of light with dark interspaces.
When a diaphragm opening is interposed between the mirror, and a plate of ruled lines placed upon the stage such as Fig. 27, the appearance shown in Fig. 27_a_, will be observed at the back of the objective on removing the eye-piece and looking down the tube of the microscope. The centre circles are the images of the diaphragm opening produced by the direct rays, while those on the other side (always at right angles to the direction of the lines) are the diffraction images produced by the rays which are bent off from the incident pencil. In homogeneous light the central and lateral images agree in size and form, but in white light the diffraction images are radially drawn out, with the outer edges red and the inner blue (the reverse of the ordinary spectrum), forming, in fact, regular spectra the distance separating each of which varies inversely as the closeness of the lines, being for instance with the same objective twice as far apart when the lines are twice as close.
The influence of these diffraction spectra may be demonstrated by some very striking experiments, which show that they are not by any means accidental phenomena, but are directly connected with the image which is seen by the eye.
The first experiment shows that with the central beam, or any one of the spectral beams alone, only the contour of the object is seen, the addition of at least one diffraction spectrum being essential to the visibility of the structure.
When by a diaphragm placed at the back of the objective, as in Fig. 28, we cover up all the diffraction spectra of Fig. 27_a_, and allow only the central rays to reach the image, the object will appear to be wholly deprived of fine details, the outline alone will remain, and every delineation of minute structure will disappear, just as if the microscope had suddenly lost its optical power, as in Fig. 28_a_.
This experiment illustrates a case of the obliteration of structure by obstructing the passage of the diffraction spectra to the eye-piece. The next experiment shows how the appearance of fine structure may be created by manipulating the spectra.
When a diaphragm such as that shown in Fig. 29 is placed at the back of the objective, so as to cut off each alternate one of the upper row of spectra in Fig. 27_a_, that row will obviously become identical with the lower one, and if the theory holds good, we should find the image of the upper lines identical with that of the lower. On replacing the eye-piece, we see that it is so, the upper set of lines are doubled in number, a new line appearing in the centre of the space between each of the old (upper) ones, and upper and lower set having become to all appearance identical, as seen in Fig. 29_a_.
In the same way, if we stop off all but the outer spectra, as in Fig. 30, the lines are apparently again doubled, as seen in Fig. 30_a_.
A case of apparent creation of structure, similar in principle to the foregoing, though more striking, is afforded by a network of squares, as in Fig. 31, having sides parallel to this page, which gives the spectra shown in Fig. 31_a_, consisting of vertical rows for the horizontal lines and horizontal rows for the vertical ones. But it is readily seen that two diagonal rows of spectra exist at right angles to the diagonals of the squares, just as would arise from sets of lines in the direction of the diagonals, so that if the theory holds good we ought to find, on obstructing all the other spectra and allowing only the diagonal ones to pass to the eye-piece, that the vertical and horizontal lines have disappeared and are replaced by two new sets of lines at right angles to the diagonals.
On inserting the diaphragm, Fig. 32, and replacing the eye-piece, we find in the place of the old network the one shown in Fig. 32_a_, the squares being, however, smaller in the proportion of 1 : √2, as they should be in accordance with the theory propounded.
An object such as Pleurosigma angulatum, which gives six diffraction spectra arranged as in Fig. 33, should, according to this theory, show markings in a hexagonal arrangement. For there will be one set of lines at right angles to b, a, e, another set at right angles to c, a, f, and a third at right angles to g, a, d. These three sets of lines will obviously produce the appearance shown in Fig. 33_a_.
A great variety of appearances may be produced with the same arrangement of spectra. Any two adjacent spectra with the central beam (as b, c, a) will form equilateral triangles and give hexagonal markings. Or by stopping off all but g, c, e (or b, d, f), we again have the spectra in the form of equilateral triangles; but as they are now further apart, the sides of the triangles in the two cases being as √3 : 1, the hexagons will be smaller and three times as numerous. Their sides will also be arranged at a different angle to those of the first set. The hexagons may be entirely obliterated by admitting only the spectra g, c, or g, f, or b, f, etc., when new lines will appear at right angles, or obliquely inclined, to the median line. By varying the combinations of the spectra, therefore, different figures of varying size and positions are produced, all of which cannot, of course, represent the true structure. Not only, however, may the appearance of particular structure be obliterated or created, but it may even be predicted before being seen under the microscope. If the position and relative intensity of the spectra in any particular case are given, the character of the resultant image, in some instances, may be worked out by mathematical calculations. A remarkable instance of such a prediction is to be found in the case recorded by Mr. Stephenson, where a mathematical student who had never seen a diatom, worked out the purely mathematical result of the interference of the six spectra b-g of Fig. 33 (identical with P. angulatum), giving the drawing copied in Fig. 34. The special feature was the small markings between the hexagons, which had not, before this time, been noticed on P. angulatum. On more closely scrutinizing a valve, stopping out the central beam and allowing the six spectra only to pass, the small markings were found actually to exist, though they were so faint they had previously escaped observation until the result of the mathematical deduction had shown that they ought to be seen.
These experiments seem to show that diffraction plays a very essential part in the formation of microscopical images, since dissimilar structures give identical images when the differences of their diffractive effect is removed, and conversely similar structures may give dissimilar images when their diffractive images are made dissimilar. Whilst a purely dioptric image answers point for point to the object on the stage, and enables a safe inference to be drawn as to the actual nature of that object, the visible indications of minute structure in a microscopical image are not always or necessarily conformable to the real nature of the object examined, so that nothing more can safely be inferred from the image as presented to the eye, than the presence in the object of such structural peculiarities as will produce the particular diffraction phenomena on which these images depend.
Further investigations and experiments led Abbe to discard so much of his theoretical conclusions relating to superimposed images having a distinct character as well as a different origin, and as to their capability of being separated and examined apart from each other. In a later paper he writes: “I no longer maintain in principle the distinction between the absorption image or direct dioptrical image and the diffraction image, nor do I hold that the microscopical image of an object consists of two superimposed images of different origin or a different mode of production. Thus it appears that both the absorption image and the diffraction image he held to be equally of diffraction origin; but while a lens of small aperture would give the former with facility, it would be powerless to reveal the latter, because of its limited capacity to gather in the strongly-deflected rays due to the excessively minute bodies the microscopical objective has to deal with.”[11]
Abbe’s theory of vision has been questioned by mathematicians, and since his death Lord Rayleigh went more deeply into the question of “the theory of the formation of optical images,” with special reference to the microscope and telescope. He has shown that two lines cannot be fairly resolved unless their components subtend an angle exceeding that subtended by the wave-length of light at a distance equal to the aperture; also, that the measure of resolution is only possible with a square aperture, or one bounded by straight lines, parallel to the lines resolved.
Lord Rayleigh’s Theory of the Formation of Optical Images, with Special Reference to the Microscope.[12]
Of the two methods adopted, that of Helmholtz’s consists in tracing the image representative of a mathematical point in the object, the point being regarded as self-luminous; that of Abbe’s the typical object was not, as we have seen, a luminous point, but a grating illuminated by plane waves of light. In the latter method, Lord Rayleigh argues that the complete representation of the object requires the co-operation of all the spectra which are focussed in the principal focal plane of the objective; when only a few are present the representation is imperfect, and wholly fails when there is only one. He then proceeds to show, by the aid of diagrams and mathematical formula, how the resolving power can be adduced.
On further criticism of the Abbe spectrum theory, he observes “that although the image ultimately formed may be considered to be due to the spectra focussed to a given point, the degree of conformity of the image to the object is another question. The consideration of the case of a very fine grating, which might afford no lateral spectra at all, shows the incorrectness of the usually accepted idea that if all the spectra are utilised the image will still be incomplete, so that the theory (originally promulgated by Abbe) requires a good deal of supplementing; while it is inapplicable when the incident light is not parallel, and when the object is, for example, a double point and not a grating. Even in the case of a grating, the spectrum theory is inapplicable, if the grating is self-luminous; for in this case no spectra can be formed since the radiations from the different elements of the grating have no permanent phase-relations.” For these reasons Lord Rayleigh advises that the question should be reconsidered from the older point of view, according to which the typical object is a point and not a grating. Such treatment will show that the theory of resolving power is essentially the same for all instruments. The peculiarities of the microscope, arising from the divergence-angles not being limited to be small, and from the different character of the illumination, are theoretically only differences of detail. These investigations can be extended to gratings, and the results so obtained confirm for the most part the conclusions of the spectrum theory.
Furthermore, that the function of the condenser in microscopic practice in throwing upon the object the image of the lamp-flame is to cause the object to behave, at any rate in some degree, as if it were self-luminous, and thus to obviate the sharply-marked interference bands which arise when permanent and definite phase-relations are permitted to exist between the radiations which issue from various points of the object. This is capable of mathematical proof; and in the case where the illumination is such that each point of the row or of the grating radiates independently, the limit to resolution is seen to depend only on the width of the aperture, and thus to be the same for all forms of aperture as for those of the rectangular. That Abbe’s theory of microscopic vision is fairly open to the criticisms passed on it by Lord Rayleigh must be taken for granted.
Definition of Aperture; Principles of Microscopic Vision.
It must be well within the last half-century that the achromatic objective-glass for the microscope was brought to perfection and its value became generally recognised. Prior to the discovery of the achromatic principle in the construction of lenses it was assumed that the formation of the microscopic image took place (as we have already seen) on ordinary dioptric principles. As the image is formed in the camera or telescope, so it was said to be in the microscope. This belief existed, it will be remembered, at a time when dry objectives only were in favour and the use of the term angle of aperture was misunderstood, when it was supposed that the different media with diffraction-indices were used; and the angle of the radiant pencil was believed not only to admit of a comparison of two apertures in the same medium, but likewise to admit of a standard of comparison when the media were entirely different in their refractive qualities.
It was during my tenure of office as secretary of the Royal Microscopical Society (1867 to 1873), that the aperture question, and also that of numerical aperture, came under discussion, both being met by the majority of the Fellows of the Society and practical opticians by a non-possumus.
Opticians alleged, that is, before the value of aperture became fully recognised (1860), that the achromatic objective had reached a stage of perfection, beyond which it was not possible to go; indeed, not only opticians, but physicists of high standing, as Professor Helmholtz, who made many important contributions to the theory of the microscope, and who, after duly weighing all the known physical laws on which the formation of images can be explained, emphatically stated that in his opinion “the limit of possible improvement of the microscope as an instrument of discovery had been very nearly reached.” A quarter of a century ago I ventured to throw a doubt upon so questionable a statement. I determined, if possible, to submit the aperture question to an exhaustive examination. My views were accordingly submitted to two of the highest authorities in this country--Sir George Airy, the then Astronomer Royal, and Sir George Stokes, Professor of Physics at Cambridge University--both of whom agreed with me that the possible increase of aperture would be attended with great advantage to the objective, and open the way to an extension of power resolution in the microscope.[13] The discussion afterwards took a warm turn, as will be seen on reference to “The Monthly Microscopical Journals” of 1874, 1875 and 1876.
The confusion into which the aperture question at this period had lapsed was no doubt due to the fact that its opponents had not yet grasped the true meaning of the term aperture. It was believed to be synonymous with “angular aperture,” much in use at the time. It will, however, appear quite unaccountable that even the older opticians should have confounded the latter with the former; and so entirely disregarded the fact that the angles of the pencil of light admitted by the objective cannot serve as a measure of its aperture, and that high refractive media can greatly reduce the value length of waves of light.
When the medium in which the objective works is the same as air, it is not that a comparison can be made by the angles of the radiant pencils only, but by their sines. For example, if two dry objectives admit pencils of 60° and 180°, their real apertures are not as 1 : 3, but as 1 : 2 only. Aperture in fact is computed by mathematicians by tracing the rays from the back focus through the system of lenses to the front focus, the front focus being the point at which the whole cone of rays converge as free as may be from aberration. If the front focus be in air, no pencil greater than 82°, “double the angle of total reflection,” can emerge from the plane front of the lens; and, obviously, if no greater cone can emerge to a focus one way, neither can any greater cone enter the body of the lens from the radiant. This angle, then, of 82°, must be regarded as the limit for dry lenses or objectives.
This limit, it will be seen on more careful examination, is very nearly the maximum angle that can be computed for a lens to have a front focus in air. This can be proved by the consideration of the angle of the image of rays, as they are radiated from the object itself in balsam: for although this angle of image rays viewed as nascent from a self-luminous object capable of scattering rays in all directions, may be 180° in the substance of the balsam and cover-glass, of the 180° only 82° of the central portion will emerge into air--all rays beyond this limit are internally reflected at the cover-glass. This cone, then, of 82° becomes 180° in air, and a large part must necessarily be lost by reflection at the first incidence on the plane front of the lens. But with a formula permitting the use of a water medium between the front lens and the cover-glass, the aperture of the image rays may reach 126°--double the critical angle from glass to water; and with an oil medium, the aperture will be found to be limited only by the form of the front lens that can be constructed by the optician.
To sum up, then, the effect of the immersion system, greatly assists in the correction of aberration, gives increased magnification and angular aperture, increase of working distance between the objective and object, and renders admissible the use of the thicker glass-cover.
The aperture question would in all probability have remained unsolved many years longer (ten or twelve years elapsed after I brought the question under discussion before opticians gave way), but for the fortunate circumstance that the eminent mathematical and practical optician, Professor Abbe, of Jena, was about to visit London. This came off in the early part of the seventies, when the late Mr. John Mayall and myself had the good fortune to interview him. The subject discussed was naturally the increase of aperture and the theory of microscopical vision. He readily at our request undertook to re-investigate the question in all its bearings on the microscope. It is almost unnecessary to add that the conclusions he came to, and the results obtained, have proved of inestimable value to the microscopist and practical optician, and it may well seem necessary to explain somewhat at greater length the conclusions the learned Professor came to, and by the adoption of which the microscope has been placed on a more scientific basis than it had before attained to. Several papers were published in extenso in the “Journal of the Royal Microscopical Society,” and I am greatly indebted to Mr. Frank Crisp, LL.D., for an excellent resumé of Abbe’s Monograph.[14]
The essential step in the consideration of aperture is, as I have said, to understand clearly what is meant by the term. It will at once be recognised that its definition must necessarily refer to its primary meaning of opening, and must, in the case of an optical instrument, define its capacity for receiving rays from the object, and transmitting them to the image received at the eye-piece.
In the case of the telescope-objective, its capacity for receiving and transmitting rays is necessarily measured by the expression of its absolute diameter or “opening.” No such absolute measure can be applied in the case of the microscope objective, the largest constructed lenses of which having by no means the largest apertures, being, in fact, the lower powers of the instrument, whose apertures are for the most part but small. The capacity of a microscope objective for receiving and transmitting rays is, however, as will be seen, estimated by its relative opening, that is, its opening in relation to its focal length. When this relative opening has been ascertained, it may be regarded as synonymous with that denoted in the telescope by absolute opening. That this is so will be better appreciated by the following consideration:--
In a single lens, the rays admitted within one meridional plane evidently increase as the diameter of the lens (all other circumstances remaining the same), and in the microscope we have, at the back of the lens, the same conditions to deal with as are in front in the case of the telescope; the larger or smaller number of emergent rays will therefore be measured by the clear diameter, and as no rays can emerge that have not first been admitted, this will give the measure of the admitted rays under similar circumstances.
If the lenses compared have different focal lengths but the same clear “openings,” they will transmit the same number of rays to equal areas of an image at a definite distance, because they would admit the same number if an object were substituted for the image; that is, if the lens were used as a telescope-objective. But as the focal lengths are different, the amplification of the images is different also, and equal areas of these images correspond to different areas of the object from which the rays are collected. Therefore, the higher power lens with the same opening as the lower power, will admit a greater number of rays in all from the same object, because it admits the same number as the latter from a smaller portion of the object. Thus, if the focal lengths of two lenses are as 2 : 1, and the first amplifies N diameters, the second will amplify 2 N with the same distance of the image, so that the rays which are collected to a given field of 1 mm. diameter of the image are admitted from a field of 1/N mm. in the first case, and of 1/(2N) mm. in the second. As the “opening” of the objective is estimated by the diameter (and not by the area) the higher power lens admits twice as many rays as the lower power, because it admits the same number from a field of half the diameter, and, in general, the admission of rays by the same opening, but different powers, must be in the inverse ratio of the focal lengths.
In the case of the single lens, therefore, its aperture is determined by the ratio between the clear opening and the focal length. The same considerations apply to the case of a compound objective, substituting, however, for the clear opening of the single lens the diameter of the pencil at its emergence from the objective, that is, the clear utilised diameter of the back lens. All equally holds good whether the medium in which the objective is placed is the same in the case of the two objectives or different, as an alteration of the medium makes no difference in the power.
Thus we arrive at a general proposition for all kinds of objectives: 1st, when the power is the same, the admission of rays (or aperture) varies with the diameter of the pencil at its emergence; 2nd, when the powers are different, the same aperture requires different openings in the ratio of the focal lengths, or conversely with the same opening the aperture is in inverse ratio to the focal lengths. We see, therefore, that just as in the telescope the absolute diameter of the object-glass defines its aperture, so in the microscope the ratio between the utilised diameter of the back lens and the focal length of the objective defines its aperture also, and this is clearly a definition of aperture in its primary and only legitimate meaning as “opening;” that is, the capacity of the objective for admitting rays from the object and transmitting them to the image.
If, by way of illustration, we compare a series of dry and oil-immersion objectives, and commencing with small air angles, progress up to 180° air angle, and then take an oil-immersion of 82° and progress again to 180° oil angle, the ratio of opening to power progresses also, and attains its maximum, not in the case of the air angle of 180° (when it is exactly equivalent to the oil angle of only 82°), but is greatest at the oil angle of 180°. If we assume the objectives to have the same power throughout we get rid of one of the factors of the ratio, and we have only to compare the diameters of the emergent beams, and can represent their relations by diagrams.
Fig. 35 illustrates five cases of different apertures of 1/4-in. objectives, viz.: those of dry objectives of 60°, 97°, and 180° air angle, a water-immersion of 180° water angle, and an oil-immersion of 180° oil angle. The inner dotted circles in the two latter cases are of the same size as that corresponding to the 180° air angle.
A dry objective of the maximum air angle of 180° is only able to utilise a diameter of back lens equal to twice the focal length, while an immersion lens of even only 100° utilises a larger diameter, i.e., it is able to transmit more rays from the object to the image than any dry objective is capable of transmitting. Whenever the angle of an immersion lens exceeds twice the critical angle for the immersion fluid, i.e., 96° for water or 82° for oil, its aperture is in excess of that of a dry objective of 180°.
This excess will be seen if we take an oil-immersion objective of, say 122° balsam angle, illuminating it so that the whole field is filled with the incident rays, and use it first on an object not mounted in balsam, but dry. We then have a dry objective of nearly 180° angular aperture, for, as will be seen by reference to Fig. 36, the cover-glass is virtually the first surface of the objective, as the front lens, the immersion fluid, and the cover-glass are all approximately of the same index, and form, therefore, a front lens of extra thickness. When the object is close to the cover-glass the pencil radiating from it will be very nearly 180°, and the emergent pencil (observed by removing the eye-piece) will be seen to utilise as much of the back lens of the objective as is equal to twice the focal length, that is, the inner of the two circles at the head of Fig. 35.
If now balsam be run in beneath the cover-glass so that the angle of the pencil taken up by the objective is no longer 180°, but 122° only (that is, smaller), the diameter of the emergent pencil is larger than it was before, when the angle of the pencil was 180° in air, and will be approximately represented by the outer circle of Fig. 35. As the power remains the same in both cases, the larger diameter denotes the greater aperture of the immersion objective over a dry objective of even 180° angle, and the excess of aperture is made plainly visible.
Having settled the principle, it is still necessary, however, to find a proper notation for comparing apertures. The astronomer can compare the apertures of his various objectives by simply expressing them in inches, but this is obviously not available to the microscopist, who has to deal with the ratio of two varying quantities.
In consequence of a discovery made by Professor Abbe in 1873, that a general relation existed between the pencil admitted into the front of the objective and that emerging from the back of the objective, he was able to show that the ratio of the semi-diameter of the emergent pencil to the focal length of the objective could be expressed by the formula n Sin u, i.e., by the sine of half the angle of aperture (u) multiplied by the refractive index of the medium (n) in front of the objective (n being 1·0 for air, 1·33 for water, and 1·52 for oil or balsam).
When, then, the values in any given cases of the expression n Sin u (which is known as the “numerical aperture”) has been ascertained, the objectives are instantly compared as regards their aperture, and, moreover, as 180° in air is equal to 1·0 (since n = 1·0 and the sine of half 180° = 1·0) we see, with equal readiness, whether the aperture is smaller or larger than that corresponding to 180° in air. Thus, suppose we desire to compare the apertures of three objectives, one a dry objective, the second a water immersion, and the third an oil immersion; these would be compared on the angular aperture view as, say 74° air angle, 85° water angle, and 118° oil angle, so that a calculation must be worked out to arrive at the actual relation between them. Applying, however, the numerical[15] notation, which gives ·60 for the dry objective, ·90 for the water immersion, and 1·30 for the oil immersion, their relative apertures are immediately recognised, and it is seen, for instance, that the aperture of the water immersion is somewhat less than that of a dry objective of 180°, and that the aperture of the oil immersion exceeds that of the latter by 30%.
The advantage of immersion, in comparison with dry objectives, becomes at once apparent. Instead of consisting merely in a diminution of the loss of light by reflection or increased working distance, it is seen that a wide-angled immersion objective has a larger aperture than a dry objective of maximum angle, so that for any of the purposes for which aperture is essential an immersion must necessarily be preferred to a dry objective.
That pencils of identical angular extension but in different media are different physically, will cease to appear in any way paradoxical if we recall the simple optical fact that rays, which in air are spread out over the whole hemisphere, are in a medium of higher refractive index such as oil compressed into a cone of 82° round the perpendicular, i.e., twice the critical angle. A cone exceeding twice the critical angle of the medium will therefore embrace a surplus of rays which do not exist even in the hemisphere when the object is in air.
The whole aperture question, notwithstanding the innumerable perplexities which heretofore surrounded it, is in reality completely solved by these two simple considerations: First, that “aperture” is to be applied in its ordinary meaning as representing the greater or less capacity of the objective for receiving and transmitting rays; and second, that when so applied the aperture of an objective is determined by the ratio between its opening and its focal length; the objective that utilises the larger back lens (or opening) relatively to its focal length having necessarily the larger aperture. It would hardly, therefore, serve any useful purpose if we were here to discuss the various erroneous ideas that gave rise to the contention that 180° in air must be the maximum aperture. Amongst these was the suggestion that the larger emergent beams of immersion objectives were due to the fact that the immersion fluid abolished the refractive action of the first plane surface which, in the case of air, prevented there being any pencil exceeding 82° within the glass. Also the very curious mistake which arose from the assumption that a hemisphere did not magnify an object at its centre because the rays passed through without refraction. A further erroneous view has, however, been so widespread that it seems to be desirable to devote a few lines to it, especially as it always appears at first sight to be both simple and conclusive.
If a dry objective is used upon an object in air, as in Fig. 37, the angle may approach 180°, but when the object is mounted in balsam, as in Fig. 37_a_, the angle at the object cannot exceed 82°, all rays outside that limit (shown by dotted lines) being reflected back at the cover-glass and not emerging into air. On using an immersion objective, however, the immersion fluid which replaces the air above the cover-glass allows the rays formerly reflected back to pass through to the objective, so that the angle at the object may again be nearly 180° as with the dry lens. The action of the immersion objective was, therefore, supposed to be simply that it repaired the loss in angle which was occasioned when the object was transferred from air to balsam, and merely restored the conditions existing in Fig. 37_a_ with the dry objective on a dry object.
As the result of this erroneous supposition, it followed that an immersion objective could have no advantage over a dry objective, except in the case of the latter being used upon a balsam-mounted object, its aperture then being (as was supposed) “cut down.” The error lies simply in overlooking the fact that the rays which are reflected back when the object is mounted in balsam (Fig. 37_a_) are not rays which are found when the object is in air (Fig. 37), but are additional and different rays which do not exist in air, as they cannot be emitted in a substance of so low a refractive index.
Lastly, it should also be noted that it is numerical and not angular aperture which measures the quantity of light admitted to the objective by different pencils.
First take the case of the medium being the same. The popular notion of a pencil of light may be illustrated by Fig. 38, which assumes that there is equal intensity of emission in all directions, so that the quantity of light contained in any given pencils may be compared by simply comparing the contents of the solid cones. The Bouguer-Lambert law, however, shows that the quantity of light emitted by any bright point varies with the obliquity of the direction of emission, being greater in a perpendicular than in an oblique direction. The rays are less intense in proportion as they are more inclined to the surface which emits them, so that a pencil is not correctly represented by Fig. 38, but by Fig. 38_a_, the density of the rays decreasing continuously from the vertical to the horizontal, and the squares of the sines of the semi-angles (i.e., of the numerical aperture) constituting the true measure of the quantity of light contained in any solid pencil.
If, again, the media are of different refractive indices, as air (1·0), water (1·33), and oil (1·52), the total amount of light emitted over the whole 180° from radiant points in these media under a given illumination is not the same, but is greater in the case of the media of greater refractive indices in the ratio of the squares of those indices (i.e., as 1·0, 1·77 and 2·25). The quantity of light in pencils of different angle and in different media must therefore be compared by squaring the product of the sines and the refractive indices, i.e. (n Sin u^2), for the square of the numerical aperture.
The fact is therefore made clear that the aperture of a dry objective of 180° does not represent, as was supposed, a maximum, but that aperture increases with the increase in the refractive index of the immersion fluid; and it should be borne in mind that this result has been arrived at in strict accordance with the ordinary propositions of geometrical optics, and without any reference to or deductions from the diffraction theory of Professor Abbe.
There still remains one other point for determination, namely, the proper function of aperture in respect to immersion objectives of large aperture. The explanation of the increased power of vision obtained by increase of aperture was, that by the greater obliquity of the rays to the object “shadow effects” were produced, a view which overlooked the fact, first, that the utilisation of increased aperture depends not only on the obliquity of the rays sent to the object, but also to the axis of the microscope; and exactly as there is no acoustic shadow produced by an obstacle, which is only a few multiples of the length of the sound waves, so there can be no shadow produced by minute objects, only a few multiples from the light waves, the latter then passing completely round the object. The Abbe diffraction theory, however, supplies the true explanation of this, and shows that the increased performance of immersion objectives of large aperture is directly connected (as might have been anticipated) with the larger “openings” in the proper sense of the term, which, as we have already explained, such objectives really possess. Furthermore, in order that the image exactly corresponds with the object, all diffracted rays must be gathered up by the objective. Should any be lost we shall have not an actual image of the object, but a spurious one. Now, if we have a coarse object, the diffracted rays are all comprised within a narrow cone round the direct beam, and an objective of small aperture will transmit them all. With a minute object, however, the diffracted rays are widely spread out, so that a small aperture can admit only a fractional part--to admit the whole or a very large part, and consequently to see the minute structure of the object, or to see it truly, a large aperture is necessary, and in this lies the value of aperture and of a wide-angled immersion objective for the observation of minute structures.
Numerical Aperture.
=Measure of Apertures of Objectives. N.A.=--Numerical aperture, as it is termed, is measured by the scale of measurement calculated by the late Professor Abbe, and which has since been generally recognised and adopted. He showed that even in lenses made for the same medium (as air) their comparative aperture as compared with their focus was not correctly measured by the angle of the rays grasped, but by the actual diameters of the pencil of rays transmitted, which depend, as already seen, more upon the back of the lens than the front. To get a geometric measure for comparison, he took the radii, or half diameters (whose relative proportions would be the same), and which geometrically are the sines of the semi-angle of the outermost rays grasped. Abbe further showed that if this sine of half the outside angle were multiplied by the refractive index of the medium used we should have a number which would give the comparative aperture of any lens, whatever the medium. This number, then, determines both the numerical aperture and the resolving power of the objective.
The following table of numerical apertures shows the respective angular pencils which they express in air, water and cedar oil, or glass.[16] The first column gives the numerical apertures from 0·20 to 1·33; the second, third, and fourth, the air, water and oil (or balsam) angles of aperture from 23° 4′ air angle to 180° balsam angle. The theoretical resolving power in lines to the inch is shown in the sixth column; the line E of the spectrum being taken from about the middle of the green, the column giving “illuminating power” being of less importance; while in using that of penetrating power, it must be remembered that several data beside that of 1/a go to make up the total depth of vision with the microscope.
ABRIDGED NUMERICAL APERTURE TABLE.
=====+=========================+==========================+======+====== | Corresponding Angle |Limit of Resolving Power, | | | (2 u) for | in Lines to an Inch. | | +--------+-------+--------+--------+-------+---------+ | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) -----+--------+-------+--------+--------+-------+---------+------+------ 1·33 | ... |180° 0′|122° 6′| 128,225| 138,989|168,907 | 1·769| ·752 1·32 | ... |165° 56′|120° 33′| 127,261| 137,944|167,637 | 1·742| ·758 1·30 | ... |155° 38′|117° 35′| 125,333| 135,854|165,097 | 1·690| ·769 1·28 | ... |148° 42′|114° 44′| 123,405| 133,764|162,557 | 1·638| ·781 1·26 | ... |142° 39′|111° 59′| 121,477| 131,674|160,017 | 1·588| ·794 1·24 | ... |137° 36′|109° 20′| 119,548| 129,584|157,477 | 1·538| ·806 1·22 | ... |133° 4′|106° 45′| 117,620| 127,494|154,937 | 1·488| ·820 1·20 | ... |128° 55′|104° 15′| 115,692| 125,404|152,397 | 1·440| ·833 1·18 | ... |125° 3′|101° 50′| 113,764| 123,314|149,857 | 1·392| ·847 1·16 | ... |121° 26′| 99° 29′| 111,835| 121,224|147,317 | 1·346| ·862 1·14 | ... |118° 0′| 97° 11′| 109,907| 119,134|144,777 | 1·300| ·877 1·12 | ... |114° 44′| 94° 55′| 107,979| 117,044|142,237 | 1·254| ·893 1·10 | ... |111° 36′| 92° 43′| 106,051| 114,954|139,698 | 1·210| ·909 1·08 | ... |108° 36′| 90° 34′| 104,123| 112,864|137,158 | 1·166| ·926 1·06 | ... |105° 42′| 88° 27′| 102,195| 110,774|134,618 | 1·124| ·943 1·04 | ... |102° 53′| 86° 21′| 100,266| 108,684|132,078 | 1·082| ·962 1·02 | ... |100° 10′| 84° 18′| 98,338| 106,593|129,538 | 1·040| ·980 1·00 | 180° 0′| 97° 31′| 82° 17′| 96,410| 104,503|126,998 | 1·000| 1·000 0·98 | 157° 2′| 94° 56′| 80° 17′| 94,482| 102,413|124,458 | ·960| 1·020 0·96 | 147° 29′| 92° 24′| 78° 20′| 92,554| 100,323|121,918 | ·922| 1·042 0·94 | 140° 6′| 89° 56′| 76° 24′| 90,625| 98,223|119,378 | ·884| 1·064 0·92 | 133° 51′| 87° 32′| 74° 30′| 88,697| 96,143|116,838 | ·846| 1·087 0·90 | 128° 19′| 85° 10′| 72° 36′| 86,769| 94,053|114,298 | ·810| 1·111 0·88 | 123° 17′| 82° 51′| 70° 44′| 84,841| 91,963|111,758 | ·774| 1·136 0·86 | 118° 38′| 80° 34′| 68° 54′| 82,913| 89,873|109,218 | ·740| 1·163 0·84 | 114° 17′| 78° 20′| 67° 6′| 80,984| 87,783|106,678 | ·706| 1·190 0·82 | 110° 10′| 76° 8′| 65° 18′| 79,056| 85,693|104,138 | ·672| 1·220 0·80 | 106° 16′| 73° 58′| 63° 31′| 77,128| 83,603|101,598 | ·640| 1·250 0·78 | 102° 31′| 71° 49′| 61° 45′| 75,200| 81,513| 99,058 | ·608| 1·282 0·76 | 98° 56′| 69° 42′| 60° 0′| 73,272| 79,423| 96,518 | ·578| 1·316 0·74 | 95° 28′| 67° 37′| 58° 16′| 71,343| 77,333| 93,979 | ·548| 1·351 0·72 | 92° 6′| 65° 32′| 56° 32′| 69,415| 75,242| 91,439 | ·518| 1·389 0·70 | 88° 51′| 63° 31′| 54° 50′| 67,487| 73,152| 88,899 | ·490| 1·429 0·68 | 85° 41′| 61° 30′| 53° 9′| 65,559| 71,062| 86,359 | ·462| 1·471 0·66 | 82° 36′| 59° 30′| 51° 28′| 63,631| 68,972| 83,819 | ·436| 1·515 0·64 | 79° 36′| 57° 31′| 49° 48′| 61,702| 66,882| 81,279 | ·410| 1·562 0·62 | 76° 38′| 55° 34′| 48° 9′| 59,774| 64,792| 78,739 | ·384| 1·613 0·60 | 73° 44′| 53° 38′| 46° 30′| 57,846| 62,702| 76,199 | ·360| 1·667 0·58 | 70° 54′| 51° 42′| 44° 51′| 55,918| 60,612| 73,659 | ·336| 1·724 0·56 | 68° 6′| 49° 48′| 43° 14′| 53,990| 58,522| 71,119 | ·314| 1·786 0·54 | 65° 22′| 47° 54′| 41° 37′| 52,061| 56,432| 68,579 | ·292| 1·852 0·52 | 62° 40′| 46° 2′| 40° 0′| 50,133| 54,342| 66,039 | ·270| 1·923 0·50 | 60° 0′| 44° 10′| 38° 24′| 48,205| 52,252| 63,499 | ·250| 2·000 0·45 | 53° 30′| 39° 33′| 34° 27′| 43,385| 47,026| 57,149 | ·203| 2·222 0·40 | 47° 9′| 35° 0′| 30° 31′| 38,564| 41,801| 50,799 | ·160| 2·500 0·35 | 40° 58′| 30° 30′| 26° 38′| 33,744| 36,576| 44,449 | ·123| 2·857 0·30 | 34° 56′| 26° 4′| 22° 46′| 28,923| 31,351| 38,099 | ·090| 3·333 0·25 | 28° 58′| 21° 40′| 18° 56′| 24,103| 26,126| 31,749 | ·063| 4·000 0·20 | 23° 4′| 17° 18′| 15° 7′| 19,282| 20,901| 25,400 | ·040| 5·000 =====+========+========+=======+========+========+========+======+======
(1) Numerical Aperture. (n sin u = a.) (2) Air (n = 1·00). (3) Water (n = 1·33). (4) Homogeneous Immersion (n = 1·52). (5) White Light. (λ = 0·5269 μ, Line E.) (6) Monochromatic (Blue) Light.(λ = 0·4861 μ, Line F.) (7) Photography. (λ = 0·4000 μ, Near Line _h__k_.) (8) Illuminating Power (a^2.) (9) Penetrating Power (1/a.)
Abbe’s Apertometer.
The apertometer is an auxiliary piece of apparatus invented by Abbe, for testing the fundamental properties of objectives and determining their numerical and angular apertures. This accessory of the microscope involves the same principles as that of Tolles, which the late Mr. J. Mayall and myself brought to the notice of the Royal Microscopical Society of London in 1876. Abbe’s apertometer (Fig. 39) consists of a flat cylinder of glass, about three inches in diameter, and half an inch thick, with a large chord cut off, so that the portion left is somewhat more than a semicircle; the part where the segment is cut is bevelled from above downwards, to an angle of 45°, and it will be seen that there is a small disc with an aperture in it denoting the centre of the semicircle. To use this instrument the microscope is placed in a vertical position, and the apertometer is placed upon the stage with its circular part to the front and the chord to the back. Diffused light, either from the sun or lamp, is assumed to be in front and on both sides. Suppose the lens to be measured is a dry one-quarter inch; then with a one-inch eye-piece having a large field, the centre disc, with its aperture on the apertometer, is brought into focus. The eye-piece and the draw-tube are now removed, leaving the focal arrangement undisturbed, and a lens supplied with the apertometer is screwed into the end of the draw-tube. This lens, with the eye-piece in the draw-tube, forms a low-power compound microscope. This is now inserted into the body-tube, and the back lens of the objective whose aperture we desire to measure is brought into focus. In the image of the back lens will be seen stretched across, as it were, the image of the circular part of the apertometer. It will appear as a bright band, because the light which enters normally at the surface is reflected by the bevelled part of the chord in a vertical direction, so that in reality a fan of 180° in air is formed. There are two sliding screens seen on either side of the figure of the apertometer; they slide on the vertical circular portion of the instrument. The images of these screens can be seen in the image of the bright bands. These screens should now be moved so that their edges just touch the periphery of the back lens. They act, as it were, as a diaphragm to cut the fan and reduce it, so that its angle just equals the aperture of the objective and no more.
This angle is now determined by the arc of glass between the screens; thus we get an angle in glass the exact equivalent of the aperture of the objective. As the numerical apertures of these arcs are engraved on the apertometer, they can be read off by inspection. A difficulty is not infrequently experienced from the fact that it is not easy to determine the exact point at which the edge of the screen touches the periphery of the back lens, or rather the limit of the aperture. Zeiss, to meet this difficulty, made a change in the form of the apparatus--furnished a glass disc mounted on a metal plate, with a slot for the purpose of its more accurate adjustment.[17]
Stereoscopic Binocular Vision.
Professor Wheatstone’s remarkable discovery of stereoscopic vision led, at no distant period, to the application of the principle to the microscope. It may therefore prove of interest to inquire how stereoscopic binocular vision is brought about. Indeed, the curious results obtained in the stereoscope cannot be well understood without a previous knowledge of the fundamental optical principles involved in this contrivance, whereby two slightly dissimilar pictures of any object become fused into one image, having the actual appearance of relief. The invention of the stereoscope by Sir Charles Wheatstone, F.R.S., 1838, and improved by Brewster, was characterised by Sir John Herschel as “one of the most curious discoveries, and beautiful for its simplicity, in the entire range of experimental optics,” led to a more general appreciation of the value of the conjoint use of both eyes in conveying to the mind impressions of the relative form and position of an object, such as the use of either eye singly does not convey with anything like the same precision. When a near object having three dimensions is looked at, a different perspective representation is seen with each eye. Certain parts are seen by the right eye, the left being closed, that are invisible to the left eye, the right being closed, and the relative positions of the portions visible to each eye in succession differ. These two visual impressions are simultaneously perceived by both eyes, and combined in the brain into one image, producing the effect of perspective and relief. If truthful right-and-left monocular pictures of an object be so presented to the two eyes that the optic axes when directed to them shall converge at the same angle as when directed to the object itself, a solid image will be at once perceived. The perception of relief referred to is closely connected with the doubleness of vision which takes place when the images on corresponding portions of the two retina are not similar. But, if in place of looking at the solid object itself we look with the right and left eyes respectively at pictures of the object corresponding to those which would be formed by it on the retina of the two eyes if it were placed at a moderate distance in front of them, and these visual pictures brought into coincidence, the same conception of a solid form is generated in the mind just as if the object itself were there.
Professor Abbe, however, contended that the method by which dissimilar images are formed in the binocular microscope differs materially from that of ordinary stereoscopic vision, and that the pictures are united solely by the activity of the brain, not by the prisms which ordinarily give rise to sensations of solidity. This can be only partially true, as binocularity in the microscope is due to difference of projection exhibited by the different parallax displacement of the images, and also to the perception of depth imparted by the instrument.
Wheatstone was firmly convinced that his stereoscopic principle could be applied to the microscope, and he therefore applied first to Ross and then to Powell to assist him in its adaptation. But whether either of these opticians made any attempt to give effect to his wishes and suggestions is not known. In the year 1851 Professor Riddell, of America, succeeded in constructing a binocular microscope by employing two rectangular prisms behind the objective. M. Nachet also constructed a binocular with two body-tubes and a series of prisms. But neither Riddell’s nor Nachet’s instrument was ever brought into use; they were either too complicated or too costly.
It will be understood, however, that the binocular stereoscope combines two dissimilar pictures, while the binocular microscope simply enables the observer to look with both eyes at images which are essentially identical. Stereoscopic vision, to be effective, requires that the delineating pencil shall be equally separated, so that one portion of the admitted cone of light is conducted to one eye, and the other portion to the other eye.
Select any object lying in an inclined position, and place it in the centre of the field of view of the microscope; then, with a card held close to the object-glass, stop off alternately the right or left hand portion of the front lens: it will then appear that during each alternate change certain parts of the object will change their relative positions.
To illustrate this, Fig. 40 a, b are enlarged drawings of a portion of the egg of the common bed-bug (Cimex lecticularis), the operculum which should cover the opening having been forced off at the time the young was hatched. The figures exactly represent the two positions that the inclined orifice will occupy when the right- and left-hand portions of the object-glass are stopped off. This object is viewed as an opaque object, and drawn under a two-thirds object-glass of about 28° aperture. If this experiment is repeated, by holding the card over the eye-piece, and stopping off alternately the right and left half of the ultimate emergent pencil, exactly the same changes and appearances will be observed in the object under view. The two different images just produced are such as are required for obtaining stereoscopic vision. It is therefore evident that if instead of bringing them confusedly together into one eye we can separate them so as to bring together a, b into the left and right eye, in the combined effect of the two projections we obtain at once all that is necessary to enable us to form a correct judgment of the solidity and distance of the several parts of the object.
Nearly all objectives from the one inch upwards of any considerable aperture give images of the object seen from a different point of view with the two opposite extremes of the margin of the cone of rays; the resulting effect is that there are a number of dissimilar perspectives of the object blended together at one and the same time on the retina. For this reason, if the object under view possesses bulk, a more accurate image will be obtained by reducing the aperture of the objective.
Diagram 3, Fig. 41, represents the method employed by Mr. Wenham for bringing the two eyes sufficiently close to each other to enable them both to see through the double eye-piece at the same moment. a a a are rays converging from the field lens of the eye-piece; after passing the eye-lens b, if not intercepted, they would come to a focus at c; but they are arrested by the inclined surfaces, d d, of two solid glass prisms. From the refraction of the under incident surface of the prisms, the focus of the eye-piece becomes elongated, and falls within the substance of the glass at e. The rays then diverge, and after being reflected by the second inclined surface f, emerge from the upper side of the prism, when their course is rendered still more divergent, as shown by the figure. The reflecting angle given to the prisms is 47-1/2°, to accommodate which it is necessary to grind away the contact edges of the prisms, as represented, otherwise they prevent the extreme margins of the reflecting surfaces from coming into operation, which are seldom made quite perfect.
Fig. 42 represents a sectional view of Abbe’s stereoscopic eye-pieces, which consist of three prisms of crown glass, a, b and b′, placed below the field-glass of the two eye-pieces; the tube c is slipped into the tube or body like an ordinary eye-piece. The two prisms a and b are united so as to form a thick plate with parallel sides, inclined to the axis at an angle of 38·5°. The cone of rays from the objective is thus divided into two parts, one being transmitted and the other reflected; that transmitted passing through a b and forming an image of the object in the axial eye-piece B. Adjustment for different distances between the eyes is effected by the screw placed to the right-hand side of the figure, which moves the eye-piece B′, together with the prism b′, in a parallel direction. The tubes can also be drawn out, if greater separation is required. The special feature of this instrument is that on halving the cone of rays by turning the caps, an orthoscopic or pseudoscopic effect is produced. This double-eyed piece arrangement of Abbe’s has not been at all brought into use in this country; this is partly owing to its original adaptation for use with the shorter Continental body-tube of 160 mm., and not for our 10-inch body.
The most perfect method of securing pleasing satisfactory stereoscopic vision of objects is that devised by Mr. Wenham. In his binocular microscope an equal division of the cone of rays, after passing through the objective is secured and again united in the eye-pieces, which act as one, so that each eye is furnished with an appropriate and simultaneous view of the object. The methods contrived by the earlier experimenters not only materially interfered with the definition of the objective and object, but also required expensive alterations and adaptations of the microscope, and sometimes separate stands for their employment. Mr. Wenham’s invention, on the contrary, offers no such obstacle to its use, and the utility of the microscope as a monocular is in no way impaired either when using the higher powers.
The most important improvement, then, effected by Wenham consists in the splitting up or dividing the pencil of rays proceeding from the objective by the interposition of a prism of the form shown in Fig. 43. This is placed in the body or tube of the microscope so as to interrupt only one-half (a c) of the pencil, the other half (a b) proceeding continuously to the field-glass, eye-piece, of the principal body. The interrupted half of the pencil on its entrance into the prism is subjected to very slight refraction, since its axial ray is perpendicular to the surface it meets. Within, the prism is subjected to two reflections at b and c, which send it forth again obliquely on the line b towards the eye-piece of the secondary body, to the left-hand side of the figure; and since at its emergence its axial ray is again perpendicular to the surface of the glass, it suffers no further refraction on passing out of the prism than on entering. By this arrangement, the image sent to the right eye is formed by rays which have passed through the left half of the objective; whilst the image sent to the left eye is formed by rays which have passed through the right half, and which have been subjective to two reflections within the prism, and passing through two surfaces of glass. The prism is held by the ends only on the sides of a small brass drawer, so that all the four polished surfaces are accessible, and should slide in so far that its edge may just reach the central line of the objective, and be drawn back against a stop, so as to clear the aperture of the same.
The binocular, then (Fig. 44), consists of a small prism mounted in a brass box A, which slides into an opening immediately above the object-glass, and reflects one-half of the rays which form an image of the object, into an additional tube B, attached at an inclination to the ordinary body C. One half of the rays take the usual course with their performance unaltered; and the remainder, though reflected twice, show no loss of light or definition worthy of notice, if the prism be well made.
As the eyes of different persons are not the same distance apart, the first and most important point to observe in using the binocular is that each eye has a full and clear view of the object. This is easily tried by closing each eye alternately without moving the head, when it may be found that some adjustment is necessary by racking out the draw-tubes D, E, of the bodies by means of the small milled head near the eye-pieces; this will increase the distance of the centres; and, on the contrary, the tubes, when racked down, will suit those eyes that are nearer together.
If the prism be drawn back till stopped by the small milled head, the field of view in the inclined body is darkened, and the rays from the whole aperture of the object-glass pass into the main body as usual, neither the prism nor the additional body interfering in any way with the use of the instrument as a monocular microscope.
The prism can be withdrawn altogether for the purpose of being wiped: this should be done frequently, and very carefully, on all four surfaces, with a perfectly clean cambric or silk handkerchief or a piece of wash-leather; but no hard substance must be used. During this process the small piece of blackened cork fitted between the prism and the thick end of the brass box may be removed; but it must be carefully replaced in the same position, as it serves an important purpose in stopping out extraneous light.
As the binocular microscope gives a real and natural appearance to objects, this effect is considerably increased by employing those kinds of illumination to which the naked eye is accustomed. The most suitable are all the opaque methods where the light is thrown down upon the surface; but for those objects that are semi-transparent, as sections of bone or teeth, diatomaceæ, living aquatic animalcules, &c., the dark-field illumination by means of the parabolic reflector will give an equally good result.
For perfectly transparent illumination, it is much better to diffuse the light by placing under the object various substances, such as tissue-paper, ground glass, very thin porcelain, or a film of yellow bees’ wax, run between two pieces of thin glass.
To ensure the full advantage and relief to both eyes in prolonged observations with high as well as low powers, and with objectives of large aperture, Mr. Wenham devised a compound prism for use with his binocular microscope, the body tubes of which are also made expressly to suit the prism, as extreme accuracy is necessary to bring them into proper position. The main prism somewhat resembles in form the ordinary Wenham prism. Over the first reflecting surface is placed a second smaller prism, the top plane of which is parallel with the base of the first, so that direct rays pass through without deviation, but at the two inclined surfaces of the prisms (nearly in contact) there is a partial reflection from each, which, combined, give as much light as in the direct tube. The reflected image from these two surfaces is directed up into the inclined tube as usual. A somewhat later improvement is that of Dr. Schroeder, the high power prism, by means of which the whole of the rays emanating from the objective pass through it, and the full aperture of any power is thereby effectively utilised. Furthermore, Messrs. Ross have also constructed a right- and left-hand pair of eye-pieces, which ensure greater perfection of the image. It was, in fact, noticed that the size of the image in the left-hand field glass slightly differed from that of the right when examined by the ordinary Huyghenian eye-pieces. To compensate for this difference, the left-hand eye-piece has been carefully calculated, and its focus is now so accurately adjusted that the position of each eye in observing is brought into one plane of the binocular. The pairs of the several series of eye-pieces A, B and C have also been altered, and the effect is to greatly improve the image and give increased comfort to the observer.
Dr. Carpenter, who warmly espoused the binocular, and constantly employed it in his work, very truly said of it: “The important advantages I find it to possess are in penetrating power, or focal depth, which is in every way superior to that of the monocular microscope, so that an object whose surface presents considerable inequalities is very much more distinctly seen with the former than with the latter.”
This difference may in part be attributed to the practical modification in the angle of aperture of the objective, produced by the division of the cone of rays transmitted through the two halves, so that the picture or image received through each half of the objective of 60° is formed by rays diverging at an angle of only about 30°. He confesses, however, that this does not satisfactorily explain the fact that the binocular brings to the mind’s eye the solid image of the object, and thus gives to the observer a good idea of its form and which could hardly be obtained by the monocular microscope. Carpenter cites in support of his views the wing of a little-known moth, Zenzera Œsculi, which has an undulating surface, whereon the scales are set at various angles instead of having the usual imbricated arrangement, a good object for demonstrating; the general inequality of surface and the obliquity of its scales, which are at once seen by the binocular with a completeness not obtained by the monocular instrument.
To one unaccustomed to work with the binocular the views expressed by Dr. Carpenter as to the extreme value of the instrument for ordinary work may appear somewhat exaggerated, but from my own experience, having long had in constant use a Ross-Zentmayer binocular, furnished with a special prism, constructed for working with a 1/8 dry objective or a 1/10 immersion, the perfection of picture obtained was in every case quite equal to that of the monocular microscope. The relief to the eyes can hardly be over-estimated; the slight inequality of the pencil rays may be regarded rather as a part of the welcome rest afforded when a prolonged examination is made; it certainly appears to me to equalise the slight physiological difference known to exist between the eyes of most people. If one image is seen a little clearer by the stronger eye, the weaker eye assists rather more the stereoscopic effect of the object under observation. The advantage gained by the binocular is perhaps more appreciated when opaque objects are under examination, as the eggs of insects, and the tongue of the blow-fly, specimens of mosses, lichens, parasites (vegetable and animal), whose planes and inequalities of surface require penetration, and which usually demand more time for their observation.
No variation or change of any kind proposed either in the form of the instrument or the prism has proved of sufficient value or importance to bring it into use, and therefore Wenham’s instrument is scarcely likely to be superseded. It must be admitted that the improvement effected in the eye-piece form by Mr. Tolles, of Boston, U.S., is an exception to the rule laid down. It consists in mounting the prisms in a light material, vulcanite, made to fit into the monocular microscope body, thus taking the place of the ordinary eye-piece. The image transmitted by the objective is brought to a focus on the face of the first equilateral triangular prism by the intervention of an erector-eye-piece inserted beneath it. The second set of prisms have a rack and pinion movement to adjust them to any visual angle. The illumination of both fields in this eye-piece is nearly equal in brightness. Mr. Stephenson’s erecting binocular (Fig. 45) has proved to be of some practical value. It has the advantage of being of equal use with high and low powers, and with little loss of definition. When used for dissecting purposes it gives an erect image of the object. It is equally useful as a working microscope, for arranging diatoms and botanical specimens of every kind. The sub-stage tube will receive a diaphragm or illuminating apparatus; the eye-pieces have a sliding adjustment for regulating the widths between eyes.