Elementary lessons in physics

Introduction

This volume, which is the First Part of Hall and Bergen's revised Text-booh of Physics (1897), may be regarded as the second edition of Hair's Elementary Lessons in Physics. It is intended for the use of pupils in the early years of a high-school course or even the last year of a grammar-school course, and it assumes no previous systematic study of physics.

The course of study here given includes laboratory work, to be done by the pupils, combined with a considerable amount of general 'instruction, to be illustrated by lectures given by the teacher. The laboratory work is mainly or wholly quantitative, as it must be for large classes, qualitative laboratory work in such classes making impossible demands upon the time and energy of the teacher.

A First Course made up, as this one is, of simple experiments in mechanics (including hydrostatics) and optics, more difficult matters in mechanics, together with heat, sound, electricity, and magnetism, being deferred, is unusual; but it is here proposed as better suited to many pupils and to many schools than the more familiar practice of going through the whole of mechanics before entering upon any other part of physics, and putting light, or optics, after heat. The laboratory outfit required for these early exercises is much less complicated and expensive than that required for much of the later laboratory work ; so that many schools which would be quite unable to offer a labo-

iii iv INTRODUCTION.

ratory course extending over the whole field of elementaryphysics will find it possible to do what this book requires. Moreover, those teachers w r ho have ample means and facilities, and who intend to take their pupils through the whole range of elementary laboratory work, will find it advantageous to interrupt the course in mechanics lest their classes grow tired of what is, for many young pupils, the least interesting part of the study.

The book follows, as a rule, the method of leading up to the statement of laws by means of carefully chosen experiments, rather than the opposite one of giving experiments as illustrations or proofs of laws already stated. It can hardly be said for the former method that it teaches the art of making discoveries, — that art is as difficult to teach as the art of getting rich, — but it has a tendency to keep the pupil in a more active, self-dependent state of mind than the latter method, and in particular it prevents iu a large measure that state of bias, or preconception, in the performance of experiments, which is so dangerous not merely to accuracy of observation but to mental rectitude. On the other hand, the teacher using the method of this book must not allow his pupils to think that their experiments, even when most satisfactory, really demonstrate the rigid accuracy of any numerical law, — the law of a balanced lever, for instance. He should ask of them, " What law do your experiments indicate as true ?" and after their answer he should tell them whether their inference is or is not in accordance with the opinion held by those best qualified to judge of the matter in question.

It is the firm conviction of the writer that class laboratory work not accompanied by persistent, energetic teaching is sure to be a failure. We are often told that the favorite method of the elder Agassiz with a new pupil was

INTROD UCTION. V

to set him to gaze in solitude at a single fish for two or three days. Those who would make this the model for science-teaching in general forget that pure observation of numerous, minute, varied details plays a much more important part in natural history than in physics. The teacher of physics who would produce good and lasting results must see to it not merely that the laboratory work shall be carefully done, but that the proper lessons shall be drawn from it and the proper applications made. In fact, the young pupil should give as much time to the study of physics in the lecture- or recitation-room as in the laboratory proper.

The course of study described in this book is intended to run through a school year and to occupy the pupil at least two school-periods, each forty minutes long, or more, per week; one usually in the laboratory, and the other in the lecture- or recitation-room. The number of laboratory Exercises is considerably less than the number of schoolweeks in the year, but some of them may prove to be too long for a single school-period, and teachers will welcome an occasional opportunity for repetition or review. The amount of time required for the course will depend somewhat upon the age of the pupils taking it, and classes in the first year of a high-school course may find three school-periods a week for one year none too much time for doing the work well.

It is highly desirable that pupils whose laboratory work is confined to that described in this book should have lecture-room illustrations of many things not here dealt with, elementary facts and principles in heat, sound, electricity, and magnetism. It is therefore recommended that every teacher of such pupils be provided with the means necessary for such illustrations, for example much of the appavi INTRODUCTION.

rat us designated by Roman numerals in Hall and Bergen's Physics.

The following estimates of cost for apparatus and materials are only approximate. It is hardly possible to make an accurate estimate, as prices will vary from time to time, and different dealers have somewhat different grades of apparatus. The cheapest is not necessarily the best to buy.

FOR THIS BOOK.

Teacher's apparatus and supplies, pp. 174-178 .... $78.00 Students' apparatus, pp. 170-173, for each member

of a laboratory squad 6.00

Table, accommodating six workers, p. 178 25.00

Total for all Exercises and Experiments of this

book, with laboratory squads limited to twelve.. . 200.00

FOR THE SECOND PART OF HALL AND BERGEN'S

PHYSICS.

Teacher's apparatus, pp. 581-586 350.00

By omittiug the thermopile and accompanying apparatus and the Roentgen-ray apparatus this expense can be reduced about $100.

Apparatus for the course can be obtained from the following well-known manufacturers:

The Chicago Laboratory Supply and Scale Company, 39 West Randolph Street, Chicago.

The Franklin Educational Company, Harcourt Street, Boston.

The Knott Company, 16 Ashburton Place, Boston.

The Ritchie Company, Brookline, Mass.

The Ziegler Electric Company, 141 Franklin Street, Boston.

E. II. H.

January 16, 1900

Table Of Contents

PAGE

Introduction iii

Chapter I. Introductory

Definition of Physics. — Use of Physics. — Qualitative and Quantitative Knowledge. — Object of this Course.— Preliminary Exercises: Measurement of Distance, of Area, of Volume, — with Estimation of Errors 1

MECHANICS.

Chapter II. Density And Specific Gravity

Density.— EXERCISE 1: Weight of Unit Volume of a Substance.— Density of Water.— Weight.— Mass.— EXERCISE 2: Lifting Effect of Water.— EXERCISE 3: Specific Gravity of a Solid that will Sink in Water.— EXERCISE 4: Specific Gravity of Wood by Use of Sinker.— EXERCISE 5: Weight of Water Displaced by a Floating Body. — EXERCISE 6: Specific Gravity by Floating Method.— EXERCISE 7: Specific Gravity of a Liquid by two Methods 15

Chapter III. Fluid-pressure

Fluids: Liquids and Gases— Experiments with Pressure-gauge in Water. — Torricelli's Experiment. — Atmospheric Pres-

vii viii TABLE OF CONTENTS.

PAGE

sure. —Barometer. — Boyle's Law.— Hydraulic Press. — Waterpumps. — Siphon. — Balancing Columns 28

Chapter IV

EXERCISE 8 : The Straight Lever, First Class, — Circular Lever.— EXERCISE 9: Centre of Gravity and Weight of Lever. — EXERCISE 10: Levers of the Second and Third Class: s.— EXER- CISE 11: Force Exerted at the Fulcrum. — Pulleys. — General Law for Relation of Power to Weight 41

CHAPTER Y.

THREE FORCES ACTING THROUGH ONE POINT — THE PARALLELO- GRAM OF FORCES.

Introductory. — EXERCISE 12: Errors of a Spring-balance. — EXERCISE 13: Parallelogram of Forces.— The Inclined Plane: Wedge, Screw. — Equilib i ant aDd Resultant 61

Chapter VI. Friction

EXERCISE 14: Friction between Solid Bodies.— EXERCISE 15: Coefficient of Friction.— Friction in Applied Mechanics.— Rolling Friction. — Friction between Solids and Fluids , 78

Chapter VII. The Pendulum

Use in Clocks.— Experiments.— Springs in Place of Pendulums 86

LIGHT.

CHAPTER VIII. Nature of Light— Visibility of Objects

Light is Something that Travels. — Velocity.— A Wave-motion.— Pencils and Rays.— Shadows.— EXERCISE 16: Use of

TABLE OF CONTEXTS. ix

PAGE

Rumford Photometer. — Bunsen's Photometer. — Effect of Body on which Light Falls. — Visibility of Objects 90

Chapter IX. Regular Reflection Of Light

EXERCISE 17: Images in a Plane Mirror. — Images of Images, Kaleidoscope. — EXERCISE 18: Images Formed by a Convex Cylindrical Mirror. — EXERCISE 19 : Images Formed by a Concave Cylindrical Mirror. — Relation of Cylindrical to Spherical Mirrors. — The Ophthalmoscope. — Formulas relating to Curved Mirrors 103

Chapter X. Refraction Of Light

Introductory Experiments. — Angles of Incidence and Refraction.— EXERCISE 20: Index of Refraction of Glass.— EX- ERCISE 21 : Index of Refraction of Water.— Index Different for Different Colors. — Index of Refraction and Velocity. — Internal Reflection, Critical Angle. — Transparent Plates and Prisms. — Dispersion, the Spectrum.— Lenses.— EXERCISE 22; Focal Length of Converging Lens.— EXERCISE 23 : Conjugate Foci of a Lens. — EXERCISE 24 : Shape and Size of Real Image Formed by a Lens. — EXERCISE 25 : Virtual Image Formed by a Lens. — Spherical and Chromatic Aberration in Lenses. — Achromatic Lenses. ..,,,,,,,, 123

CHAPTER XL

THE EYE : SIGHT AND COLOR.

Description of the Eye.— Accommodation, etc. — The Color-sense. — Mixing Color Impressions.;— Complementary Colors. — Fatigue of Retina. — After-images 152

Chapter XII. Optical Instruments

Photographer's Camera. — Magic Lantern. — Projecting a Spectrum. — Simple Microscope. — Compound Micro-cope. — Telescope 156

X TABLE OF CONTENTS.

APPENDIX I.

PAGE

Focal Length, etc., of Lenses and Combinations 168

APPENDIX II.

Indices of Refraction e . 169

APPENDIX III.

List of Apparatus, etc., for the Exercises and Experiments of the Preceding Pages 170

ELEMENTS OF PHYSICS.

Chapter I. Introductory

1. Definition of Physics. — Physics is the science of. mechanics, heat, sound, light, electricity, and magnetism,. Everybody knows something about these things before he begins to study them in a regular way, but sometimes he does not know them by the names which are given to them in books.

2. Use of Physics. — In sailing boats or flying kites, in walking or swimming, in almost any kind of bodily work or play, we have to do with physics, that part of physics which is called mechanics. We learn to do many mechanical acts very well indeed by observation and experience, without thinking very much about them or knowing exactly how we do them ; but when w T e have to do something that we have never done before and have never seen any one else do, something, perhaps, that nobody ever did before, we must think and study.

3. Illustrations. — Thus no man who has practiced swimming need study mechanics to improve himself in that art; but if he would build a ship and make it swim through all kinds of weather and water, he must study mechanics a good deal in order to know what size and shape to give the various parts, how best to put them together, and how to balance the whole. If it is to be a steamship, some one must know a good deal about heat, to make the furnaces and boilers right. We must know about magnetism to make and use the ship's compass. We may use electricity to furnish light on board at night. We must study sound in order to make the best fog-signals to guard against collisions and shipwreck in thick weather.

In short, the science of physics in all its main divisions is not only a very interesting study to many minds, but it is of great use to civilized mankind. Man has become civilized, indeed, not by merely imitating what his fathers have done, but by studying, that is, observing and thinking, and gradually improving upon the work of those who have gone before him.

4. Qualitative Knowledge. — Everybody knows that a piece of wood will float in water, and that a stone will sink. Everybody knows that if a stick and a stone are tied together and put into water, the stone tends to sink the stick, and the stick tends to float the stone. This kind of knowledge is called qualitative. It tells in a general way how the stick and the stone act toward each other.

5. Quantitative Knowledge. — Some people know enough about the laws of flotation to calculate with accuracy how large a stick of a known kind of wood will be needed to float a stone of known size and weight. They have what is called quantitative knowledge of the matter. They can tell how much the stone will pull down on the wood, and the wood pull up on the stone, when the two are together in water.

Everybody knows that a beam has a quality which we call strength — it can bear a load. This is qualitative knowledge. Everybody knows that a thick beam is stronger than a thin beam. This is quantitative knowledge of a kind, a rather indefinite kind. Some people know how much stronger the thick beam is than the thin beam. They have a more complete quantitative knowledge.

6. Comparison of the Two Kinds of Knowledge. — It is

evident that quantitative knowledge is more useful than mere qualitative knowledge. The former includes the latter. The qualitative man says, " I want to build a house. I shall need some land to put it on, and some beams and boards and bricks," etc. The quantitative man says, " Yes, you will need ail these things, but if you don't make your ideas more precise you will have a lumber-yard when you have done, not a house."

7. Object of this Course in Physics. — The knowledge of physics which children and older people get by merely knocking about in the world is mostly qualitative. The course of work laid out in this book is intended to add greatly to the pupil's stock of this kind of knowledge, and to do something more. It aims to make the pupil familiar with quantitative work, and to give him a considerable amount of quantitative knowledge.

We shall begin at once with simple introductory measurements. All the exercises of this chapter are called Preliminary Exercises.

Measurement of Distance.

8. The Straight Line. — The line to be measured may be along the edge of a table (or sheet of paper) from one fine scratch to another, a distance of about 15 inches. It is a great convenience to have all the pupils measure equal distances; accordingly, the teacher is advised to lay off these distances by some method like the following: A carpenter's square is placed a~ along the edge of the table as in Fig. 1, FlG - 1 -

and while it is held firmly in place a fine light scratch is made with the point of a sharp knife-blade at right angles with the edge of the table at the points a and b. The distance from a to i is the one to be measured by the pupil. The first-described method of using the measuring-stick in the following Exercise is not a good method, but it is one that many will use if they are not properly instructed. The second method is a good one, and the two are here brought together in order that the pupil may see at once the right way and the wrong way to use such an instrument. Much of the interest and profit of this Exercise will come from the opportunity given each pupil to compare his own work with that of others.

EXERCISE A.

MEASUREMENT OF A STRAIGHT LINE.

Apparatus : A short measuring-stick (No. 1) * and a meter-rod (No. 2).

To each pupil is given a measuring-stick about one-fourth as long as the distance from a to b. We will suppose that these sticks are made by sawing a meter-rod, graduated to millimeters, into ten equal parts. The saw-cut will usually leave the divisions at the very ends of the sticks imperfect, and these divisions should not be used in the measurements.

Let each pupil measure his distance at least twice carefully, with his measuring-stick laid flat upon the table, the marks upon the stick being thus horizontal, and let him write upon the blackboard the results of his two measurements.

Then let each pupil measure his distance twice again, this time placing his measuring-stick upon its edge, so that the marks upon it will be vertical, making a light, fine mark upon the table with a sharp pencil to set the stick by, whenever it is moved forward a length. These new measurements are also to be placed upon the blackboard under the first ones.

Finally let each pupil measure his whole distance at once with his meter-rod and write this last measurement with the others.

* Any piece of apparatus to be used in the Exercises will usually be referred to by the number it bears in the list of apparatus given at the end of the book.

INTBODUCTOBT. 5

9. Errors. — To judge of the accuracy of a set of measurements it is not enough to know how much these differ among themselves, for the importance of the difference usually depends upon the ratio which the difference bears to the whole quantity measured. A thousandth part of an inch might be a very serious difference to a watchmaker in the measurement of some small cylinder, while a difference of several inches in the measurement from one mile-post to another would be of little consequence. The pupil should therefore form the habit of comparing his errors, or the differences of his measurements, with the whole quantity that he had to measure.

Let us suppose, for instance, that in Exercise A the measurements made by one pupil are 37.30 cm., 37.00 cm., and 37.10 cm. The greatest difference is found between the first and second. It is 0.3 cm., and its ratio to 37.15 cm., which is midway between 37.30 cm. and 37.00 cm., is 0.0081 — . We see, then, that the difference between the two measurements of the line is about eight one-thousandths, not quite one per cent, of the length of the line.

Each pupil should make a similar calculation from his own measurements in Exercise A.

10. Units and Standards of Measurement. — The importance of having definite units of length, of weight, etc., so that any man in dealing with his neighbor may know just how much is meant by the words foot, pound, and the like, is so great that in all civilized countries the exact meaning of such words is fixed by law, and very great care is taken to make and preserve government standards, as they are called, standard yard-sticks, standard pound-weights, for instance, with which as patterns the measuring instruments used in business are compared and tested.

Interesting accounts of the foot, the yard, the meter, etc., can be found in almost any encyclopedia.

Meter-rods for school use are in many cases marked off in inches on one side. With the information given by such a rod, the class can find how many centimeters are equal to one inch. This number carried to two places of decimals is accurate enough for most purposes.

11. The Right Triangle. — Eight triangles, that is, triangles having one right angle (see Fig. 2), are much used in the study and application of physics. In such triangles

Fig. 2.

there is a simple and important relation between the length of the longest side and the length of the other two sides. Part 1 of the following Exercise B is intended to show this relation and at the same time to give practice in measurement.

12. Circles. — The relation between the length of the diameter of a circle and the length of its circumference is also very frequently used in physics. Part 2 of Exercise B has to do with this relation.

EXERCISE B.

THE LINES OF THE RIGHT TRIANGLE AND THE CIRCLE.

Apparatus : A 30-cm. measuring- stick (No. 3). A sheet of paper upon which is drawn carefully a right triangle no side of which is less than 10 cm. long. (No two pupils should use exactly similar triangles.) A cylinder of wood 4 or 5 cm. in diameter (No. 4). A narrow straight-edge strip of thin paper.