Illumination, its distribution and measurement

Front matter

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Preface

This book is intended to advance the subject of illuminating engineering or the art of directing and adapting light. It is divided into three parts. The first deals with the primary and the derived units of light, the theory of the distribution of illumination and the application of that theory to the spacing and the height of lamps. The second part describes instruments and methods employed for measuring light and illumination. The last part gives a few practical examples of the measurement of illumination.

“ The art of illumination,” wrote Count Rumford in the year 1789, “although it is undoubtedly one of the most useful that has been invented by man, and contributes perhaps more than any other to his comfort and convenience in all countries and in every class of society, has not even been considered as an art ; for the technical terms have not been invented which are indispensably necessary in order to render it possible to treat of it in a clear and satisfactory manner.”

One hundred and three years later, on May to, 1892, a paper, of which the present volume is an expansion, was read before the Institution of Civil Engineers, was awarded a Telford Medal and a Telford Premium, and was published in volume cx. of the Proceedings of the Institution. The subject still continued to attract little attention, and after sixteen years, at the invitation of Mr. Leon Gaster, and with the permission of the Council of the Institution of Civil Engineers, the Paper

was rewritten and appeared in The Illuminating Engineer.

vii viii

It has now been revised and extended and is offered not as a complete treatise, but as a record of the work of others and of my own investigations in evening hours, scant holidays, and spare moments.

It would not be possible within the compass of a single volume to deal comprehensively with the art of illumination. The scope of this book is limited to the principles and methods of distribution and measurement of illumination. The subject of photometry proper has been made subordinate, descriptions of systems of lighting and various kinds of lamps and appliances have been excluded, and the temptation to touch on innumerable side issues of scientific interest has been resisted. The theory of the distribution of illumination is excellently adapted for mathematical treatment, but I have preferred to deal with it in the manner in which it appeals to me, believing that for practical engineers the use of graphic methods will be more useful than equations and formulae. The calculated curves and diagrams have been drawn on a large scale and most of them are accurate within the thickness of the line.

The original works of nearly all the quoted writers have been consulted, not only for the purpose of verifying references and correcting them when erroneous, but for presenting in their own words and with their own illustrations some idea of the work of the old masters of photometry.

I have to express my thanks to Professor Silvanus Thompson for the loan of valuable old books, and to Professor J. T. Morris for reading most of the manuscript, and for his useful criticisms and suggestions, to Mr. J. Rennie for help with some of the computations, and to Mr. P. Webberley for assistance in revising proofs.

A. P. TROTTER.

London, March 1910.

CHAPTER I Units and Standards of Candle-Power

Introductory, i. Intensity or Candle-power, 2. Units and Standards, 3. The Carcel, 3. The British Candle, 4. The German Candle, 4. The Harcourt or Pentane Lamp, 4. The Hefner or Amyl-acetate Lamp, 5. The Violle, 7. The Bougie-decimale, 8. The Relative Values of the Standards, 8. Corrections for Flame Standards, 9. The Advantages of the Pentane and the Hefner, 11. The Arc Standard, 12. Radiation Standards, 13. Glow-lamp Sub-standards, 13.

Chapter II

Illumination, 15. The Foot-candle, 15. The Lux, 17. The Law of Inverse Squares, 17. The Cosine Law, 19. Mean Spherical Candle-power, 20. Flux of Light or Total Light, 21. Brightness or Intrinsic Brilliancy, 23. Quantity of Light and Quantity of Illumination, 23. Diffused Reflection, 24.

CHAPTER III The Distribution of Illumination

Distribution of Illumination on a Plane, 2 7. Theoretical Examples of Distribution, 29. Distribution from an Arc-lamp, 32. Distribution from a Vertical Filament, 34. General Cases of Distribution, 35. Distribution by Lamps at Varying Heights, 37. Relation between Height and Spacing of Lamps, 38. The Spacing of Street Lamps, 40. ■

IX

X

CHAPTER IV Distribution of Illumination over a Plane

The Construction of Contours, 45. Contours or Iso-lux Curves, 47. Bases of Comparison of Cases of Illumination, 52. Characteristic Curves, 58.

Chapter V

Photometry, 65. Discrimination Photometers, 70. Photometers, 74. The Bouguer Photometer, 74. The Rumford Photometer, 77. The Foucault Photometer, 80. The Harcourt or Gas Referees’ Photometer, 81. The Bunsen Photometer, 83. The Ritchie Photometers, 87. The Angle of the Ritchie Wedge, 91. Angle Errors, 95. The Conroy Photometer, 97. The Thompson-Starling Photometer, 98. The Lummer-Brodhun Photometer, 99. The Wild Mirror Photometer, 102. The Perforated Screen Photometer, 102. The Slot or Limit- Gauge Photometer, 106. The Grid Photometer, 109. The Joly Photometer, 110.

Chapter VI

Photometer Scales, 112. The Compensation Method, 115. The Illumination Gradient, 120. The Limitation of the Law of Inverse Squares, 121. The Moving Mirror Method, 123. The Construction of the Bar and Scales, 125. Rotating Sectors, 127. Milne Paddle, 130. The Lampholder, 130. Observation Recorder, 132. Screens and Stray Light, 134. Dead Black Paints, 138. Control of Electric Glow-lamp Sub-standards, 138.

CHAPTER VII Distribution of Light from a Source

Mean Horizontal and Spherical Candle-power, 141. The Horizontal Distribution of Light from Glow-lamps, 14 1. Mean Horizontal Candle-power, 143. The Distribution of Light from Glow-lamps and other Lamps, 145. The Distribution of Light from Arc-lamps, 146. Mean Spherical Candle-power, 149. Calculation of Mean Spherical Candle-power, and Rousseau’s Diagram, 1 50. Russell’s Construction, 151. Measurement of Mean Spherical Candle-power, 153. Ulbricht’s Globe, 157.

CONTENTS xi

CHAPTER VIII The Photometry of Coloured Lights

Introductory, 1 6 1 . Abney’s Method, 164. The Purkinje Effect, 166. Colour Vision, 168. Crova’s Method, 170. Coloured Screens, 174. The Flicker Photometer, 174. The Speed of Flicker photometers, 179. Selective Emissivity, 181.

Chapter IX

Accuracies, Errors, and Mistakes, 183. The Calculation of Errors, 185. Familiarity with the Photometer, 189. General Experience with Photometry, 190. Physical Conditions of the Observer, 190. Speed of Working, 192. Colour Difference, 193. Steadiness of the Light, 193. The Illumination on the Photometer, 194. Instrumental Errors, 196. Stray Light, 196. Precision, 197.

Chapter X

Illumination Photometry, 199. The Preece Illumination Photometer, 200. The Preece and Trotter Illumination Photometer, 202. Millar’s Criticisms on Illumination Photometers, 206. The Trotter Illumination Photometer, 208. Low Readings and Zero, 209. Adjustment of the Lamp, 210. The Nalder-T rotter Illumination Photometer, 210. Later Pattern Trotter Illumination Photometer, 21 1. Everett-Edgcumbe’s Pattern of Trotter Illumination Photometer, 212. Direction of View, 214. Adjustment of the Lamp, 215. The Screens, 216. Angle Errors, 217. Error due to Glaze, 2 1 8. Measurement of Angle Errors, 218. Scale of Angles of Incidence, 223. Measurement of Candle-power, 224. The Battery, Switch, and Contacts, 226. Height of the Photometer, 227. Direction of the Test-plate, 229. The Use of Coloured Screens, 232. The Harrison Photometer, 234. The Weber Photometer, 236. The Sharp and Millar Photometer, 239. The Wingen-Kriiss Photometer, 241. The Martens Photometer, 242. Iris Diaphragm Photometers, 243. Brightness Photometers, 244. The Dow and Mackinney Lumeter, 244. The Everett-Edgcumbe Luxometer, 245. The Trezise Photometer, 246. Photometry of the Daylight Illumination of the Interior of Buildings, 246.

xii

CHAPTER XI Practical Examples of Measurements of Illumination

Wimbledon, 250. London, 250. South Kensington Museum, 251. Charing Cross and Cannon Street Stations, 253. City of London, 254. Whitehall, 257. Modern Practice, 260. Ordinary Streets, Theatre Lighting, etc., 261. Characteristic Curves, 262.

CHAPTER XII Dioptric Distribution and Diffusion of Light, 263

Table I. Round Numbers of cos3#, 275. Table II. Cos3#. Round Numbers of #, 276. Table III. Powers of cos#. Round Numbers of tan#, 277. Table IV. Foot-candles, 278. Table V. Graduation of Ratio Scale, 279. Refraction Goniometer, 280.

PAGE

Bibliography . . . . . . . .283

Index

ILLUSTRATIONS

Portrait of Pierre Bouguer, by Perroneau. Engrav de France

1. The Vernon Harcourt Pentane io-candle Lamp

2. The Hefner Amyl- Acetate Lamp Law of Inverse Squares Slide-rule set for Calculating Illumination

1 1. 12.

21. 2 2.

23>

31- 32.

Frontispiece 5

Cosine Law ....

Cube of Cosines Curve of Cosines cubed

Illumination Curves, Lights at a distance apart equal to their height ,, ,, ,, twice their height

,, ,, ,, three times their height

,, ,, six times their height

Illumination Curve of Arc-lamp, Candle-power, and cos4# Curve Candle-power Curve of a Vertical Filament Illumination Curve of a Vertical Filament Curves of cos#, cos2#, cos3#, cos4#, and cos2# sin #

Curve of Variation of Illumination at a point, for Lamp at varying height Illumination Curves for Horizontal Plane, Lamp at varying heights Illumination Curves for Plane facing a Lamp at varying heights Locus of Lamp giving constant illumination at a point on a plane Locus used in connection with spacing and height of Lamps 24. Locus for Vertical Filament giving Constant Illumination . 43.

Construction of Contours by Intersecting Circles ,, ,, Trammels

Contours for two Lights at a distance apart equal to three times their height „ ,, ,, four times their height

Contours for three Lights, derived from Fig. 28 .

Contours for three Lights at a distance apart equal to one and a half times their height .......

Illumination Curve, section of Fig. 30

Contours for three Arc Lights, distance apart, one and a half times their height ........

xiii

20 2 7

34 34

44 46

49 49

XIV

55- 56.

62. 63-

70. 71- 72.

75- 76.

Illumination Curve, section of Fig. 32

Contours for three Arc Lights, distance apart, three times their height Illumination Curve, section of Fig. 34 Double Curve of cosines cubed ....

Archimedes’ Theorem of Surface of Cylinder and of Sphere

Curve of Flux, or Solid Contents Flux or Solid Content over given radius Graphical Construction to find Flux Characteristic Curve

55 55

Construction for Characteristic Curve Ordinates of Characteristic Curve

Characteristic Curves derived from Figs. 10, 1 1, and 12 Contours derived from Fig. 29 .

Illumination Curve along middle of Fig. 48

Illumination Curve for a line passing through the lamps in Fig. 48 Characteristic Curve for Fig. 48 .

Curves of Maxima and Minima, or Diversity Factor Curves for cases in Figs. 10, 11, 12, and 13 .

Houston and Kennelly’s Photometer Fleming’s Discrimination Photometer Bouguer’s Photometer .

Rumford’s Photometer .

Foucault’s Photometer .

Photoped of Vernon Harcourt or Gas Referees’ Photomet Bunsen’s Photometer, front view Bunsen’s Photometer, plan Ritchie’s Photometer

55 55

Mirrors of Ritchie’s Photometer

55 55 55

Angles of the Ritchie Wedge

Relation of Brightness to Angle for different Screens Angle Errors .....

Conroy’s Photometer, plan and elevations ,, perspective view .

Thompson and Starling’s Photometer Lummer-Brodhun Photometer .

,, „ Contrast Field

Perforated Screen Photometer

„ „ plan

51 51

55 55

63 63

72 76

93 93 96 98 98 98

101 104 104

ILLUSTRATIONS xv

FIG. PAGE

78. Slot Photometer — arrangement of Lamps . . . .107

81. Grid Photometer . . . . . . .109

82. Joly’s Photometer . . . . . . .110

83. Photometer Scales . . . . . . .113

84. Slide Rule set for calculating Photometer Scale . . .114

85. The Ratio Scale . . . . . , 1 1 5

86. Double Scale of Squares . . . . . .116

87. Photometer Head and Working Lamp coupled together . .117

88. Illumination Gradient . . . . . . . . 120

89. Light from a finite straight Filament . . . . .121

90. Deviation from the Law of Inverse Squares . . . .123

91. The Moving Mirror Method . . . . . .124

92. Everett-Edgcumbe Bar and Carriage . . . . .126

93. The Abney Sectors . . . . . . .130

94. Lamp mounted on Carriage . . . . . .131

95. Observation Recorder . . . . . . .132

98. Electrical Arrangements for use with Sub-standard Lamps . .139

99. Reflection from Bulb . . . . . . .142

100 A, B. Candle-power of Glow-lamp at various horizontal angles, and polar

1 01. Wild’s Mirrors for Mean Horizontal Candle-power . . .144

102. Auxiliary Mirrors . . . . . . .145

104. Candle-power of Glow-lamp at various angles with the horizon . .146

106. Mirror and Lens for projecting image of arc . . . .147

107. Images of Carbons of Arc-lamp viewed at different angles . .148

108. Candle-power and Visible Area of Crater at different angles . .148

109. Relation of Area of Crater to Candle-power . . . .149

1 10. Rousseau’s Diagram . . . . . . .150

hi. Candle-power of “ Oriflamme ” Arc . . . . .151

1 1 2. Russell’s Construction of Rousseau’s Diagram . . . .152

1 1 3. Rousseau Diagram for Crompton-Blondel Arc . . . 153

1 1 4. Blondel’s Annular Ellipsoidal Lumenmeter . . . .154

1 1 5. Blondel’s Diffusing Cone Lumenmeter . . . . .154

1 16. Dyke’s Arrangement of Mirrors for Mean Spherical Candle-power . 156

1 18. Theory of Ulbricht’s Globe . . . . . .158

120. The Ulbricht Globe . . . , , . ,160

XVI

FIG.

I3I-

138. 139-

1 4 1.

1 48. 149-

1 6 1 .

Crova’s Diagram of Luminosities Abney and Festing’s Diagram of Luminosities .

Relation of Luminosity of various Rays with Intensity .

Whitman’s First Flicker Photometer Whitman’s Diagram of his Flicker Photometer Whitman’s Disc for Flicker Photometer Views of Simmance-Abady Disc for Flicker Photometer Relation of Illumination to frequency at which Flicker disappears Kennedy and Whiting Relation of Illumination to frequency at which Flicker disappears Morris and Trotter Relation of Illumination to frequency at which Flicker disappears. Dow Ambiguous and Clear View of Scale Relation of Illumination to Precision Broca’s Disc ....

Preece’s Illumination Photometer Preece and Trotter Illumination Photometer Early Pattern Trotter Illumination Photometer Second Pattern ,, ,, ,,

Levers of ,, ,, ,,

Scale of ,, ,, ,,

Later Pattern of ,, ,, ,,

Everett-Edgcumbe’s Pattern of Trotter Illumination Photomete Scale of „ ,, „ „

Movable Screen ,, ,, ,,

External View „ ,, ,, ,,

Worst Position for Error due to reflected light .

Best Position for „ ,,

Polar Diagram of Errors due to glaze

Cartesian Diagram

View of Illumination Photometer showing Graduated Q

Dimensions used in Street Work

Height of Illumination Photometer, calculated .

,, ,, practical example

Illumination on Vertical Planes The Harrison Photometer, outside view

,, ,, end view of interior

,, ,, side view

The Weber Photometer

,, ,, section

Sharp and Millar’s Photometer uadrant

PAGE

172 172 175

176 176

239 239

ILLUSTRATIONS

XVII

FIG.

191. 192. 193-

Angle Errors of Sharp and Millar’s Photometer

55 55

Wingen-Kriiss Photometer

Martens Photometer

Dow and Mackinney’s Lumeter

Everett-Edgcumbe’s Luxometer

Daylight Attachment for Photometer .

Illumination Curve, Wimbledon, 1884 .

„ „ in Cannon Street Station

77. ,, ,, in City of London .

Contours in Queen Victoria Street Illumination Curve in Queen Victoria Street

55 55 55 55

,, ,, of Arc-lamps. Preece

Contours in Whitehall 87. Illumination Curves, Whitehall

Westmin

Characteristic Curves Diagram, Double cos3 curve Diagram, Equal Annuli Reflector for Uniform Distribution Profile of Distributing Prisms .

Profiles of Dioptric Pane Enlarged Profiles of Distributing Prisms Dioptric Lantern Diffusing Fluting Dioptric Shades

Plan of Street for Dioptric Distribution Profile of Compound Diffusing Fluting Early Illumination Curve, Reflectors

55 55 55

Illumination Curve, Dioptric Distributing Shade One of Fredureau’s Prismatic Shades .

Holophane Diffusing Fluting .

Holophane Compound Prism .

Korting and Mathieson’s Dioptric Shade Polar Curve, showing effect of Korting and Mathieson’s Dioptric Shade ster

PAGE

241 241 242 243

246 248 250 253

54-255 256 256 257

258 58-260

Refraction Goniometer Family of Curves, Angles of Prisms Diagram of Path of Ray through Prism Refraction Diagram

Chapter I Units And Standards Of Candle-power

Introductory. — Light being an expenditure of energy, it is accurate to speak of “candle-power,” since it is the measure of the rate of expenditure of energy. The art of illumination is therefore, in a very definite sense, a matter which comes within the province of civil engineers, since it is the art of directing this power for the use and convenience of man. The study of light, its nature and laws, belongs to the science of optics, but we may look to optical treatises in vain for any useful information on the present subject. Illumination, if alluded to at all, is passed over in a few lines, and it has remained for engineers to study and to work out the subject for themselves. Fortunately the geometrical laws of the distribution of illumination are very simple, and those of photometry are as easy. The physiological side of the question presents some puzzles, and these should receive attention from psychologists who are conversant with the practical difficulties of subjective investigations. Notwithstanding the attention which has been given to the matter during the last few years, the specification of a required illumination of a street or of a railway station would perplex most contractors. The time is only now arriving in which a required illumination may be intelligently expressed by a specification.

The vocabularies of the French and English languages are remarkably rich in words connected with light. Such terms as illumination, brilliance, brightness, intensity, and luminosity are generally employed by different writers to express different

B i

CHAP.

ideas, and are often used in a confused and vague way. The terms force, power, work, energy, and efficiency have been used by the general public, and will continue to be used, in a very loose and inexact manner. It has been the business of engineers to attach precise meanings to them for their own purposes, to recognise these as the only proper meanings, and to regard a misuse of one of them as a mark of ignorance of the elements of engineering science.

Light for the present purposes means visible radiation emitted from a flame or incandescent surface, or reflected from a surface. The word “ light ” is often loosely used instead

of intensity of light or quantity of light. In one sense light

is no more a physical quantity than dimness or darkness, it

is a general term ; in another sense it is luminous radiant

energy. The particular terms which denote the chief physical quantities are intensity, commonly called candle-power ; flux, or spherical candle-power ; illumination ; brightness, or intrinsic brilliancy ; and quantity of light.

One of the difficulties of this subject is that the use of light and illumination is to satisfy the eye, and the eye is a very poor judge of the physical quantities in question. It is well known that even experts cannot make a tolerable estimate of the candle-power of a lamp by merely looking at it when alight. An estimate of the “heft” of a letter, whether it is over or under 4 ounces, the temperature of the air, a length in inches or feet, or the contents of a vessel in pints or gallons can be made by most persons with greater accuracy than a guess at the candle-power of a lamp. Comparative estimates are not much better. It is easy to see that a 12-candle-power lamp gives less light than a 1 6-candle-power lamp, but it is very difficult to say how much less.

Intensity or Candle-Power. — Candle-power is measured as an intensity in any direction. It is also measured as a flux by the product of a solid angle into the candle-power. At an unofficial congress at Geneva in 1896 the name “pyr” was suggested for a unit of intensity, and Dr. J. A. Fleming* has

* Journ. Inst. Elec. Engs, xxxii. 164.

i UNITS AND STANDARDS OF CANDLE-POWER 3

proposed the name “lamp” for a 10-candle standard, on the ground that the candle itself having been abandoned, the name need not be retained. It is unfortunate that the word candle-power has taken such a firm position in technical language, and it is curious that we seldom use the word intensity, and its use by the French in connection with electric current appears to us redundant. If the word candle-power were not so well established, there would be a better chance of agreeing on an international standard of intensity. If a “ daniel ” had been in extensive use as a unit of electromotive force there would have been more difficulty in introducing the volt.

Units and Standards . — -A distinction must be made between an abstract unit of light and an actual standard. It would be convenient, but it is not necessary, that they should be of the same magnitude. The unit of electromotive force is one volt, but the Clark cell, reputed to have an electromotive force of 1.434 volt, was used for many years; and now the Normal Weston cell, having an electromotive force of 1.0184, is the standard. Similarly, the Hefner amyl-acetate lamp, having a candle-power of 0.9, is a very convenient standard, while the one recognised in England is the 10-candle Pentane lamp. It is quite possible that a more satisfactory apparatus of quite another kind may be discovered. If the electric arc standard had been found practicable it would have been about 150 candle-power. Our English expression candle-power confuses the matter by begging the question.

A brief account will be given of the more important standards which have been proposed and used from time to time. Further information may be obtained from the writings of those who have given special attention to the subject.*

The Cancel. — The earliest standard of light was the Carcel lamp, introduced in 1800, and used by Regnault and Dumas for testing gas, and is still employed officially for that purpose in France. It is a colza oil lamp containing a clock-work

* Palaz, Trait 6 de photomCtrie industrielle ; J. W. Dibdin, Practical Photometry ; W. M. Stine, Photometrical Measurements ; Dr. J. A. Fleming, Journ. Inst. Elec. Engs. vol. xxxii. ; C. C. Paterson, Journ. Inst. Elec. Engs. vol. xxxviii.

CHAP.

pump, and has an Argand burner and glass chimney of certain specified dimensions.*

The value in British candle-power was determined by Sugg in 1870 as 9.6; in 1885 Dibdin made it 9.4; while C. C. Paterson, at the National Physical Laboratory, gave 9.82 ; and at a photometric meeting held at Zurich in July 1907, this last value was confirmed. The discrepancies may be accounted for by the many sources of error in the use of this standard, the charring of the wick, the irregular consumption of oil, and the use of a glass chimney. Even in the hands of a single observer successive measurements vary widely.

The British Candle. — The so-called English Parliamentary candle of spermaceti was not more scientific, and hardly more accurate, than the barley-corn, of which three went to the inch. That candle, six going to the pound (but neither length nor diameter being specified), and intended to burn 120 grains of sperm per hour, was set up under the Metropolis Gas Act of i860 as an official standard, only for the purpose of testing London gas.

The German Candle. — In 1868 a carefully specified candle of paraffin was officially adopted by the German Association of Gas and Water Engineers, and was called the Vereinskerze. It was practically the same as the British candle.

The Har court or Pentane Lamp . — In 1877 Mr. A. Vernon Harcourt described a lamp burning air saturated with the vapour of pentane, a volatile hydrocarbon distilled from petroleum. This has undergone several modifications, and the present pattern, intended to represent ten times the candle-power of the Parliamentary candle, is the official standard of the Metropolitan Gas Referees, and the unofficial 10-candle British standard. A flat tank holds the liquid pentane, over the surface of which air passes, and becoming saturated with the heavy pentane vapour falls through a syphon pipe to a steatite ring or Argand burner. The flow is regulated by a tap on the outlet, or a valve on the air inlet of the pentane saturator. No wick

* See Trait £ de photomdtrie industrielle , A. Palaz, p. ioi.

UNITS AND STANDARDS OF CANDLE-POWER 5 is needed. A tall chimney draws the flame up with a considerable draught and ensures a steady light. A second outer chimney, concentric with the first, warms the air which is supplied to the flame. No glass chimney is required, but the top of the flame may be inspected for adjustment through a mica window. The top of the flame is cut off in the direction of the photometer by a screen, giving a clear opening of 47 millimetres, but notwithstanding this, the height of the flame must be carefully adjusted.

The total height of the apparatus is about 2 feet 10 inches.

The Hefner. — The amyl-acetate lamp, produced in 1884 by Hefner von Alteneck, was subjected to careful tests by Liebenthal, and after certain modifications was declared to be the official standard in Germany.

The pattern certificated by the Reichsanstalt has been adopted by the American Institute of Electrical Engineers, and, provisionally, by the Bureau of Standards of the United States, and was recommended as an international standard at the Chicago Congress of 1893, but was not adopted, for reasons which probably do not exist now. It has been widely recognised for scientific as well as for industrial work.

The container, 70 mm. (2§ in.) diameter, made of brass, holds about 4 ounces ( 1 1 5 c.c.) of amyl-acetate. The ordinary commercial quality used as a solvent for celluloid is unsuitable, and even the commercially “pure ” quality is apt to corrode the container. Unless this is well tinned or nickel-plated inside, a cock should be fitted for draining off the liquid after use. A thin German-silver tube, constructed to the exact dimensions

Fig. i. — The Vernon Harcourt Pentane io-Candle Lamp.

CHAP.

specified by the Reichsanstalt, holds the wick. Two toothed wheels, worked by worm gear, feed the wick, and give a fine adjustment for the height of the flame. A miniature camera with lens and ground glass is carried on a support at the side. A horizontal line is drawn on the ground glass, and the flame of the lamp is adjusted so that its inverted image just touches the line. The ordinary wick for spirit lamps may be used, but should be well dried ; it should be carefully trimmed level with

the top of the tube. The middle of the flame is ioo mm. (3.94 in.) above the bottom of the lamp.

The temperature of the flame, which is of an orange colour, closely resembling that of a sperm candle, is remarkably low, and owing to the feeble draught, the flame is sluggish and sensitive to very small currents of air. It is not difficult to screen it, and the screens, which should always be used in photometric work for keeping the eyes in a sensitive condition, may be arranged to protect the flame without causing an artificial upward draught.

Though the flickering of the flame sometimes makes it difficult to check its height on the gauge, it has not so much effect on the candle-power as might be supposed.

Liebenthal’s statement of the relation between the height of the flame and the luminous intensity is an equation which means that when the height of the flame is less than 40 mm., each millimetre change of height causes 3 per cent change in light ; and when the flame is more than 40 mm. each increase of a millimetre produces 2J per cent change. No doubt these two linear relations are good tangent approximations, but it is not

Fig. 2. — The Hefner Amyl- Acetate Lamp.

i UNITS AND STANDARDS OF CANDLE-POWER 7

possible to imagine a change per saltum at 40, which is the most important point. Mr. J. W. Dibdin found that the height of an amyl-acetate flame had to be increased to 51 millimetres to give one candle-power. This, according to Liebenthal’s formula, would mean that one candle-power is equal to 1.275 Hefner unit. It is difficult to account for this discrepancy.

Assuming that a change of 1 mm. in the height of the Hefner flame changes the light by 2§ per cent, a height of 44 mm. will correspond with the British, American, and French candle-power. This difference is too great to be marked on the ground glass of the gauge, but an adapter can easily be made to raise the whole gauge 4 mm. I have sent a lamp so altered to the National Physical Laboratory, and after applying the Liebenthal correction for moisture (from 12 litres per cubic metre at which the test was carried out, to 8 litres) and a small correction for barometer, the value in British candle-power was found by Mr. C. C. Paterson to be 0.995. The lamp burns perfectly well at this height.

The Violle. — More than one attempt has been made in France to set up the standard invented by Violle, and proposed for international adoption at the Electrical Congress at Paris in 1881. The standard is the lmht emitted in the normal direction

o

by one square centimetre of the surface of molten platinum at the temperature of solidification. The cost of the apparatus is as formidable as the difficulty of using it. In the earlier patterns about one kilogramme of platinum was melted in a crucible of lime by an oxy-hydrogen blowpipe. When a quantity of water begins to freeze the temperature remains practically constant until it is all converted into ice. The same thing happens when a metal solidifies, and this condition must be seized upon for the photometric measurement. A considerable mass of metal is needed to delay the process for a period long enough to allow photometric observations to be made. The crucible was run out from below the blowpipe, and brought beneath a hollow water-cooled screen of copper in which a circular hole one square centimetre in area allowed the light to ascend to a mirror. Dust, scum on the molten surface, the ascending