Edward Bright 
 
ELEMENTARY-. / 
 
 PRACTICAL PHYSICS 
 
 A GUIDE FOR THE PHYSICAL LABORATORY 
 
 BY 
 
 H. N. CHUTE, M.S. 
 
 Teacher of Physics in the Ann Arbor High School 
 
 BOSTON, U.S.A., 
 
 D. C. HEATH & CO., PUBLISHERS. 
 1890. 
 
C5 
 
 Copyright, 1889 
 BY H. N. CHUTE 
 
 JSockiuell antJ 
 
 BOSTON 
 
PREFACE. 
 
 THIS book has been written with the object of pro- 
 moting the teaching of Physics by what is known as 
 the Laboratory Method. It embodies the Experimental 
 Course which has been found suitable for students of the 
 Eleventh and Twelfth Grades at the Ann Arbor High 
 School, where the author has had several years' experi- 
 ence in conducting large laboratory classes. 
 
 It consists of a series of carefully selected exercises, 
 both qualitative and quantitative in character, in which 
 full directions are given regarding the preparation of the 
 apparatus, and the manner of conducting the experi- 
 ments, together with numerous suggestions about methods 
 of observing, note-taking, and making inferences from 
 data. The work is not designed to supplant the ordinary 
 text-book, as definitions and statements of principles have 
 been wholly omitted from its pages. It is recommended 
 that the study of some suitable elementary treatise on 
 Physics be carried on in the usual way, the teacher per- 
 forming in the presence of the class either the experi- 
 ments therein described or equivalent ones selected from 
 this guide. Such instruction should, in the opinion of 
 the author, precede the introduction of the student to the 
 
 ** 797967 . 
 
IV I'REFACE. 
 
 It is a mistaken supposition, unfortunately prevailing 
 largely among science teachers, that the Laboratory 
 Method requires a student to discover for himself the 
 important laws and truths of the physical world. The 
 race has been centuries in reaching its present knowledge 
 of Nature's laws, and it is evidently unreasonable to 
 expect the untrained mind of a boy or girl to discover 
 and formulate in one year, or even in several years, the 
 principles discussed in an elementary book on Physics. 
 The office of the school physical laboratory is not one of 
 original discovery; but, in the first place, to put the 
 student in the best possible position to see what he looks 
 at, in order that fact-knowledge may be added to word- 
 knowledge in the most impressive way by having the 
 head and hand work and learn together ; and, in the 
 second place, to train the faculties to exactness of obser- 
 vation, independence and carefulness in forming conclu- 
 sions, and good judgment in weighing evidence. 
 
 It is not necessary, neither is it advisable, that the 
 whole subject of Physics be studied in a didactic way 
 before a student enters on his experimental work. All 
 that is required is that the class instruction on any sub- 
 ject or topic shall precede the student's study of that 
 subject experimentally, for it will be found that only in 
 this way will the complete significance of the experiment 
 and its results be fully perceived, and intelligent work 
 secured to the exclusion of that which is lifeless and 
 mechanical. No fear need be entertained that the 
 
P BE FACE. V 
 
 student's interest will be lessened in the least by a 
 knowledge of what he is likely to see, obtained either 
 from seeing the experiment performed by the teacher or 
 from reading about it in the class manual. The author's 
 experience for a number of years has convinced him that 
 the opposite effect is almost invariably produced; that is, 
 a livelier and more intelligent interest is kindled thereby. 
 The student always finds that the close contact with the 
 experiment in the laboratory reveals to him enough that 
 he did not see when he witnessed it in the class-room, or 
 found no mention of in the manual he consulted, to com- 
 pensate him many times over for the time he now has 
 put upon it. 
 
 There is, however, a large class of experiments that 
 cannot be performed to any advantage outside of the 
 laboratory, particularly those of a quantitative character, 
 involving the verification of physical laws and the deter- 
 mination of physical constants. On these subjects but 
 little help is furnished by the ordinary text-books, and 
 students graduate every year from our High Schools and 
 Colleges absolutely ignorant of the difficulties in the way 
 of accurately determining the simplest physical constant, 
 or establishing the truth of the most familiar physical law. 
 To experiments of this kind special attention has been 
 given in these pages, for it is believed that it is only by 
 doing this so-called " dead-work " can a student ever come 
 to a correct and complete understanding of these laws. 
 The objection that such work is beyond the students who 
 
VI PREFACE. 
 
 ordinarily study physics in our High Schools is fully met 
 by the fact that the data appended to Exercises 275 and 
 276 of this book were taken from the note-books of two 
 young girls who had no other aid than that furnished in 
 the problems as given there. 
 
 Although in the directions accompanying the exercises 
 considerable attention is given to the construction of ap- 
 paratus, the author would not be understood as approving 
 of converting the physical laboratory into a mechanical 
 work-shop. The object in giving so many details was 
 threefold. First, to make it possible for schools, having 
 but little means for purchasing apparatus, to get together, 
 in time, through the aid of teacher, students, and local 
 mechanics, a supply of apparatus that has the one great 
 merit, " it seldom fails to do that which is required of 
 it." Secondly, to show that the verification and the illus- 
 tration of Nature's great laws require no elaborately fin- 
 ished and expensively constructed appliances; but that, 
 on the contrary, the more simple and inexpensive the 
 mechanism is, the more satisfactory is usually its per- 
 formance. Thirdly, to give the student as clear an idea 
 as possible of the instrument placed in his hands by 
 putting before him the specifications followed in its con- 
 struction. The author well remembers that no study of 
 books ever gave him as clear an idea of the induction 
 coil as he got from a working-drawing and specifications 
 of one published several years ago in a well-known scien- 
 tific periodical. 
 
PEEFACE. VII 
 
 Special attention is called to the appendices. In the 
 first, the author has attempted to outline a method of con- 
 ducting laboratory work : the equipment of a room, the 
 selection of apparatus, and the management of large 
 classes with limited facilities are some of the topics dis- 
 cussed at considerable length. In the second appendix 
 there is described a large number of operations, such as 
 teacher and student are often called on to perform, in re- 
 pairing, constructing, and adjusting apparatus. Many 
 very valuable recipes find a place there, all of which have 
 been thoroughly tried, and are known to be most excel- 
 lent. In the third appendix is given a very complete list 
 of such Constants as will be needed or found convenient 
 in the application of the truths of Physics to the solution 
 of practical problems. They will also serve as guides 
 to the student, often indicating to him what degree of 
 accuracy he has secured in his experimentation. 
 
 It is too much to expect that these pages will be found 
 free from errors ; still it is believed that a fair degree of 
 accuracy has been secured. Dr. T. C. Mendenhall, Presi- 
 dent of the Rose Polytechnic Institute, has carefully and 
 critically read the whole work in manuscript and in proof, 
 and has contributed many valuable suggestions. The fol- 
 lowing well-known science teachers have also carefully 
 read the work in proof, and aided very greatly in giving 
 it its present degree of accuracy and completeness of 
 treatment: W. Le Conte Stevens, Packer Collegiate In- 
 stitute, Brooklyn, N. Y. ; J. Montgomery, Kalamazoo Col- 
 
VIII PREFACE. 
 
 lege, Kalamazoo, Mich. ; E. P. Jackson, Latin School, 
 Boston, Mass. ; J. Y. Bergen, Latin School, Boston, 
 Mass. ; James H. Shepard, Agricultural College, Brook- 
 ings, Dak. ; George B. Merriman, Rutgers College, New 
 Brunswick, N. J. ; J. H. Pillsbury, Smith College, North- 
 ampton, Mass. ; George N. Cross, Exeter Academy, Exe- 
 ter, N. H. ; George I. Hopkins, High School, Manchester, 
 N. H.; A. C. Boyden, Normal School, Bridgewater, Mass.; 
 George L. Chandler, High School, Newton, Mass. ; Albert 
 C. Hale, Boys' High School, Brooklyn, N. Y. ; Arthur M. 
 Mo wry, High School, Salem, Mass. ; and many others. 
 
 Special acknowledgments are due to A. P. Gage, of 
 Boston, James W. Queen and Co., Philadelphia, and E. S. 
 Ritchie and Sons, of Brookline, Mass., for the use of 
 a number of illustrations. The author would also ac- 
 knowledge his indebtedness to that great company of 
 scientific workers who have furnished him, through their 
 writings, with the material, and sometimes with the 
 words, for the pages which- follow. Should this imperfect 
 effort prove itself helpful to that large body of earnest 
 men and women who are striving to solve the great 
 problem of " what is the best method of science teaching," 
 the author will feel fully repaid for the many laborious 
 hours of day and night, in laboratory and in study, he 
 has spent for a number of years in collecting, verifying, 
 selecting, and adjusting the matter contained in the 
 laboratory guide which he now offers to the teaching 
 profession. 
 
TO THE TEACHER. 
 
 I. 
 
 HOW TO USE THIS MANUAL. 
 
 1. The plan on which this book is prepared does not 
 restrict it to any particular theory of practical science 
 teaching. If you believe that a full course of didactic in- 
 struction should precede the admission of students into the 
 laboratory, and that the practical work should be entirely 
 quantitative, then omit the qualitative and select from the 
 quantitative such as is adapted to your wants. On this 
 plan, however, it will generally be found very difficult to 
 handle large classes, as it necessarily crowds all the prac- 
 tical work into a small part of the' school year, rendering it 
 nearly impossible to arrange a programme which provides 
 enough hours per week for each student to enable him to 
 accomplish much. It would be better to organize the 
 laboratory work a week or so after the class-room work 
 has begun, and carry on the two simultaneously. The 
 didactic instruction will by this plan be in advance of the 
 practical work sufficiently to enable the student to carry 
 on his work intelligently. About three hours per week 
 devoted to class recitations on some good text-book, accom- 
 
X TO THE TEACHER. 
 
 panied by illustrative experiments by the teacher ; two to 
 six hours per week spent in practical work in the labora- 
 tory ; and one hour per week spent by students in class, 
 discussing and comparing their reports on this work, is the 
 plan on which the author has taught physics for several 
 years with results that are quite satisfactory. 
 
 2. If, on the other hand, you believe that the experi- 
 mental work should precede that of the class-room, a view 
 held by many of our ablest teachers, you will find that the 
 Guide contains a very complete collection of experiments, 
 from which you can select those adapted to your facilities. 
 These experiments are accompanied by hints on observing, 
 recording observations, and correctly interpreting data 
 obtained, so that the labor of supervision will be greatly 
 reduced, and the burden of preparing the work reduced to 
 a minimum. 
 
 3. It will not interfere with the plan of the book to 
 omit any exercise not adapted to the laboratory facilities. 
 It is best to assign work to the student that he has the 
 genius requisite to do something with. See Art. 596. 
 The large variety of material from which to choose will 
 make it possible to make changes each year. Old note- 
 books will be of less value to new classes if this is done. 
 
 4. It may, occasionally, be found desirable to make 
 changes in a problem to adapt it to a piece of apparatus 
 of different design from that contemplated in the Guide. 
 These changes may be explained in the work-room or 
 class-room, as found most convenient. 
 
TO THE TEACHER. XI 
 
 5. Require students to use reference books freely in 
 studying their practical work. Also encourage them to 
 make changes in the mode of procedure. See Art. 599, 
 Rule 4. It will not unfrequently happen that a student 
 will hit on some little modification that will enable him to 
 secure much more accurate resiilts, mainly for the reason 
 that he devised it, and therefore could handle it all the 
 better on that account. 
 
 6. It will be seen that the book seldom states what the 
 results should be. Experience has convinced the author 
 that more independent and honest work can be secured on 
 this plan. Let the average student take the ordinary text- 
 book into the laboratory and work through one of its 
 experiments, and in the majority of cases he will believe 
 that he got exactly what the book account said he would, 
 nothing more and nothing less, notwithstanding the fact 
 that half of our book-makers, according to Prof. Tyndall, 
 describe experiments which they never made, their de- 
 scriptions often lacking both force and truth. 
 
 II. 
 
 HOW TO SECURE APPARATUS. 
 
 1. It is a mistake to suppose that practical work with 
 large classes necessitates a large and expensive collection 
 of apparatus. The cost of equipping a Physical Labora- 
 tory is less than is generally supposed. Nearly every school 
 
XII TO THE TEACHER. 
 
 already possesses the pieces that are expensive, as air- 
 pump, electrical machine, and their many accessories. 
 When the author decided to introduce the Laboratory 
 Method in the Ann Arbor High School, he asked the 
 School Board to do three things : furnish a room with 
 gas, water, and a few flat-top tables ; appropriate $100 to 
 purchase a few of the simpler devices for making accurate 
 measurements; and require each student to pay each term 
 a small fee, the proceeds to be devoted to enlarging the 
 equipment. The work began with over eighty students, 
 and now for several years not a dollar has been asked of 
 the School Board for purchasing apparatus ; still the 
 facilities are rapidly improving each year, and are probably 
 superior to those of most schools of the kind. 
 
 2. In Art. 595 are given many hints regarding appa- 
 ratus. 
 
 3. The majority of teachers have but little time to give 
 to the construction of apparatus ; still, in most cases, some- 
 thing can be done, especially in putting things together 
 that were prepared by some mechanic. There is such 
 work as winding the wire on galvanometer frames and 
 making the needles for the same, winding electro-magnets 
 and magnetizing steel magnets made by a local blacksmith, 
 etc. School Boards are not easily induced to appropriate 
 money to be expended outside of the district, but they 
 will generally be found willing to employ a carpenter for 
 a few days to work for the school. There are a great 
 many devices described in these pages that such a man 
 
TO THE TEACH EM. X11I 
 
 can make, and just as satisfactorily as if he lived in some 
 distant city. These instruments may require adjustment, 
 a statement true of 90 per cent, of all apparatus purchased 
 of the most noted makers. 
 
 4. Europe is the great storehouse of cheap apparatus, 
 and under the law, schools can import for their own use 
 duty free. In this way a saving of 30 to 50 per cent, can 
 often be effected. This is especially true in the matter of 
 lenses, Grenet batteries, balances, weights, etc. This im- 
 porting can be done through any of the firms referred to 
 in Art. 596. 
 
 III. 
 
 HOW TO MANAGE THE LABORATORY. 
 
 1. There are in use two methods of conducting labora- 
 tory work, known as the separate system and the collective 
 system. Under the former each section of two students 
 would work on different problems, the apparatus going 
 around in rotation. It is difficult, under this plan, to have 
 the student's work conform to a strictly logical order, but 
 it requires little or no duplication of apparatus. The 
 collective system is the ideal one. Under it all are engaged 
 on the same work at the same time. It has this advantage 
 over the separate system, a teacher can instruct all at once 
 on any point demanding more than ordinary care, and will 
 have more time to devote to the few who may be less apt 
 in their work. The author would recommend a combining 
 
XIV TO THE TEACHER. 
 
 of the two methods as better adapted to the circumstances 
 of most schools. This would involve a duplication of 
 those appliances which are less expensive, as thermometers, 
 lenses, mirrors, galvanometers, etc. 
 
 2. In Arts. 596, 597, and 599 will be found quite full 
 directions and suggestions on conducting practical work. 
 Those which relate to order are very important. The 
 student should understand that the work-room is not a 
 play-room, and that every moment of his time must be put 
 to good use. 
 
 3. By arranging the school programme so that stu- 
 dents taking physics have all their recitations in the 
 forenoon, it will be possible for them to devote at least two 
 of their afternoons to the laboratory each week. If pos- 
 sible two consecutive hours should be spent there, for it 
 will not unfrequently happen that one hour will be too 
 short to complete a line of investigation, and to stop when 
 not through is to lose all that has been done. 
 
 4. It is recommended that, generally, two students be 
 permitted to work together on the same problem, as more 
 than two hands are often required in performing an experi- 
 ment. This plan will increase the number of students 
 who can be kept at work. It is doubtful if one person 
 can look properly after more than twelve students, and 
 when large numbers necessitate admitting many more than 
 this number to the room an assistant should be employed. 
 
 5. If the students have definite places assigned them 
 in the room it will conduce to good order. Each student 
 
TO THE TEACHER. XV 
 
 should be held responsible for the apparatus put at his 
 disposal, and if broken or in any way injured through his 
 fault he should be required to make it good. 
 
 6. The work expected each week from the student 
 should be assigned him a few days in advance, and he 
 should be required to give it careful study before reporting 
 for duty, in order that he may not be hampered by igno- 
 rance of the successive steps in the experiment. The 
 author does not believe it is wise to restrict all experiments 
 to those of a quantitative character. He would require 
 the student to repeat for himself many of the experiments 
 of the class-room, with the object of bringing him into 
 actual contact with the things themselves, so that their 
 properties and relations may become familiar as solid, first- 
 hand mental acquisitions. Furthermore, there are many 
 important truths, the establishment of which involves no 
 exact measurements, that cannot be developed experiment- 
 ally in the class-room without expensive apparatus, whereas 
 a very simple device placed in the student's hands will 
 enable him to see the whole matter clearly. 
 
 IV. 
 
 HOW TO SHORTEN THE COURSE. 
 
 1. As is implied in more than one place, this book con- 
 tains much more work than a student can master in the 
 time usually devoted to the subject. There is no reason 
 
XVI TO THE TEACHER, 
 
 why a teacher should not omit any exercise or set of exer 
 cises he dhooses. It was thought advisable to have the book 
 fairly complete in its treatment of each subject, that it 
 might the better meet the wants of the greater number, 
 as it often happens that what is adapted to the needs of 
 one school is not to those of another. All subjects, how- 
 ever, are not equally important, and circumstances will 
 often compel the omission of certain questions. The author 
 would suggest that generally the following topics might 
 be omitted without seriously detracting from the value of 
 the course : Sees. III., IV., V., VI., VIII., X., and XI. of 
 Chap. I . ; VII. of Chap. III. ; IX. of Chap. IV. ; XV., XVI., 
 and XVII. of Chap. V. ; VII., XVI., XVII., and XVIII. of 
 Chap. VI. ; X., XI., and XIII. of Chap. VII. From the 
 other sections select such experiments as bring out most 
 satisfactorily with the apparatus at command the principles 
 th&y are designed to teach. Under many exercises are 
 found several methods of accomplishing the same thing. 
 It adds interest to the work to assign different methods 
 to different students and have them compare results. 
 
 2. If both time and appliances are limited, a still further 
 contraction is possible, and in that case the author recom- 
 mends that some such selection as suggested in Art. 596 
 be made. This principle should govern the work at all 
 times; a few experiments thoroughly studied will be much 
 more instructive than a great many superficially and hastily 
 gone over. 
 
CONTENTS. 
 
 CHAPTER I. 
 
 PAGE 
 
 THE PROPERTIES OF MATTER EXPERIMENTALLY DETERMINED . 1-68 
 I. Extension. Measurements of Length, Area, 
 
 and Volume ....... 1-22 
 
 II. Estimation of Mass 23-32 
 
 III. Impenetrability ....... 33-36 
 
 IV. Divisibility 36-38 
 
 V. Porosity 38-41 
 
 VI. Indestructibility 41-44 
 
 VII. Cohesion 44-50 
 
 VIII. Elasticity ........ 50-54 
 
 IX. Capillary Action 55-60 
 
 X. Solubility . 61-62 
 
 XI. Diffusion 63-68 
 
 CHAPTER II. 
 
 MECHANICS OF SOLIDS . 69-100 
 
 I. Laws of Motion ....... 69-77 
 
 II. Centre of Mass. Stability .... 77-80 
 
 III. Curvilinear Motion ...... 80-82 
 
 IV. Accelerated Motion. Gravitation. Projectiles, 83-92 
 V. The Pendulum 92-96 
 
 VI. Friction 96-97 
 
 VII. The Simple Machines 97-100 
 
 XVII 
 
XVIII CONTENTS. 
 
 CHAPTER III. 
 
 MECHANICS OF FLUIDS 101-126 
 
 I. Pressure in Fluids 101-108 
 
 II. Law of Boyle ....... 108-110 
 
 III. Law of Pascal 110-113 
 
 IV. The Siphon and Pump 113-116 
 
 V. The Principle of Archimedes . . . .116-119 
 
 VI. Determination of Density 120-126 
 
 CHAPTER IV. 
 
 HEAT 127-169 
 
 I. Heat, and Mechanical Motion .... 127-132 
 
 II. Heat and Chemical Action 132 
 
 III. Conduction of Heat 133-136 
 
 IV. Convection of Heat 136-139 
 
 V. Expansion by Heat HO-H5 
 
 VI. Thermometry 146-152 
 
 VII. Radiant Heat 153-159 
 
 VIII. Calorimetry 160-167 
 
 IX. Artificial Cold 167-169 
 
 CHAPTER V. 
 
 MAGNETISM AND ELECTRICITY 170-237 
 
 I. Magnets. Polarity. Induction . . . 170-173 
 
 II. Nature of Magnetism 173-174 
 
 III. The Magnetic Field 174-179 
 
 IV. Terrestrial Magnetism ...... 179-180 
 
 V. Frictional Electricity 180-184 
 
 VI. Statical Induction 184-186 
 
 VII. Electrical Distribution 187-190 
 
 VIII. Condensers . 190-193 
 
 IX. Electrical Machines . . . . . . 193-196 
 
 X. Voltaic Electricity. The Battery . . . 196-199 
 
 XL Effects of Electrical Currents .... 200-204 
 
 XII. Electrical Measurements . 204-221 
 
CONTENTS. 
 
 XIX 
 
 MAGNETISM AND ELECTRICITY. Continued. PAGE 
 
 XIII. Electro-Magnetism and Electro-Dynamics . . 221-227 
 
 XIV. Current Induction 227-232 
 
 XV. Luminous Effects ...... 233-236 
 
 XVI. Therrao-Electricity . . . . . . 236-237 
 
 CHAPTER VI. 
 
 SOUND 238-282 
 
 I. Wave Motion ....... 238-241 
 
 II. Sources of Sound ...... 241-244 
 
 III. Transmission of Sound ..... 244-245 
 
 IV. Velocity of Sound ...... 245-248 
 
 V. Propagation of Sound 249-250 
 
 VI. Reflection of Sound 250-252 
 
 VII. Refraction of Sound . . . . ... 252 
 
 VIII. Loudness of Sound 253-256 
 
 IX. Interference of Sound 256-258 
 
 X. Sympathetic Vibrations 258-260 
 
 XI. Pitch of Sound 261-262 
 
 XII. Laws of Vibrating Rods and Strings . . . 263-266 
 
 XIII. Overtones 266-267 
 
 XIV. Laws of Sounding Air-Columns .... 268-270 
 XV. Harmony and Discord ...... 270-271 
 
 XVI. Vibrating Plates and Bells 271-273 
 
 XVII. Attraction of Vibrating Bodies .... 273 
 
 XVIII. Graphic and Optical Study of Sound . . . 273-281 
 
 XIX. Vocal Organs 282 
 
 CHAPTER VII. 
 
 LIGHT . 283-333 
 
 I. Sources of Light 283-286 
 
 II. Rectilinear Propagation of Light . . . 287-289 
 
 III. Photometry . . 289-291 
 
 IV. Reflection of Light 291-297 
 
 V. Mirrors 297-305 
 
 VI. Single Refraction of Light . . . . 305-309 
 
 VII. Lenses . . 309-314 
 
XX 
 
 CONTENTS. 
 
 LIGHT. Continued. 
 
 VIII. Dispersion 
 
 IX. Color 
 
 X. Spectrum Analysis ..... 
 
 XI. Interference of Light ..... 
 
 XII. Optical Instruments ..... 
 
 XIII. Double Refraction and Polarization of Light 
 
 APPENDICES. 
 
 A. The Physical Laboratory 
 
 B. Laboratory Operations 
 
 C. Tables for Reference 
 
 PAGE 
 
 314-317 
 317-320 
 320-323 
 324-325 
 325-328 
 329-333 
 
 337-353 
 354-360 
 361-376 
 . 361 
 . 361 
 . 364 
 . 364 
 
 I. Capillarity 
 
 II. Densities of Various Substances .... 
 
 III. Limit of Elasticity 
 
 IV. Electrical Conductivity 
 
 V. Approximate Electro-motive Force of Primary Bat- 
 teries ......... 365 
 
 VI. Electrical Resistance, Diameter, etc., of Pure Copper 
 
 Wire 365 
 
 VII. Acceleration due to Gravity 367 
 
 VIII. Heat, Absorbing, Conducting, Radiating, Reflecting 
 
 Power 367 
 
 IX. Boiling-points of Substances at Bar. Pres. 76 cm. . 368 
 
 X. Coefficients of Expansion 368 
 
 XI. Latent Heat of Liquefaction and Vaporization . 369 
 
 XI [. Melting Points 369 
 
 XIII. Specific Heat 370 
 
 XIV. Indices of Refraction 370 
 
 XV. Mensuration Rules 371 
 
 XVI. Length of Seconds' Pendulum 371 
 
 XVII. Velocity of Sound at C 372 
 
 XVIII. Elasticity of Traction .372 
 
 XIX. Tenacity 373 
 
 XX. Trigonometrical Functions ...... 373 
 
 XXI. Some Useful Numbers . . . . . . . 375 
 
 XXII. Weights and Measures . .... 375 
 
PEACTICAL PHYSICS. 
 
 CHAPTER I. 
 
 THE PROPERTIES OF MATTER EXPERIMENTALLY 
 DETERMINED, 
 
 I. EXTENSION. MEASUREMENTS OF LENGTH, AREA, 
 AND VOLUME. 
 
 1. Apparatus. The fundamental principle involved in 
 all measurements is that of direct comparison with some 
 assumed standard, the accuracy of the results depending upon 
 that of the standard, and the methods adopted to insure close 
 comparisons. Among the many instruments employed in this 
 kind of investigation may be mentioned the Dividers, Diagonal 
 Scale, Metre-Rod, Verniered Steel Caliper, Micrometer Caliper, 
 Spherometer, Outside and Inside Caliper, Graduated Measure, 
 Beam Compass, Proportional Dividers, Protractor, etc. These 
 are described in the following articles of this section, their 
 methods of use explained, and in many cases simple and 
 efficient substitutes suggested. 
 
 2. Exercise. Measure the distance between two points 
 situated on any plane surface, as a sheet of brass or card- 
 board. 
 
 I 
 
*< PRACTICAL PHYSICS. 
 
 This can be done with sufficient accuracy by means of a pair 
 of Dividers (Fig. 1) and a Diagonal Scale (Fig. 3). Spring 
 Dividers (Fig. 2) are preferable. Any accurately and finely 
 divided scale can be used ; but of cheap scales, the diagonal 
 scale, boxwood or ivory, is the most suitable for this problem. 
 
 Open the dividers, and place one of its points exactly on one 
 of the given points on the plane surface, and the other point 
 on the second given point. Now place one point of the dividers 
 at one of the divisions 1, 2, 3, etc., of the scale, as 2, 
 being careful to select one that will cause the other point 
 to fall at 0, or between and the vertical line bounding 
 the scale. If the right-hand point falls at 0, 
 then the required distance is 2 units. If the 
 right-hand point falls to the right of 0, as at 
 the diagonal line 3, then the distance is 2.3 
 units. If the right-hand point falls between 
 two of these diagonal lines, as 3 and 4, then 
 move the dividers toward the opposite edge of 
 the scale, keeping the line of the points parallel 
 to the lines running lengthwise of the scale, 
 FIG. i. and at the same time the left-hand point in FIG. 2. 
 the line 2, until the right-hand point meets the intersection of 
 a diagonal line with a horizontal one. Should such a point 
 be where the diagonal line 3 intersects the horizontal one 7, 
 then the distance is 2.37 units. This multiplied by the value 
 of the scale unit, expressed either in inches or centimetres, will 
 give the absolute length. 
 
 In conveying the measurements to the scale, there is danger 
 that the dividers may get closed up a little from pressure of 
 the fingers in holding the instrument. This must be carefully 
 guarded against. Again, the points of the dividers must be 
 placed with accuracy on the given points, and no pressure 
 
TEE PROPERTIES OF MATTER. 
 
 3 
 
 applied that would be likely to indent the surface in the least. 
 Several independent measurements must always be made ; 
 then, by adopting their arithmetical mean, a result differing 
 less from the exact one is more likely to be obtained. These 
 
 30 
 
 40 
 
 50 
 
 0246 
 
 different measurements should all be neatly and accurately 
 recorded at the time they are made, in a suitable note-book 
 provided for the purpose, observing some such plan as the 
 following : 
 
 LINEAR MEASUREMENTS. 
 
 Problem. Determination of distance between two points on card- 
 board. Sept. 5, 1888. 
 
 Method. Dividers and scale. 
 Results. 
 
 First measurement 
 
 Second " . 
 
 Third " 
 
 Mean 
 
 Mean in cm 
 
 Value of scale unit . . 
 
4 PRACTICAL PHYSICS. 
 
 3. Exercise. Draw on paper three straight lines whose 
 lengths are respectively 2.34 inches, 3.57 inches, and 1.89 
 inches. 
 
 4. Exercise. Cut a circle, as accurately as possible, from 
 cardboard. Measure its circumference by rolling it along a 
 straight line drawn on paper. Measure its diameter, and com- 
 pute the ratio of the circumference to the diameter. 
 
 A pair of dividers and a diagonal scale will be found con- 
 venient for the purpose. 
 
 Make several independent measurements and record the 
 results. 
 
 The record may be made as follows : 
 
 Problem. Determination of the ratio of the circumference of a 
 circle to its diameter. Sept. 5, 1888. 
 
 Method. Dividers and diagonal scale. 
 
 Results. 
 
 Circumference. Diameter. 
 
 First measurement ... 
 Second " ... 
 
 Third " 
 
 Mean 
 
 Ratio, Error, Per cent of error, 
 
 The error is the difference between the ratio obtained and the true value, 3.1416. 
 
 5. Exercise. Measure the length and the breadth of one 
 of the tables in the room, employing both the P^nglish and the 
 French measure. Reduce each to the other, then compare and 
 point out in how many ways the differences in the final results 
 may be accounted for. 
 
THE PROPERTIES OF MATTER. 
 
 The metre-rod, such as is furnished by the American Metric 
 Bureau, is a suitable instrument for solving this problem. The 
 results may be recorded as follows : 
 
 Problem. Determination of the length and breadth of laboratory 
 table No. . Sept. 5, 1888. 
 Method. The metre-rod. 
 Results. 
 
 Length. Breadth. 
 
 First measurement . . cm. in. cm. ..in. 
 
 Second " . . 
 
 Third 
 
 Mean 
 
 Reduced . 
 Difference . 
 
 6. Exercise. Measure the length of a short rod or bar 
 of wood or metal. 
 
 miiiiiiliiiiliiiiliiiiliiiiliiiiliiiiliiiiliiiiliMiliiii'iiiiiii 
 
 j Dartir-g, Ero-vp& StiArpe.Pl-OTida'.CE. R.I 
 
 liliiiiliiiiliiiiliiiiliiiili 
 
 
 |llll!llllll!lll|!|ll|l![ll ! 
 
 1 
 
 JF 
 
 gEgt 
 
 c 
 
 FIG 
 
 
 
 ... ^ 
 
 If great accuracy is required, it will be necessary to employ 
 some such instrument as the Verniered Steel Caliper, an 
 appliance so constructed that measurements as small as fiftieths 
 of a millimetre can be made by its aid. Figs. 4, 5, and 6 
 exhibit some of the forms given it ; the latter being without 
 the Vernier, a device for estimating fractional parts of the 
 
6 
 
 PRACTICAL PHYSICS. 
 
 smallest division on the scale. Where the verniered form 
 cannot be had, for financial reasons, this simpler form may be 
 used instead, generally with sufficient accuracy, if the fractional 
 parts of the divisions are carefully estimated by the eye. 
 
 
 
 
 
 
 
 
 
 
 i"" 
 
 
 lll[l!ll|lllllllll|llll|lll!|!li:j 
 'L... 
 
 Wl I 1 1 i ! I 
 
 
 '^ ' a | ' ' ' ' 1 'so 1 
 
 T'i .1.1,1. ill. hi 
 
 
 
 
 
 'I'M 
 
 u aa * L, 
 
 _i[j 
 
 I 
 
 h_ 
 
 
 _r 
 
 
 FIG. 5 
 
 ""^ 
 
 
 To measure the rod, unclamp the screws A and B (Fig. 4), 
 and slide the jaw C away from D, so that the rod can be 
 placed between C and D, with its axis parallel to the bar of 
 the caliper. Then clamp A, and move the jaw C by the slow- 
 
 FIG. 6. 
 
 motion screw E till the rod is just firmly held between the jaws 
 C and D, as it is an easy matter by springing the frame of the 
 instrument, or compressing the rod, to change the reading one 
 or more of the smallest units given by it. It now remains to 
 read on the scale the length of the rod. On C will be seen a 
 
THE PROPERTIES OF MATTER. 1 
 
 short scale, called a Vernier, 20 of whose divisions equal 19 on 
 the bar or limb, the bar divisions being fiftieths of an inch. 
 Hence, each division of the vernier is y^^ of an inch shorter 
 than each bar division. Therefore, write down the number of 
 inches and fiftieths of an inch up to the zero of the vernier 
 scale ; then if the zero of the vernier does not register exactly 
 with a division on the bar, observe which one of the vernier 
 divisions coincides with a division on the bar, and this gives the 
 inimber of thousandths to be added to the quantities already 
 obtained. Express all fractional parts decimally. Make 
 several independent measurements, and obtain their mean. 
 Record the results after the manner described in previous 
 exercises. 
 
 The index on the opposite side of this instrument is ar- 
 ranged for both inside and outside measurements. The outer 
 edges of the jaws are rounded for insertion in tubes, or hollow 
 cylinders ; then, by reading from the index marked inside, the 
 distance between the outer surfaces of the jaws is given, that 
 is, the diameter of the tube. 
 
 This caliper can also be used for measuring the diameter 
 of a cylinder, the diameter of a small ball, or the thickness of 
 plates. 
 
 7. Exercise. Determine the dimensions of a piece of 
 brass tubing. Compute the lateral surface and the volume. 
 
 The best instrument for this purpose is the Verniered 
 Caliper. Fair results can be got by the direct application of 
 a good scale. 
 
 Enter results in the note-book as follows : 
 
 Problem. Determination of the dimensions of a piece of brass 
 tubing. Sept. 7, 1888. 
 
 Method. Verniered caliper. 
 
8 
 
 PRACTICAL PHYSICS. 
 
 Results. 
 
 First measurement . 
 Second " 
 Third " 
 
 Length, 
 in. 
 
 Outside 
 Diameter. 
 
 Inside 
 Diameter. 
 
 Mean . . . 
 Computed area = 
 
 .sq. in. 
 
 Volume 
 
 8. Exercise. Cut from a piece of wire the following 
 lengths : 5 mm., 1.26 inches, 2.39 inches, 149 mm., 3.06 inches. 
 
 With a pair of Cutting Pliers (Fig. 7), or a file, cut off 
 a piece of wire a little longer than is required. Set the 
 
 FIG. 7. 
 
 verniered caliper to the required length, and then, with a fine 
 file, shorten the wire till it fits accurately between the jaws. 
 A flat scale may be used in place of the caliper by laying 
 the wire directly on the scale, carefully avoiding parallax in 
 reading by always sighting across the ends of the wire 
 perpendicularly to the scale. 
 
 9. Exercise. Measure the diameter of a wire, and also 
 determine the gauge-number. 
 
 The diameter can be found by means of the verniered 
 caliper (Fig. 4), but a better instrument for the purpose is 
 the Micrometer Caliper (Fig. 8). In using this appliance, it 
 is necessary to find the pitch of the screw C by observing 
 the graduation of the linear scale a. This is usually either 
 
THE PROPERTIES OF MATTER. 
 
 9 
 
 fiftieths of an inch, or half -millimetres. The circular scale on 
 D is generally divided into 20 parts when the graduation is in 
 English measure, and 25 when French ; so that a circular 
 division represents -fa x ^ = y^^ f an mcn * n the one case, 
 and ^ X aV = A ^ a m iUi m etre in the other. As these 
 circular divisions are large, it is easy to estimate to quarters of 
 these spaces. When the screw C is in contact with B, the 
 zero of the scale on D should be at the zero of the linear 
 scale a. If this is not the case, the set-screw which holds B 
 should be changed till the zeroes of the two scales coincide. 
 
 Now place the wire to be measured between B and C. and, by 
 turning D, advance C till the wire is held between B and C ; 
 being careful not to exert undue pressure, as it is an easy 
 matter to vary the reading one or more divisions of the circular 
 scale by springing the frame of the instrument. To get the 
 reading, observe how many divisions on the linear scale a are 
 exposed, and what division of the circular scale on D coincides 
 with the line running lengthwise of the cylinder having the 
 linear scale. As shown in Fig. 8, we have the following 
 reading : 
 
 On the linear scale, 4 small divisions .08 inch. 
 On the circular scale, 5 divisions = .005 inch. ' 
 
 Total reading 
 
 = .085 inch. 
 
10 
 
 PRACTICAL PHYSICS. 
 
 When the linear scale is graduated to read to fortieths of an 
 inch, the larger divisions being tenths, then the circular scale is 
 divided into 25 parts, and hence the reading is to thousandths. 
 
 A simple method of measuring the diameter of a wire is to 
 wrap it closely around a cylinder whose diameter is large com- 
 pared with that of the wire, till some 25 or more convolutions 
 are obtained. Then the diameter will equal the width of the 
 surface covered divided by the number of turns. 
 
 The diameter can also be determined by weighing accurately 
 a known length of the wire, first having made the ends square 
 
 with a file. Then the diameter in centimetres = 
 
 , in 
 
 which w = weight in grammes, d = density (see Table II.), 
 
 and I = length in 
 centimetres. For an 
 explanation of this 
 formula, consult the 
 subject of density as 
 presented in any trea- 
 tise on Physics. 
 
 To ascertain the 
 gauge-number, a Wire- 
 Gauge (Fig. 9) is em- 
 ployed. This consists 
 of a steel plate with 
 a graduated series of 
 notches around the 
 edge, each one numbered according to some specified table 
 of wire-gauges. Find, by trial, into which notch the wire 
 will just fit, and read off the number on the gauge. By 
 reference to Table VI., the diameter can be approximately 
 found. 
 
 FIG. 
 
THE PROPERTIES OF MATTER. 
 
 11 
 
 10. Exercise. Measure the thickness of specimens of 
 the following : Paper, mica, tin-foil, tinsel, etc. 
 
 The most suitable instrument for this problem is the microm- 
 eter caliper. Make several measurements of each specimen, 
 and devise some convenient form for recording the results. 
 
 11. Exercise. Measure the thickness of a very thin piece 
 of mica. 
 
 This can be done by the aid of the micrometer caliper ; but 
 a more desirable instrument for making such measurements is 
 the Spherometer (Fig. 10), as 
 it is less likely to break the 
 thin plate, and the moment 
 of contact of the parts of the 
 instrument with the substance 
 can be more accurately deter- 
 mined, as the phenomenon is 
 independent of the delicacy of 
 the sensation of touch. This 
 instrument consists of a metal 
 platform supported by three 
 steel legs whose extremities are 
 the vertices of an equilateral triangle. In the middle of this tri- 
 angle is a fourth leg, which can be raised or lowered by means of 
 a fine thread cut upon it. This leg passes through the platform, 
 and terminates above in a finely graduated disk of such a size as 
 to be tangent to a straight scale which is normal to the plane of 
 the triangle. A true glass plane must accompany the instru- 
 ment. In the absence of any thing better, a piece of double- 
 thick French plate glass may be used. When the spherometer 
 is placed on the plane with the four legs touching it, the zero 
 on the disk should be exactly at the zero of the straight scale. 
 
 Fro. 10. 
 
12 PRACTICAL PHYSICS. 
 
 If found not to be in adjustment, loosen the screw A, and 
 move the disk the necessary amount. In reading the instru- 
 ment, the pitch of the screw must be known, and also the 
 number of divisions on the disk. Let us suppose that the pitch 
 is ^ mm., and that the disk is divided into 500 parts ; then one 
 turn of the disk will raise or depress the end of the screw 
 ^ mm., and to turn the disk through one division of its scale 
 will move the screw J X -g-Jo = -001 mm. 
 
 To measure the thickness of the mica plate, place the 
 spherometer on the glass plane, with the mica under the fourth 
 leg. Turn the screw till the instrument starts to turn on the 
 plate from the friction of the screw-leg on the plate. To 
 the reading on the straight scale, add that on the disk, and the 
 thickness is obtained. Several determinations should be made, 
 and their average adopted as the true thickness, making a 
 tabulated record of the work as directed in the previous 
 exercises. 
 
 In some forms of the instrument, the screw-leg terminates 
 below, in a bent lever very delicately pivoted, the long arm 
 serving as a pointer. By watching the pointer, the exact 
 moment of contact with the surface is known. 
 
 Instead of adjusting the zero of the instrument, it is probably 
 better to take the mean of several readings, when standing on 
 the plane, without the mica, and then subtract this from the 
 mean of as many readings taken with the mica under the screw- 
 leg. Should the reading in the first case be below zero, and 
 in the second case above, the two must be added. 
 
 12. Exercise. Measure the diameter of a sphere, as a 
 croquet-ball. 
 
 First Method. Place the sphere between two square-cut 
 blocks whose faces press against a third block, and measure 
 
THE PROPERTIES OF MATTER. 13 
 
 the distance between the first two by means of a good scale. 
 To avoid errors, the angles of the blocks must be square, and 
 the thickness of the blocks must not be less than half the 
 diameter of the ball. Why? 
 
 Second Method. Employ the Outside Caliper (Fig. 11) and 
 a good scale. This caliper is a kind of compass with curved 
 legs. By means of a screw, the distance between the inner 
 faces of the points can be set so that they just glide over the 
 
 FIG. 11. 
 
 surface of the sphere. Now apply the points to the scale to 
 determine the distance between them. This will be the diameter 
 of the"ball. Measure the ball in several different positions, record 
 the results as in previous exercises, and obtain the mean. 
 
 This instrument can be used in all kinds of end measure- 
 ments where actual contact between the instrument and the 
 object is possible. 
 
 13. Exercise. Measure the depth and also the diameter 
 of a cylindrical jar, compute its contents, and compare the 
 result with that obtained by the use of a graduated measure. 
 Employ both English and French measure. 
 
14 PRACTICAL PHYSICS. 
 
 To find the depth of the jar, stand vertically in it a lineai 
 scale, taking the reading on it at the point opposite the lower 
 edge of a straight-edge resting across the top of the jar. This 
 measurement should be made at several places, as the bottom 
 of the jar is not perfectly level. The inside diameter can best 
 be found by means of the Inside Caliper (Fig. 12). Place 
 the instrument within the jar, and open it as far as possible. 
 Apply the points to a linear scale, and find the distance 
 between their outer faces. The figure shows a form of the 
 caliper that can be used for both inside and outside measure- 
 ments. 
 
 FIG. 12. 
 
 To compute the volume, apply the formula V vIPH, in 
 which TT = 3.1416, R = radius, and H = depth. 
 
 In the absence of an inside caliper bend a piece of annealed 
 wire into a U-shape, and use it in the same way as a caliper. 
 The lack of elasticity will cause the points to stay wherever 
 placed. 
 
 To measure the volume of the jar, ascertain how much water 
 it takes to fill it, as measured both in and out with a Graduate 
 (Fig. 254.) In filling the graduate, place it on a horizontal 
 table, and in taking the reading hold the eye on a level with 
 the surface of the water. 
 
 A simple method of finding the volume of small vessels of 
 any shape is to subtract their weight when empty from that 
 when filled with ice- water. This difference, in grammes, will, 
 be the volume in cubic centimetres. 
 
THE PROPERTIES OF MATTER. 15 
 
 Record the results after some such plan as the following : 
 
 Problem. Determination of the contents of a cylindrical jar. 
 Sept. 7, 1888. 
 
 Method. Linear scale, inside caliper, water, and a graduate. 
 
 Results. 
 
 Depth. Diameter. Capacity. 
 
 First measurement . cm. in. cm. in. ccm. oz. 
 
 Second " 
 Third 
 
 
 Mean .... 
 
 Computed volume . ccm. oz. 
 
 Measured " 
 
 Mean .... 
 
 14. Exercise. Copy a scale on glass, brass, or paper. 
 
 Thoroughly clean the piece of glass or brass, and coat it 
 evenly with a thin film of beeswax or paraffin e by plunging 
 it into a dish filled with the melted substance. Fasten both the 
 
 FIG. 13. 
 
 scale to be copied and the piece of brass or glass to a board by 
 means of tacks so as to be about 50 cm. apart. In a wooden 
 bar about 52 cm. long, 2 cm. wide, and 1 cm. thick, insert at 
 each end, and perpendicular to the length, a stout needle-point 
 2 cm. long (Fig. 13). Place one of the needle-points of the 
 bar on the first division of the scale, and with the other point 
 draw a line in the wax cutting entirely through it. Next place 
 
16 PRACTICAL PHYSICS. 
 
 the needle-point on the second division of the scale, and so on 
 till a scale of sufficient length has been obtained. Every fifth 
 division should be made a little longer than the others, and 
 every tenth should be longer still. With a sharp-pointed 
 instrument add the proper figures. If the scale is on brass, 
 flow the plate with nitric acid for a few moments, and then 
 wash in water. If the scale is on glass, place the plate, writing 
 downward, over a rectangular dish made of sheet-lead, and 
 containing a spoonful of powdered fluor-spar well moistened 
 with sulphuric acid. Warm the vessel slightly over a lamp, 
 being careful not to melt the wax, and set aside for a few hours. 
 Remove the wax with a cloth wet with benzine. A scale will 
 be found etched in the glass or brass, as the case may be. 
 
 To copy a scale on paper, substitute for one of the needles 
 on the bar a draughtsman's right-line pen or a hard lead- 
 pencil, inserting it in a hole bored through one end of the bar. 
 
 15. Exercise. Test the accuracy of the divisions of a 
 common linear scale. 
 
 To obtain the deviation from a standard scale, employ the 
 Beam-Compass (Fig. 14). It consists of a graduated bar of 
 wood or metal, the standard scale, to which are attached by 
 clamps two points, one of which has a fine adjustment by 
 means of a tangent-screw, C, causing the index-mark on B 
 to move in front of a fine scale. The instrument may also 
 be used in measuring distances between points, in copying 
 scales, etc. 
 
 Fasten the scale to be tested to a board. Slide the point A 
 along the bar till the distance between A and B is, roughly, 
 equal to the distance on the scale to be tested. Then clamp A, 
 place the point on the scale, and move B, by means of C, till 
 the points fall exactly on the scale divisions. Use a magni- 
 
THE PROPERTIES OF MATTER. 
 
 17 
 
 fying-glass to insure accuracy in the coincidence of the points 
 with the divisions of the scale. Now read the distance on the 
 beam, and combine it with the reading on C, for the distance 
 between the scale divisions. Proceed in this way till as much 
 of the scale as needed has been tested. 
 
 The results may be recorded as follows : 
 
 Problem. Testing the accuracy of a linear scale. Sept. 8, 1888. 
 Method. The beam-compass. 
 Results. 
 Scale Reading. Compass-Bar Reading. Scale C Reading. True Distance. 
 
 16. Exercise. Divide a straight line into a number of 
 equal parts. 
 
 First Method. Through one end of the line to be divided, 
 draw an indefinite straight line making any angle between 30 
 and 45. Lay off on this line with the dividers as many 
 equal distances as there are parts required of the given line, 
 
18 PRACTICAL PHYSICS. 
 
 beginning at the vertex of the angle. Join the last division 
 with the free end of the given line, and through the other points 
 of division draw lines parallel to this line. This set of parallels 
 will divide the line as required. 
 
 To draw parallel lines, place one side of a wooden triangle, 
 such as draughtsmen use, firmly against the edge of a ruler rest- 
 ing on the paper. Then on sliding the triangle along the ruler, 
 either of the other sides will move parallel to its first position. 
 /Second Method. Employ a pair of Proportional Dividers 
 (Fig. 15). This instrument is a variety of a 
 double compass with a movable axis, a scale 
 &u the side indicating the ratio of the distance 
 between one pair of points to that between the 
 other pair as the compass is opened. It is some- 
 times furnished with a micrometer adjustment. 
 The same instrument is also graduated so as to 
 give the length of the side of any regular 
 polygon for any given radius. 
 
 To divide the given line, set the index at that 
 division on the scale of the instrument indicating 
 the required number of parts into which the line 
 is to be divided. Now open the dividers till the 
 distance between the points of the longer legs is 
 the length of the line ; then the distance between 
 the other two points is the required part of the 
 line. Lay this distance off on the line, and the 
 required division is obtained. 
 FIG. 15. By reversing the process, a line may be ex- 
 
 tended to any number of times its original length. 
 
 17. Exercise. Draw a circle on cardboard, and divide it 
 into degrees. 
 
THE PROPERTIES OF MATTER. 19 
 
 This will require the use of a Protractor (Fig. 16), a brass, 
 German- silver, or translucent horn circle or semicircle divided 
 to degrees or half degrees. It is frequently provided with an 
 arm turning about its centre, and so constructed that one edge 
 of it moves exactly as a radius of the circle. For very accu- 
 rate work the readings are made by means of a vernier. When 
 not provided with an arm, a ruler will have to be used instead. 
 
 FIG. 16. 
 
 Place the protractor on the cardboard circle so that the cen- 
 tres coincide. Then set the radial arm at zero, and with a 
 sharp pencil draw a line along the edge cutting the circumfer- 
 ence of the circle. Now move the arm to the successive 
 divisions of the scale, and mark as before. Make every fifth 
 division line longer than the others, and every tenth longer 
 still. Should the circle be smaller than the protractor, rule the 
 radial lines as before ; then remove the instrument, and by the 
 aid of a ruler extend the lines toward the centre till they 
 intersect the circumference. 
 
 18. Exercise. Draw a triangle on a piece of cardboard, 
 measure its angles and sides, and also compute its area. 
 
 The length of the sides can be obtained by the method of 
 Art. 2. To measure an angle, place the protractor so that its 
 
20 PRACTICAL PHYSICS. 
 
 centre is exactly on the vertex, and the zero is in one side of 
 the angle, or that side produced. Now move the arm till it is 
 iii the other side ; the reading will be the value of the angle. 
 The area can be computed by the aid of the formula 
 
 ~~ a ) (P ~~ fy(P ~ c )-> m which p is the semi-perimeter, 
 and a, 6, and c are the sides. An approximation to the area 
 of the triangle, and in fact of any plane figure, can be obtained 
 by transferring it to what is known as cross-section paper, 
 paper divided accurately into small squares of known size, and 
 counting the number of these squares that the figure includes. 
 Wherever but part of a square falls within the triangle, the 
 value of that part will have to be carefully estimated. 
 
 Another simple method is to cut the figure out of cardboard, 
 and compare its weight with that of a square inch or a square 
 centimetre cut from the same cardboard. 
 
 19. Exercise. Draw on paper a figure bounded by 
 several straight lines, and determine its area. 
 
 Divide the figure into triangles, and compute their areas as 
 in Art. 18. Check the work by applying the approximative 
 methods suggested in the same article. 
 
 20. Exercise. Find the volume of any irregular piece of 
 stone or metal. 
 
 First Method. Measure the volume of water the substance 
 displaces. To do this readily and accurately, a Cylindrical 
 Graduate (Fig. 254) and an Erdmann's Float (Fig. 17) are 
 needed. The float is a short glass cylinder, closed at both ends, 
 and weighted with mercury so as to cause it to take an upright 
 position in the water. A mark is etched around the cylinder, and 
 the position of this mark with reference to the scale on the 
 graduate is the reading to be used. To make a float, select a 
 
THE PROPERTIES OF MATTER. 21 
 
 short piece of thin glass tubing, close one end by heating it in 
 a gas-flame, then introduce mercury or shot sufficient to cause 
 the tube to float in a vertical position in water. Now close the 
 other end of the tube by softening the glass and draw- 
 ing it out to form a hook. A fine thread tied around 
 the tube at a point which will be below the surface 
 when the instrument floats in water will serve as an 
 index. The office of the float is to avoid the error due 
 to the liquid's climbing up the side of the cylinder, 
 rendering it difficult to tell where the upper surface is. 
 Fill the graduate part full of water, introduce the 
 float by means of a wire hook, and observe the position FlG 17 
 of the line on the float with reference to the scale on 
 the graduate. By introducing water drop by drop, this reading 
 can always be made a whole number. In taking readings, 
 always read to that division on the scale that is in line with two 
 opposite points of the line around the float. Now remove the 
 float, and introduce the object to be measured ; then replace 
 the float, and take the readings as before. The difference 
 between the two readings is the volume. Make several 
 measurements, varying the quantity of water, and record the 
 results after some such plan as the following : 
 
 Problem. Determination of the volume of an irregular piece of 
 stone. Sept. 10, 1888. 
 
 Method. Water, Erdmann's float, and graduated cylinder. 
 
 Results. 
 
 Float-reading before introducing Float-reading after introducing 
 the Stone. the Stone. 
 
 First observation . ccm. ccm. 
 
 Second " . 
 
 Third " 
 
 Mean 
 
 Volume. .....*.. ccm. 
 
22 PRACTICAL PHYSICS. 
 
 Second Method. The volume of a substance whose density 
 is known can be found in cubic centimetres by dividing its 
 weight in grammes by the density. Consult Art. 187 and 
 Table II. 
 
 21. Exercise. Find the volume of a substance soluble in 
 water, as rock-candy, common salt, etc. 
 
 Sugar and saltpetre are insoluble in strong alcohol ; common 
 salt in sulphuric ether, etc. 
 
 22. Exercise. Find the capacity of a vessel whose form 
 is that of the frustum of a cone. 
 
 If the vessel is a small one its capacity can be readily 
 obtained by means of a graduated measure. If, however, the 
 vessel is large, like a water-pail, its capacity is easily com- 
 puted by the formula (R 2 + r 2 + Rr), in which TT = 3.1416, 
 3 
 
 H = depth, R = radius of the top, and r = radius of the 
 bottom. These dimensions are found as directed in Art. 13. 
 Record the results as follows : 
 
 Problem. Determination of the capacity of a vessel whose form is 
 that of the frustum of a cone. Sept. 10, 1888. 
 Method. By calipers and scale. 
 Results. 
 
 Diameter of Diameter of 
 
 Top. Bottom. Depth. 
 
 First measurement . . cm. cm. .cm. 
 
 Second " . . 
 
 Third 
 
 Mean _ . 
 
 Volume ccm. 
 
THE PROPERTIES Of MATTER. 23 
 
 II. ESTIMATION OF MASS. 
 
 23. Apparatus. As the mass of a substance that is, the 
 quantity of matter in it is estimated in terms of some quantity 
 of matter assumed as a standard, as the gramme or avoirdupois 
 pound, there is therefore needed for its determination a copy 
 of the standard unit, together with multiples and sub-multiples, 
 as well as some form of balance for making the comparison. 
 
 FIG. 18. 
 
 The Balance (Fig. 18) consists of a metal beam supported 
 on an axis perpendicular to its length, and about which it is 
 free to turn in a vertical plane. Pans are attached at the 
 extremities of the beam in such a manner as to move freely 
 about an axis parallel to the axis supporting the beam. All 
 the bearings are usually knife-edges of hardened steel resting 
 on polished agate or steel plates. Attached to the centre of 
 the beam is a long pointer moving in front of a graduated 
 scale, to tell the user when the beam is horizontal. In order 
 
24 
 
 PRACTICAL PHYSICS. 
 
 that the beam may not rest on the bearings when the balance is 
 not in use, a provision is made, such that by turning a mill- 
 head in front, the beam is lifted from its supports. To protect 
 from air-currents when weighing, a glass case covers the 
 
 balance. This case is sup- 
 ported on levelling-screws to 
 facilitate the adjustment of 
 the instrument to that posi- 
 tion in which the pointer is 
 opposite the middle division 
 of the scale. Fig. 19 illus- 
 trates a cheaper form of 
 FIG. 19. balance, which will be found 
 
 sufficiently accurate for all requirements of this book. In fact, 
 the common hand-balance so largely used by jewellers, if 
 suspended from some simple support, will give, with care and 
 patience, very good results. 
 
 Jolly's Balance (Fig. 20) is a cheap and efficient substitute 
 for the beam balance. To construct one, proceed as follows : 
 Provide a stout supporting-rod set into a square block for 
 a base. Suspend, from an arm projecting from the top, a 
 delicate spiral spring 30 cm. long. Two or three of these 
 springs should be provided, varying in stiffness. They are 
 made by winding spring brass wire closely around a cylinder 
 2 cm. in diameter. Wires ranging from No. 20 to No. 30 may 
 be used, according to the sensitiveness required. Attach 
 two small scale-pans as seen in the figure, the lower to be 
 used in density determinations for weighing objects in water, 
 an adjustable shelf being necessary to support the tumbler. 
 On the standard back of the spring, tack a long strip of mirror 
 on which is a millimetre scale (see Art. 14). Instead of etching 
 the scale on the face of the mirror, it will be simpler to cut it 
 
THE PROPERTIES OF MATTER. 
 
 25 
 
 in the amalgam, and then cover the back with black paper. A 
 paper scale cemented along the edge of the mirror will answer 
 nearly as well. Just above the scale-pan, attach a small white 
 bead, or a wire pointer, at right angles to 
 the spring, to serve as an index. The 
 scale-reading is where the line joining 
 the index with its reflection intersects the 
 scale. 
 
 The Weights (Fig. 21), when large, 
 are made of brass ; when small, of either 
 aluminum or platinum. Each weight has 
 its value stamped upon it, and should 
 have its assigned place in a neat box. 
 In handling them, always use the small 
 pair of pincers found in the case. The 
 milligramme weights are not much used 
 where the balance-beam is graduated. 
 Their place is supplied by what is known 
 as the Rider, a U-shaped piece of wire, 
 usually weighing one centigramme, that is 
 placed astride of the beam. If the arms, 
 for example, are each divided into ten 
 
 parts, then the 
 
 rider placed at 
 
 division six repre- 
 
 sents a weight of 
 
 six - tenths of a 
 
 FlG - 21 - centigramme, or 6 
 
 milligrammes, placed on the scale-pan. By estimating fractions 
 of these divisions, or using lighter riders, fractions of milli- 
 grammes can be weighed. 
 
 FIG. 20. 
 
26 
 
 PRACTICAL PHYSICS. 
 
 24. Exercise. Find the weight of a small piece of any 
 substance. 
 
 Set the balance vibrating, with empty pans, to determine 
 the position of the resting-point of the pointer on the ivory 
 scale. Since it will take too much time to allow the beam to 
 come to rest, it is better to determine where the resting-point 
 would be by observations made on the oscillations. This would 
 be an easy matter if the resting-point was the middle point of 
 the arc described by the pointer. But the distance the pointer 
 swings each side of the resting-point gradually diminishes ; 
 hence it will be necessary to average a number of oscillations 
 after the manner described below. 
 
 Suppose the ivory scale to be divided into thirty parts. To 
 avoid the use of signs in distinguishing the deviations of the 
 pointer to the right or left of the middle division, number 
 the scale from left to right, the extreme left being marked 0, 
 the middle 15, and the extreme right 30. Then record five 
 vibrations of the pointer. This will give the greatest and 
 the least arc to the side toward which the pointer was first 
 observed to move. These would be recorded as follows : 
 
 TURNING-POINTS. 
 
 RESTING-POINT. 
 
 Left. 
 
 Right. 
 
 First vibration, 
 Third " 
 Fifth " 
 
 Mean . . 
 
 3 
 5.3 
 
 7 
 
 Second vibration, 
 Fourth " 
 
 Mean . . . 
 
 25 
 22.2 
 
 5.1 + 23.6 
 
 Mean - 14. oo. 
 
 a 
 
 5.1 
 
 23.6 
 
 Hence 14.35 is the resting-point of the unloaded balance. 
 By means of the le veiling-screws, the balance could be adjusted 
 
THE PROPERTIES OF MATTER. 27 
 
 so that the resting-point would be the middle division of the 
 scale, but it is unnecessary. Now place the article to be 
 weighed on the left-hand scale-pan, and as near the middle as 
 practicable. In the other pan, place a weight such as you 
 estimate will balance it. Now throw the balance in action, 
 and watch the pointer to determine which pan is the heavier, 
 since, if the equilibrium is not close, the pointer will move 
 sharply to one side of the resting-point, whereas, if close, the 
 resting-point will be seen to be near the middle of the arc 
 described. If the weight is found too heavy, remove it, and 
 substitute a smaller one ; if too small, a heavier one. Let us 
 suppose that the twenty-gramme weight is found too heavy. 
 Then replace it by the ten-gramme weight. If this is found 
 too light, then add the five-gramme weight ; if still too light, 
 add two more ; if now too heavy, then replace the two-gramme 
 by the one-gramme ; if now too light, add .5 gramme ; if still 
 too light, add .2 gramme ; if now too heavy, replace .2 gramme 
 by .1 gramme, and so on. When traced down to centigrammes, 
 the centigramme rider may be used if the balance has a 
 graduated beam, and the milligrammes determined. 
 
 When the swinging of the pointer shows that the balance is 
 nearly secured, find the resting-point of the loaded balance in 
 the same manner as in the case of the unloaded. Let us 
 suppose that is found to be 13.5. This shows that the right- 
 hand pan is the heavier. 1 To determine the amount, place 
 .001 gramme in the left-hand pan, and again determine the 
 resting-point. Let us suppose that this resting-point is found 
 to be 15. Hence it follows that .001 gramme has moved the 
 pointer through 15 13.5 = 1.5 divisions, whereas it was 
 
 1 This applies to a balance having the ivory scale below the beam. Where this scale 
 is above the beam, the opposite is indicated. 
 
28 PRACTICAL PHYSICS. 
 
 necessary to move it 14.35 13.5 = .85 division. Therefore 
 the amount to be placed in the left-hand pan, that is, the 
 amount to be deducted from the weights in the right-hand pan, 
 is (.85 -r- 1.5) x .001 = .00057 gramme. Finally add together 
 the weights in the pan, and deduct from the sum .00057 gramme 
 to obtain the weight of the substance. 
 
 To prevent errors in determining the total value of the 
 weights on the pan, first, add up the values of those which 
 the empty pockets of the case show to be in use ; secondly, 
 check the same by adding the values of the weights as they are 
 removed from the pan to the case. 
 
 In weighing with fine balances, observe the following precau- 
 tions : 
 
 1. Remove all dust from the pans by means of a camel-hair 
 brush. 
 
 2. Set the balance in action by turning the mill-head to find 
 the resting-point of the pointer, as it is not always the middle 
 division of the scale. 
 
 3. When it is necessary to stop the swinging of the beam, 
 wait till the pointer is directly over the centre of the scale, then 
 turn the mill-head. To do otherwise jars the instrument, and 
 injures the bearings. 
 
 4. Always stop the swinging of the balance when adding or 
 removing weights. 
 
 5. The position of the observer should be central so as to 
 avoid any parallax in reading the scale. 
 
 6. Always put on weights in the order in which they come 
 in the box or case, handling them with the pincers, and never 
 with the fingers. 
 
 7. When the weighing is finished, replace the weights in the 
 box, and in no case leave the balance swinging if there is any 
 provision for avoiding it. 
 
THE PROPERTIES OF MATTER. 29 
 
 8. Avoid all air-currents, and have a firm support for the 
 balance, so that there may be as little trembling as possi- 
 ble. 
 
 9. Never be in a hurry, as accurate weighing is slow 
 work. 
 
 10. All substances liable to injure the pans, when being 
 weighed, must be placed in appropriate vessels ; a watch-glass 
 of known weight will be found very useful for such pur- 
 poses. 
 
 To weigh with Jolly's balance, place the substance in the 
 upper pan, and take the reading of the index. Now remove 
 the substance, and add weights till the same reading is 
 obtained. The sum of the weights is evidently the weight of 
 the substance. If, with the weights given, it is found 
 impossible to bring the index to the same reading, add weights 
 till a reading less than the required one is obtained, but such 
 that the smallest weight on hand, when added, brings the index 
 too low. If, for example, the reading required is 300, and 
 1 mg. changes it from 299 to 301.5, then the weight required 
 
 will be of 1 mg., or .4 mg. 
 
 2i.D 
 
 25. Exercise. Determine the weight of a number of 
 lead balls by weighing five of them separately, selected at 
 random, finding their average, and multiplying that average 
 by the number of balls in the lot. Weigh each ball several 
 times. 
 
 The record may have the following form : 
 
 Problem. Determination of the weight of a number of lead balls. 
 
 Method. Weighing five of them separately, selected at random, 
 finding their average, and multiplying that average by the number of 
 balls in the lot. 
 
30 PRACTICAL PHYSICS. 
 
 Results. 
 
 First Ball. Second Ball. Third Ball. Fourth Ball. Fifth Ball. 
 
 First weighing . 
 
 Second " . 
 
 Third " 
 
 Mean . . . 
 Average weight of a ball = Weight of lot = 
 
 26. Exercise. Determine how many grains of wheat in a 
 bushel, 60 pounds, by weighing five lots of 20 grains each, and 
 from these data determining the average weight of a grain. 
 
 Devise a convenient form for recording the results. 
 
 27. Exercise. Determine how much chalk it takes to 
 write your name on a common blackboard. Also determine 
 the amount used in writing your name on a slate. Which is the 
 more economical surface on which to use chalk ? 
 
 Use the mean of several times' writing. Devise some 
 suitable form for tabulating results. 
 
 28. Exercise. Determine the weight of a silver five-cent 
 piece, and also that of a silver dollar. What is the value of 
 the silver dollar on the standard adopted for the five- cent piece ? 
 
 29. Exercise. Determine the percentage of water in 
 crystallized sodium sulphate. 
 
 Weigh carefully a large crystal of the salt, and then set it 
 aside for several days in a place where dust is excluded. 
 The crystal will fall to powder, owing to the escape of the 
 water of crystallization. Find the weight of the powder, and 
 then compute the percentage of loss. 
 
THE PROPERTIES OF MATTER. 31 
 
 30. Exercise. Compare the weights of equal volumes of 
 several substances, expressing each in terms of the lightest 
 taken as the unit. 
 
 Get a competent mechanic to make out of lead, brass, tin, 
 iron, maple, lignum-vitse, etc., cubical blocks 1.5 cm. on an 
 edge, that is, blocks of equal volumes, and determine their 
 weights in the regular way. 
 
 31. Exercise. Determine the length of a twisted piece of 
 wire. 
 
 Weigh several straight pieces of wire of the same material 
 and gauge-number, and also measure their lengths. From 
 these data, compute the average weight of a centimetre of the 
 wire. Now weigh the twisted piece, and compute its length. 
 
 The results may be recorded as follows : 
 
 Problem. Determination of the length of a twisted piece of wire. 
 Method. Weighing and measuring. 
 
 Results. 
 
 Length. Weight. Weight per Centimetre. 
 
 Wire No. 1 . . 
 
 " " 2 
 
 Mean 
 
 Weight of the twisted piece, Computed length, 
 
 32. Exercise. Cut a piece of smooth tin-foil of some 
 simple figure ; determine its area and weight. Compute its 
 thickness, allowing that 1 ccm. of tin weighs 7.29 grammes. 
 Compare the result with that obtained by the use of the 
 micrometer caliper. Devise a suitable form of record in the 
 note-book. 
 
32 PRACTICAL PHYSICS. 
 
 33. Exercise. Make out of aluminum-foil a centigramme 
 weight. 
 
 First find both the area and the weight of a piece of the 
 foil, and then compute how large a piece will be required to 
 weigh one centigramme. As the thickness of the metal may 
 not be uniform, cut the piece a trifle larger than the estimated 
 one. By means of a fine file, adjust the piece to the required 
 weight. 
 
 34. Exercise. Measure the cross-section of a capillary 
 glass tube. 
 
 Clean the tube thoroughly by washing it, first in nitric acid, 
 then in distilled water, then in a solution of sodium hydrate, 
 and finally in distilled water. To do this, connect a small 
 glass syringe to the tube to be washed, by half a metre of 
 rubber tubing ; then, by placing one end of the capillary tube 
 in a vessel containing the wash, the corrosive liquid is made to 
 pass backward and forward through the tube without coming 
 in contact with the hand. After thoroughly washing the tube 
 with distilled water, rinse it out with alcohol, and then dry it 
 by passing it back and forth over a gas or spirit flame. Fill 
 the tube part full of pure mercury by dipping it into a dish 
 filled with the liquid ; lay it on a horizontal surface and by 
 means of a pair of dividers and a diagonal scale, ascertain 
 the length of the mercury filament. Pour the mercury out 
 of the tube into a suitable vessel of known weight, and ascer- 
 tain its weight. Now the volume of mercury in the tube is 
 equal to the weight of mercury divided by 13.6, and the cross- 
 section of the tube equals the volume of mercury divided 
 by the length of the filament, provided the centimetre and 
 the gramme are the units used. How would you find the 
 diameter ? 
 
THE PROPERTIES OF MATTER. 33 
 
 III. IMPENETRABILITY. 
 
 35. Apparatus. The principal appliances needed in the 
 study of this subject are as follows : Battery -Jar, Cubes of 
 "Wood, Funnel, Funnel-Tube with a Stop-Cock, Rectangular 
 Prism of Wood, Wide-Mouthed Bottle, Tumbler, Glass Tubing 
 and a Cylindrical Graduate. 
 
 36. Exercise. Graduate a glass battery-jar of two or 
 more litres capacity to decilitres by means of a graduated 
 measure and water, marking the divisions on a paper strip 
 pasted on the outside. Cut out of wood two cubes, one 
 decimetre and one-half a decimetre on their edges respectively. 
 Give each block a coat of thin shellac varnish, made by 
 dissolving shellac in alcohol, or of hot paraffine. Now fill the 
 jar about half full of water, and observe by the scale on 
 the side exactly how much there is. Then place in the jar 
 these blocks successively, holding the block under water by 
 means of a slender knitting-needle, and, while submerged, note 
 exactly the volume of water as shown by the scale on the side 
 of the jar. Compare the increase of volume with the volume of 
 the block. Inference. 
 
 Owing to the climbing-up of the water on the side of the jar, 
 it is difficult to get the exact position of the surface. This 
 may be partly corrected by rubbing a thin film of paraffine on 
 the inside of the jar opposite the scale. 
 
 37. Exercise. Partly close the throat of a funnel with a 
 perforated cork. Fit a second cork accurately to a wide- 
 mouthed bottle with the stem of the funnel passing tightly 
 through this cork (Fig. 22). Bore a small hole through this 
 cork of about 2 mm. diameter. Now pour water into the 
 
34 
 
 PRACTICAL PHYSICS. 
 
 funnel, holding a finger firmly over this small hole in the cork. 
 Observe the difference on removing the finger. 
 Why would the water not run in at first ? What 
 do you learn from this experiment about water 
 and air? 
 
 As large corks are usually very open, they 
 should first be boiled in paraffine. In fitting 
 corks, a flat wood- file and a small round file 
 will be indispensable. 
 
 38. Exercise. Make a wooden rectangu- 
 lar prism 5 cm. by 2 cm. by 20 cm. In a cylin- 
 drical jar, put 100 ccm. of water. Graduate 
 the longest edge of the prism to centimetres. 
 Insert the bar vertically into the water. Mark on the side 
 of the jar the change of level of the water ; then remove the 
 bar, and ascertain what volume of water will produce the same 
 change of level. How does this volume compare with that 
 of the part of the bar submerged? Repeat the experiment 
 two or three times, varying the amount of the bar submerged. 
 What property does this experiment show that matter pos- 
 sesses ? 
 
 FIG. 22. 
 
 39. Exercise. Adjust a U-shaped delivery tube to a 
 bottle containing a known quantity of water, the inner end of 
 the tube opening beneath the water, and the outer end opening 
 within a common tumbler (Fig. 23). Pass through the same 
 cork a funnel-tube with a stop-cock. All these fittings must be 
 made air-tight. For this reason, a rubber stopper is to be pre- 
 ferred. Now shut off the stop-cock, and pour into the funnel 
 a measured quantity of water. Then turn the stop-cock, and 
 let the water pass into the bottle. Measure the water in the 
 
THE PROPERTIES OF MATTER. 
 
 35 
 
 Fw. 23. 
 
 tumbler, and compare the amount with that poured into the 
 
 bottle. Pour in another known 
 
 quantity, and then ascertain the 
 
 amount in the tumbler. Continue 
 
 in this way till at least five separate 
 
 amounts of water have been added 
 
 to the bottle. Find the average of 
 
 the five amounts of water poured 
 
 into the bottle, and also of the five 
 
 amounts collected in the tumbler. 
 
 Measure the amount of water left 
 
 in the bottle, and correct these 
 
 averages by the difference between 
 
 this amount and the amount in 
 
 the bottle at the beginning. What 
 
 inference can you make from comparing these averages? 
 
 40. Exercise. Fit a delivery- tube, and also a funnel- tube 
 
 provided with a stop-cock, 
 to a well-corked bottle 
 (Fig. 24). Let the deliv- 
 ery-tube open beneath an 
 inverted cylindrical grad- 
 uate filled with water over 
 a small pneumatic trough. 
 Pour a known quantity 
 of water into the funnel- 
 tube, opening the stop- 
 cock as soon as the air 
 has escaped from the 
 - 24- throat of the funnel. 
 
 Measure the air now found in the graduate. Repeat the opera- 
 
36 PRACTICAL PHYSICS. 
 
 tion several times, and measure the air in the graduate after each 
 pouring. Each of these results should be corrected by subtract- 
 ing from it the capacity of the tube below the stop-cock. Why ? 
 This capacity can be easily determined by closing the end with 
 the finger, and finding the amount of water required to fill the 
 tube. Compare the amounts of water and air. Inference. 
 
 The funnel-tube may be replaced by a common funnel joined 
 to a glass tube by a rubber connector. A pinch-cock (Fig. 
 269) on the rubber will serve for a stop-cock. 
 
 41. Exercise. Float a cork on the surface of water. 
 Cover it with a wide-mouthed bottle, and push the glass vessel, 
 mouth downward, into the water. What phenomenon do you 
 observe? Insert one arm of a U-tube made of glass tubing 
 under the edge of the bottle, and again push it down into the 
 water. Does the same phenomenon occur as before? What 
 do you learn by holding a burning match over the outer end of 
 the U-tube as the vessel is pushed into the water? What is the 
 lesson from this experiment? 
 
 42. Exercise. Fill a tumbler level full of water. Now 
 drop in carefully, and one at a time, a number of small nails. 
 In the fact that the water does not flow over the side of the 
 vessel, have you an exception to the principle that matter 
 is impenetrable ? State the evidence on which your answer is 
 based. 
 
 IV. DIVISIBILITY. 
 
 43. Apparatus. The appliances needed are Balance, 
 Weights, and Micrometer Caliper- 
 
THE PROPERTIES OF MATTER. 37 
 
 44. Exercise. Put two or three drops of nitric acid on a 
 piece of copper ; let it stand till the boiling action ceases, and 
 then wash it off in a half -litre of clear water. To this add a 
 few cubic centimetres of ammonia water. The blue discolora- 
 tion denotes the presence of copper. Have you any evidence 
 that copper is present in every drop of the liquid? What 
 physical property do you find belongs to copper? Determine 
 the amount of copper in each cubic millimetre of the blue 
 solution by weighing the copper before applying the nitric 
 acid, and after washing it in the water, and by measuring the 
 solution. 
 
 45. Exercise. Dissolve .01 gramme of an aniline dye in 
 one litre of water. By dropping water 
 
 from a bottle or a dropper into a gradu- 
 ated measure, ascertain, by averaging five 
 trials, the number of drops in a cubic 
 centimetre of the solution. Now compute 
 how much aniline there is in each drop of 
 the colored solution. What property does 
 aniline possess to a very marked extent? 
 
 46. Exercise. Weigh accurately a clean silver coin. 
 Place on it two or three drops of nitric acid, letting it remain 
 till the action of the acid on the silver ceases. Then wash it 
 in a tumbler of pure water. Stir the water thoroughly, and 
 divide it into two parts. To the one add a few drops of a 
 strong solution of common salt, and to the other add a few 
 centimetres of ammonia-water. Remembering that common 
 salt turns a solution of silver milky, and ammonia-water turns 
 a solution of copper blue, what inference can you draw from 
 the experiment? Now weigh the coin, and compute how much 
 
38 PRACTICAL PHYSICS. 
 
 silver and how much copper there is in each cubic centimetre 
 of the solution. 
 
 NOTE. American silver coin is 10 per cent copper. 
 
 47. Exercise. Measure with a micrometer caliper the thick- 
 ness of a piece of mica. Measure the thickness of the thinnest 
 piece you can split from the original one. Is it due to the lack 
 of skill, or to some property inherent in the mica, that you are 
 unable to obtain a piece still thinner? 
 
 V. POROSITY. 
 
 48. Apparatus. For the study of porosity, procure a Gas- 
 Bottle, a Three-Necked Bottle, some Glass Tubing, a Common 
 Tumbler, a Cylindrical Graduate, and a Florence Flask. 
 
 49. Exercise. Determine whether rubber is porous or not. 
 
 Fit a deli very- tube to a*gas- 
 bottle (Fig. 26) , and let it open 
 into a three-necked bottle in 
 which is some water. Through 
 the middle neck, pass a long 
 glass tube reaching to the bot- 
 tom of the bottle. Close the 
 third neck with a perforated 
 cork, through which passes a 
 short piece of glass tubing. 
 Now put some zinc clippings 
 in the gas-bottle, and cover 
 PIG. 26. them with dilute sulphuric acid, 
 
 one part acid to three of water. Hydrogen gas will be given 
 
THE PROPERTIES OF MATTER. 39 
 
 off, which will pass over into the second bottle. If you press 
 your finger firmly over the end of the tube in the third neck, 
 you will notice that the water will rise higher and higher in 
 the second one till it flows out of the top (why?). Remove 
 the finger, and tie a small rubber balloon over the end of the 
 tube. The water in the second tube soon begins to rise, but 
 does not get beyond a certain point, notwithstanding that the 
 evolution of gas still continues in the gas-bottle. What be- 
 comes of this gas? What must be the physical structure of 
 the rubber? 
 
 All the corks must be firmly tied down with stout cord to 
 prevent them from being driven out by the pressure of the 
 gas. 
 
 50. Exercise. Test a piece of chamois for porosity. 
 Tie it over the end of a stout glass tube about 
 
 two- thirds of a metre long, and 15 mm. in diameter. 
 Hold the tube over a large glass vessel, and 
 with a test-glass (Fig. 27), or some vessel with 
 a lip, pour mercury into the tube, filling it nearly 
 full. What does this experiment teach about the 
 structure of chamois? Would very fine shot sub- 
 stituted for the mercury act in the jsame way ? 
 Why ? What property of mercury is also revealed 
 in this experiment? 
 
 51. Exercise. Test thin sheets of several substances for 
 evidences of porosity. 
 
 Select two plain tumblers of thin glass and of the same size. 
 After thoroughly warming one of them, fill it about half full of 
 boiling water. Now cover the glass with a piece of cardboard, 
 
40 
 
 PRACTICAL PHYSICS. 
 
 and invert the other glass upon it (Fig. 28). After the lapse 
 of one or two minutes, ascertain if there is any change in the 
 
 condition of the interior of the 
 upper tumbler. What does 
 the experiment teach regarding 
 the structure of cardboard? 
 
 Now re-heat the water, and 
 test in a similar manner pieces 
 of felt, chamois, and wood. In 
 the case of wood, ascertain in 
 FlG - 28 - what manner a change in the 
 
 thickness of the strip affects the phenomenon. 
 
 52. Exercise. Fit to a Florence flask a delivery-tube 
 leading to an inverted bottle standing over the pneumatic 
 trough (Fig. 29). Fill the flask, tube, and inverted bottle with 
 
 FIG. 29. 
 
 water, and apply heat to the flask. After the boiling of the 
 water has continued for some time, remove the lamp, and 
 examine closely the collection-bottle. Whence the gas found 
 in it? Repeat the experiment, filling the apparatus this time 
 
THE PROPERTIES OF MATTER. 41 
 
 with water that has been boiled for some time in an open 
 vessel. What property does this experiment show that water 
 possesses ? 
 
 53. Exercise. Put 75 ccm. of water in a cylin- 
 drical graduate. To this add 2 ccm. of finely pow- 
 dered sugar. After the sugar has dissolved, observe 
 the volume of the solution. Account for the shrink- 
 age. 
 
 54. Exercise. In a glass tube graduated to 
 tenths of cubic centimetres (Fig. 30), put 30 ccm. 
 of water. Then pour in very gently, tipping the 
 tube so that it will flow down the wall of the tube, 
 20 ccm. of strong alcohol. Hold the finger firmly 
 over the mouth of the tube, and shake vigorous!}'. 
 Observe the volume of the mixture. What is the 
 percentage of shrinkage? What has been previously 
 proved of water that will assist in explaining this phenomenon ? 
 
 VI. INDESTRUCTIBILITY. 
 
 55. Apparatus. The appliances needed are Test-Tubes, 
 Beakers, Flasks, and a Balance. 
 
 56. Exercise. Prepare a saturated solution of 
 calcium chloride by adding the salt to 20 ccm. of water 
 until it refuses to dissolve any more. Pour enough of 
 the solution into a test-tube (Fig. 31) to fill it a little 
 less than half full. In a similar manner, prepare an FIG. 31. 
 equal quantity of a saturated solution of sodium sulphate in a 
 
42 
 
 PRACTICAL PHYSICS. 
 
 second test-tube. Place the test-tubes in some suitable vessel 
 to prevent them from overturning, and determine their united 
 weight. Now pour one solution into the other, and shake 
 quickly. Observe the change that takes place. Ascertain if 
 the weight has changed. 
 
 Bottles may take the place of the test-tubes. 
 
 57. Exercise. Support a piece of phosphorus of the size 
 of a small pea on the end of a wire of the form shown in 
 
 Fig. 32. Put about 400 ccm. 
 of water colored with blue 
 litmus into a thin beaker of 
 about one litre capacity. In 
 this place the wire stand sup- 
 porting the phosphorus, and 
 invert over it a Florence 
 flask, resting its neck on the 
 edge of the beaker closing its 
 top, the mouth of the flask 
 reaching nearly to the bottom 
 of the colored water. After 
 
 thoroughly drying the outside of the apparatus, place it on 
 one of the pans of a balance, and exactly counterpoise it. 
 Let it remain undisturbed for twenty-four hours, and then 
 examine the flask carefully to ascertain what changes have 
 taken place within it. 
 
 Would the same weight be required to counterpoise the 
 apparatus if no phosphorus had been placed on the wire 
 support? Has the weight of the beaker and its contents been 
 diminished by the disappearance of the phosphorus? Have 
 the phosphorus and some of the air in the flask been de- 
 stroyed ? 
 
 FIG. 32. 
 
THE PROPERTIES OF MATTER. 43 
 
 To prevent the evaporation of water from the beaker, the 
 edge should be coated with paraffine. 
 
 58. Exercise. Fill a test-tube, say 2.5 cm. diameter and 
 15 cm. long, with water ; cover the mouth with the thumb, and 
 invert the tube in a small beaker 
 
 partly filled with water (Fig. 33). 
 The tube should be full of water, no 
 air having been admitted in inverting 
 it. Slip over the tube a short piece 
 of large glass tubing, as a piece of 
 lamp-chimney, to support the test- 
 tube in a vertical position. Place a 
 small piece of zinc, say .05 gramme, 
 beneath the mouth of the tube. Pour 
 into a small beaker a few centimetres 
 of strong sulphuric acid. Place the 
 vessel supporting the tube, and also 
 
 the beaker of acid, on the pan of a fairly good balance, and 
 counterpoise them. Pour the acid into the vessel supporting 
 the tube, replacing the beaker in the scale-pan. The acid will 
 act on the zinc, and hydrogen gas will be seen to collect in 
 the top of the tube. From time to time, as these changes 
 proceed, set the balance in action to ascertain if there is any 
 gain or loss of matter. Inference. 
 
 Caution. If too much zinc is used, the tube will not hold all the 
 gas evolved. 
 
 59. Exercise. Select two thin glass beakers, each having 
 a capacity of about 100 ccm. Into one put 50 ccm. of a 
 solution of lead nitrate, and into the other put 25 ccm. of 
 
44 PRACTICAL PHYSICS. 
 
 a solution of potassium chromate. Place the two beakers on 
 the pan of a balance, and counterpoise them. Now pour the 
 contents of one beaker into the other, restoring the beaker to 
 its place on the scale-pan. Observe the changes which occur, 
 and determine if they are attended with any gain or loss of 
 matter. 
 
 VII. COHESION. 
 
 60. Apparatus. Bar of Lead, Balance, Disks of differ- 
 ent substances, Funnel with Stop-Cock, Glass Bulb, Spring- 
 Balance, Crucible, Evaporating Dish, etc. 
 
 61. Exercise. Bore a hole, about 2.5 cm. in diameter, in 
 a block of wood, and, using it as a mould, cast two disks of 
 lead 2.5 cm. thick. Dress one surface of each disk to a plane. 
 Now press the two disks firmly together, giving one of them a 
 slight twisting motion. In this way, one piece can be made to 
 hold up the other. What force is brought into action ? What 
 do the facts that pressure, as well as a very smooth surface, 
 is necessary to the success of this experiment, teach regarding 
 this force? 
 
 62. Exercise. Measure the cohesion of paper or 
 wire. 
 
 Cut a rectangular piece of the paper to be tested 25 cm. long 
 and 10 cm. wide. Fold over each end, fastening it with glue, 
 forming a loop or hem. In these insert stout wooden rods 
 somewhat longer than the width of the paper. Connect the 
 ends of one of these rods to the hook of a spring-balance by 
 means of a wire or cord bail. Fasten the other rod to some 
 
THE PROPERTIES OF MATTER. 45 
 
 suitable support. Now pull steadily on the ring of the balance, 
 recording the reading observed at the moment the paper is 
 parted. 
 
 Wire can be tested in a similar manner by fastening one end 
 to some firm object, and the other end to the hook of the 
 balance. Compare strength with the cross-section. Ascertain 
 if length affects the strength. 
 
 63. Exercise. Compare the cohesion of water, alcohol, 
 glycerine, etc., by ascertaining the degree to which such 
 cohesion affects the size of falling drops of the liquid. 
 
 Support by a clamp a funnel provided with a stop-cock so 
 that its stem is about 1 cm. above the surface of a glass sphere. 
 A small Florence flask with a round bottom, or the bulb of a 
 common air thermometer, may be used for the sphere. Pour 
 some of the liquid to be tested in the funnel, and open the 
 stop-cock so that the liquid will flow at such a rate upon 
 the sphere as to drop from the under surface at the rate of two 
 drops per second. Now catch one hundred of these drops in 
 a beaker, and determine their weight. Make at least three 
 determinations for each liquid. 
 
 Repeat the experiment, changing the drop-rate to one in two 
 seconds. How is the size of the drop affected? 
 
 Ascertain the effect on the drop-size of employing a smaller 
 glass sphere. 
 
 Record the results as follows : 
 
 COHESION. 
 
 Problem. Measurements of drop-size of several liquids. Sept. 17, 
 
 1888. 
 
 Method. Weighing one hundred drops of liquid. 
 
46 PRACTICAL PHYSICS. 
 
 Results. 
 
 DROP-RATE, DROP-RATE, 
 
 Water. Alcohol. Glycerine. Water. Alcohol. Glycerine. 
 
 First trial .... 
 
 Second " .... 
 
 Third " 
 
 Mean 
 
 Weight of drop . 
 
 64. Exercise. Measure the force necessary to pull a disk 
 away from a liquid. 
 
 Remove one of the scale-pans from a balance, the jew- 
 eller's form answers the purpose nicely, and suspend in its 
 place a glass disk, about 5 cm. diam- 
 eter, by means of three threads at- 
 tached at points 120 degrees apart 
 (Fig. 34). After accurately counter- 
 poising the disk, place a vessel of 
 water below it, raising it till the sur- 
 face of the water touches the under 
 surface of the disk, being careful to 
 keep the beam horizontal. Now add 
 weights to the scale-pan till the disk 
 
 is pulled away from the water. These weights must not be 
 dropped into the pan, as the sudden jar would tend to separate 
 the disk from the water. Ascertain whether you have pulled a 
 column of water apart, or pulled the plate away from the water. 
 Measure the disk, and then compute the force per square 
 centimetre required to effect the separation. 
 
 The disk must be perfectly clean, and in bringing it in 
 contact with the liquid, first touch one edge, and then gradually 
 shut down the disk upon the liquid, thus excluding all air 
 
THE PROPERTIES OF MATTER. 47 
 
 bubbles, and insuring good contact. The threads can be 
 attached to the disk by means of tough sealing-wax. See 
 Art. 607. 
 
 Try other liquids, as mercury, alcohol, glycerine, etc. 
 
 Try successively disks made of brass, tin, zinc, etc. 
 
 Amalgamate these disks with mercury before measuring the 
 force required to separate them from mercury. 
 
 Measure the force required to separate from water a glass 
 disk coated with a film of sweet oil. 
 
 Construct a comparative table of all the results. 
 
 65. Exercise. Select a soft glass tube about 25 cm. long 
 and 2 cm. in diameter. Close one end in the flame of a 
 blow-pipe, and then bend the tube to a V shape with its 
 branches widely diverging, and the closed arm 3 cm. the 
 longer. Nearly fill the tube with water, and boil it uniformly 
 till nearly a quarter has boiled away. Remove the flame, and 
 close the open end air-tight with a rubber stopper. When cold, 
 hold the hand against the end of the long arm ; let the water 
 in the tube fall against it. The water will be found to remain 
 suspended in that arm on holding it in a vertical position, 
 instead of falling back to the level of the water in the other 
 arm, requiring quite a jar to break it away from the end of the 
 tube. Explain. 
 
 66. Exercise. Dissolve 100 grammes of powdered alum 
 in half a litre of hot water. Hang in the solution strings, 
 twigs of plants, or wire forms, and set aside for twelve hours. 
 Make a careful study of the alum crystal. Diagram one. 
 Copper sulphate may be substituted for the alum. Make a 
 mixture of the two solutions in an evaporating dish or saucer, 
 and set aside till crystallization occurs. 
 
48 PRACTICAL PHYSICS. 
 
 67. Exercise. Wet the surface of a strip of glass with a 
 solution of ammonium chloride. As it begins to dry, examine 
 it carefully under a microscope. A good botanizing-glass will 
 answer the purpose. 
 
 68. Exercise. Melt a quantity of sulphur in a Hessian 
 crucible or common tea-cup. The vessel should be at least 
 two-thirds full. As soon as the sulphur is melted, set it aside 
 to cool, leaving it till a thin crust forms over the top. Now 
 break through the crust, and pour out the liquid interior. 
 Examine with a common magnifier the interior of the cavity, 
 determining the form of the crystals. 
 
 69. Exercise. Prepare a saturated solution of common 
 salt. Pour the solution into a common saucer or an evaporat- 
 ing dish, and set it aside protected from dust. In a few days, 
 the bottom of the dish will be covered with crystals curiously 
 grouped. Make a close study of the shape of the crystals, and 
 the manner of grouping. 
 
 By observing the following directions, quite large salt crystals 
 can be obtained : 
 
 " The salt to be crystallized is to be dissolved in water, and 
 evaporated to such a consistency that it shall crystallize on 
 cooling. Set it by, and when quite cold, pour the liquid part 
 from the mass of crystals at the bottom into a flat-bottomed 
 vessel. Solitary crystals will form at some distance from each 
 other, and gradually increase in size. Pick out the most 
 regular, put them into another flat-bottomed vessel a little 
 apart from each other, and pour over them a quantity of fresh 
 solution of the salt evaporated till it crystallizes on cooling. 
 Alter the position of every crystal once at least every day with 
 a glass rod, that all the faces may be alternately exposed to 
 
THE PROPERTIES OF MATTER. 49 
 
 the action of the liquid, for the face on which the crystal rests 
 never receives any increase. By this process, the crystals will 
 gradually augment in size. When they have acquired such a 
 magnitude that their forms can easily be distinguished, the 
 most regular are to be chosen, or those which have the exact 
 shape which you wish to obtain. Each of them should be put 
 separately into a vessel filled with a portion of the same liquid, 
 and turned by the glass rod several times a day. Whenever it 
 is observed that the angles and edges of the crystals become 
 blunted, the liquid must immediately be poured off, and fresh 
 liquid put in its place ; otherwise the crystals will be infallibly 
 destroyed." 
 
 70. Exercise. Procure pieces of mica, Iceland spar, roll 
 sulphur, common white chalk, alum, coal, feldspar, blue vitriol, 
 sal ammoniac, galena, pyrites, etc. With a knife, try to split 
 these substances in different directions. What do you discover 
 with respect to the relative ease of breaking or splitting each 
 of these substances in different directions ? Study closely the 
 surfaces exposed at each separation, and see if it indicates 
 the breaking-up of a structure, or the splitting-apart of two or 
 more complete structures. Examine the corners; in short, note 
 every thing having any bearing on the molecular structure of 
 the substance. 
 
 71. Exercise. Classify a number of substances with 
 reference to their hardness on Mohr's scale. 
 
 Mohr's scale is the hardness of the following ten substances, 
 which are ranked as shown by the attached numbers : 1 , talc ; 
 2, gypsum; 2.5, mica; 3, calcite ; 4, fluor-spar ; 5, apatite ; 
 5.5, scapolite ; 6, feldspar ; 7, quartz ; 8, topaz ; 9, sapphire ; 
 10, diamond. 
 
50 PRACTICAL PHYSICS. 
 
 To determine the hardness of any substance, draw a file over 
 it with considerable pressure, and observe whether the depth of 
 the cut made in the specimen is greater, less, or equal to, that 
 made in some one of the minerals of the scale. If, for 
 instance, the cut made in the substance is less than that made 
 in 6, and deeper than that made by the same pressure of the 
 file in 7, it ranks in hardness between 6 and 7. 
 
 Glass, slate, marble, gypsum, galena, hematite, magnetite, 
 fluor-spar, copper, silver, steel, etc., are some of the substances 
 easily obtained for the purposes of this experiment. 
 
 VIII. ELASTICITY. 
 
 72. Apparatus. The appliances required for studying 
 elasticit}^ are such as any one accustomed to the use of tools 
 can readily make by following the directions given. A stock 
 of wires, wooden bars, and metal and wooden rods of various 
 sizes and numbers, will be needed for testing. 
 
 73. Exercise. Study the elasticity of solids when mani- 
 fested by pressure. 
 
 Procure several balls, one each, of wood, glass, ivory, etc., 
 each having a diameter of about 2 cm. Drop them from the 
 same height on a marble slab, and compare the heights to 
 which they rebound. Double the height, and repeat the com- 
 parison. Triple the height, and compare. Now repeat the 
 experiment, having coated the slab with a thin film of paste 
 made of olive-oil and common whiting thoroughly mixed 
 together. Compare the marks made in the film by the balls 
 when merely laid on the marble, with those made when the 
 balls fall from a height. What inference follows respecting 
 the various substances of which the balls are made ? 
 
THE PROPERTIES OF MATTES. 
 
 51 
 
 74. Exercise. Show that the amount of extension of a 
 wire is proportional to its length, and to the weight which 
 produces the extension, within certain limits, and is inversely 
 as the cross-section. 
 
 FIG. 35. 
 
 Construct a stout wooden frame of the form shown in 
 Fig. 35, having the upright at least one metre high. Attach 
 to it a millimetre scale. Suspend in succession straight pieces 
 of iron, steel, copper, brass, etc. wires of the same size, from 
 a hook on the under side of the arm at the top of the vertical 
 support, fastening to the lower end a scale-pan made of tin or 
 brass. Fasten to the wire two pointers, A and B, and record 
 the difference in the readings for the length AB. Now put 
 some known weights in the pan, and again determine AB. Add 
 more weights, and again read the distance AB. Continue 
 
52 PRACTICAL PHYSICS. 
 
 doing this, if possible, till the wire breaks. After each reading 
 is taken, remove all the weights, and record the length of the 
 wire. Tabulate the results. Compare the increase in length 
 each time with the total weight in the pan, and you should find 
 that the wire has increased in length proportionally to its length, 
 and to the load in the pan, up to a certain point ; also, that the 
 wire has returned each time to its original length up to the same 
 point, and that beyond that point, known as the limit of 
 elasticity, the elongation is not uniform. 
 
 Repeat the experiments, employing a wire of somewhat 
 larger cross-section, and make the same changes in the weights. 
 Compare the effects on length with those previously determined. 
 Inference. 
 
 Construct a curve from the data obtained, and point out 
 how it proves the law. For method of constructing curve, see 
 Art. 598. 
 
 75. Exercise. Determine the laws governing the deflec- 
 tion of beams. 
 
 Construct of wood an apparatus such as shown in Fig. 36. 
 A and B are pyramidal pieces of hard wood 20 cm. high, stand- 
 ing on the base N, the distance between their upper edges being 
 determined by means of the linear scale S. M is a bar, wood 
 or metal, 1 metre long, 2.5 cm. wide, and 5 cm. thick, whose 
 deflection is to be measured. C is a small clevis made of sheet 
 brass, placed exactly over the centre of the bar, supporting the 
 scale-pan F. RLE is a bent lever made of wire, the weight of 
 which is sufficient to keep its foot in close contact with C as the 
 bar M deflects. Narrow grooves filed in the wire on top of 
 the post H will make it easy to secure it in place by means 
 of wire staples. Freedom of motion must be secured with as 
 little play as possible. K is a scale of equal parts. 
 
THE PROPERTIES OF MATTER. 
 
 53 
 
 Record the reading of the pointer, then keep adding weights 
 and recording the reading till a sufficient number have been 
 made for comparison. Compare the amount of deflection with 
 the weights applied. 
 
 Try a bar of the same material, having double the breadth, 
 and the same thickness as the first. Inference. Try one 
 
 FIG. 36. 
 
 having double the depth, and the same width as the first. 
 Inference. Try one having double the length, but the same 
 width and thickness as the first. Inference. 
 Construct a curve from the data. 
 
 76. Exercise. Determine the laws of elasticity by torsion. 
 
 Construct of wood an apparatus such as is shown in Fig. 37, 
 making L 90 cm. long. W is the wire to be experimented on, 
 the upper end being squared, and fitted snugly into a metal 
 plate A to keep it from turning, the lower end passing through 
 
54 
 
 PRACTICAL PHYSICS, 
 
 the pulley E, and entering a round hole in the base M. The 
 pulley is made with a hub, so that a set screw can be used to 
 clamp it rigidly to the wire. F is a pointer moving over the 
 arc D. H and K are common iron pulleys, over which cords 
 
 from the pulley E draw so 
 that weights placed in the 
 pans twist the wire or rod. 
 The shelves B and C are 
 placed so that the spaces 
 AB, BC, and CD are each 
 equal to 30 cm. Observe 
 the reading of each pointer, 
 then place equal weights in 
 the pans, and observe the 
 change in the readings. 
 Compare the change at B 
 with that at C and at D. 
 How does length affect the 
 amount of twist? Increase 
 the weights in the pans, and 
 determine, from the change 
 in the readings, how the 
 force applied affects the 
 twist. Substitute for W a 
 rod of the same material having a different diameter. Use 
 the same weights, and determine how a change in diameter 
 affects the amount of twist. 
 
 Pi. 37. 
 
THE PROPERTIES OF MATTER. 55 
 
 IX. CAPILLARY ACTION. 
 
 77. Apparatus. Sewing-Needles, small Wooden Balls, 
 Iron Wire, Soap Solution, Glass Rod, Glass Plates, Capillary 
 Tubes, Tumbler, Earthen Plate, Balance, Linear Scale, 
 etc. 
 
 C:> 
 
 78. Exercise. Place a sewing-needle on the surface of a 
 vessel of water. If carefully done, it will float. A hairpin 
 bent up slightly at the points may be used to advantage in 
 letting down the needle so that its two ends touch the water 
 about simultaneously. Observe carefully the shape of the 
 surface of the water about the needle. Estimate as well as 
 you can the area of the cross-section of the depression as com- 
 pared with that of the needle. A body floats on water when it 
 displaces a volume whose weight equals that of the body. 
 Does the needle do it? 
 
 Place two needles on the water in positions parallel to each 
 other, and separated by a few millimetres. Let a drop of 
 alcohol or ether fall on the water between them, and note the 
 effect. 
 
 If the surface of the water is covered with a powder called 
 lycopodium, quite large wires can be floated. 
 
 79. Exercise. Float two wooden balls, of about 15 mm. 
 diameter, near each other on water. Their surfaces should be 
 freed from all oily matter by washing them with a solution of 
 caustic potash. Observe the shape of the surface of the water, 
 and notice how the balls act toward each other. When quite 
 close together, let fall a drop of alcohol on the water between 
 them. 
 
56 
 
 PRACTICAL PHYSICS. 
 
 Coat one of the balls with a thin film of lard, and repeat the 
 experiment. Study the shape of the water surface. 
 Repeat after coating both balls with lard. 
 
 80. Exercise. Construct of No. 24 iron wire a ring 
 6 cm. in diameter, a tetrahedron 4 cm. on each edge, and a 
 cube 5 cm. on each edge, each wire form having a handle 
 attached (Fig. 38). In 400 ccm. of cold water that has been 
 
 FIG. 38. 
 
 previously boiled, put 10 grammes of Castile soap cut up fine, 
 or, better still, sodium oleate. Put this into a bottle, and 
 set it in hot water over a gas flame turned low so as to keep 
 the temperature about constant. Let it remain there an hour, 
 shaking it occasionally till the soap is dissolved. Set aside 
 for several hours in a place where it will not be disturbed, and 
 then pour off the clear liquid, and add to it 270 ccm. of the best 
 glycerine, shaking the whole thoroughly. Suspend in the wire 
 
THE PROPERTIES OF MATTER. 57 
 
 ring a small loop of fine silk thread, and dip it into this soap 
 solution. Break the film in the silk loop by puncturing it with 
 a hot wire, or a piece of blotting-paper, and account for the 
 shape it takes. Dip the other wire forms in this solution, 
 and study the film forms obtained. Blow a soap-bubble with a 
 common clay pipe, detach the bubble, and support it on the 
 wire ring. Bring in contact with the bubble a second ring, and 
 you will be able to draw out the bubble into a cylinder. 
 
 81. Exercise. It is required to measure the tension of a 
 soap film. 
 
 Support horizontally a knitting-needle or stout wire, AB 
 (Fig. 39). Cut from a straight, slender straw a piece of 
 uniform size and 10 cm. long, as CD. Attach to one side 
 and at the ^ 
 
 centre, a i i.m t .uL ,...^^ ..................... o 
 
 light scale- C 
 
 pan made of 
 
 paper. Find 
 
 the weight 
 
 of the straw FIG. 39. 
 
 and the attached pan. 
 
 Hold the straw against the under side of the knitting-neeaie, 
 and with a small brush introduce a layer of the soap solution 
 between them. The tension of the film will now support the 
 straw. Carefully sift fine sand on the pan till the film breaks. 
 The weight of the sand, straw, and pan measures approximately 
 the tension of the film. This divided by twice CD will give 
 the superficial tension of either surface per unit of length. 
 
 82. Exercise. Study the effect of a solution of camphor 
 on surface tension by placing a piece of camphor of the size 
 of the head of a pin on clean cold water, and noticing its 
 
58 PRACTICAL PHYSICS. 
 
 peculiar movements. Touch the water with the finger, slightly 
 oiled by rubbing it on the hair, and mark the effect. Using 
 clean water, study the movements of a drop of a solution of 
 camphor in sulphuric acid. Add other drops, and observe their 
 behavior towards one another. Using clean water, study the 
 action of a drop of a solution of camphor in benzole. Repeat 
 all of these experiments, using warm water in place of cold. 
 
 The effect of camphor films on the surface tension can be 
 learned by covering the surface of the water with lycopodium 
 powder, then lowering a fragment of camphor into the water, 
 and observing the effect that the camphor's touching the 
 water has on the powder. 
 
 83. Exercise. Suspend, by a thread, from a suitable 
 support, a glass rod, so that the lower end dips into a tumbler 
 of water colored with aniline dye or ink, the rod having a 
 vertical position. Study the form of the surface of the water 
 around the rod. 
 
 Repeat the experiment, using a glass rod thinly coated with 
 oil. 
 
 Repeat these experiments, substituting mercury for water. 
 
 Thoroughly clean a strip of zinc by scouring it with a cloth 
 after it has stood a few minutes in dilute sulphuric acid. 
 Suspend it vertically in a dish of mercury. 
 
 Diagram the appearance of the surface of the liquid about 
 the rod in each of these experiments. 
 
 Lift the rod slowly out of the liquid, observe the liquid just 
 as the end of the rod separates from it, and then see if you can 
 account for the various results obtained in these experiments. 
 
 84. Exercise. Cut two plates of glass about 10 cm. 
 square, and thoroughly clean them, In a large dinner-plate, 
 
THE PROPERTIES OF MATTER. 59 
 
 pour some water highly colored with ink or aniline dye. 
 Support one of the plates in a vertical position in the liquid. 
 Examine the surface of the liquid about the plate. Now place 
 in the liquid the second plate, securing it in a position parallel 
 to the first, and separated from it by about 5 mm. Note 
 the position of the surface of the liquid between the plates. 
 Determine the effect of decreasing the distance between the 
 plates. 
 
 Vary the experiment by making the plates touch along two 
 vertical edges, the opposite ones being separated by about 
 2 mm. This is readily done by fitting a piece of wood between 
 the two edges to be kept apart, and then slipping an elastic 
 band around the two plates. 
 
 85. Exercise. Determine the laws of capillary action. 
 
 Cut three capillary tubes of different diameters, 10 cm. long. 
 Measure their diameters as in Art. 34. Construct a paper 
 scale graduated to half -millimetres, cutting one end to a 
 V shape, the zero of the scale being the point of the V. Coat 
 the scale with transparent varnish, or with a thin film of 
 paraffine. Fasten a tube to the scale by means of rubber 
 bands, and then support the apparatus in a vertical position so 
 that the tube dips into water, the zero of the scale just touching 
 the water. Now raise the vessel containing the liquid about 
 1 cm., and then lower it to its original position in order to 
 wet the interior of the tube with the liquid. Using a 
 pocket lens to insure greater accuracy, read off the height 
 of the liquid in the tube. This reading should be taken 
 to the bottom of the meniscus, and increased by one-sixth 
 of the diameter of the tube. When the heights have been 
 ascertained for the different tubes, multiply each result by the 
 diameter of the corresponding tube. If the measurements 
 
60 
 
 PRACTICAL PHYSICS. 
 
 have all been carefully made, the products will be found to be 
 nearly equal. What law of capillarity is here shown? 
 
 Using one of the tubes, determine the heights to which the 
 following liquids rise : alcohol, benzine, turpentine, etc. The 
 tube must be thoroughly cleaned after each experiment (see 
 Art. 34) , and the inner surface must also be wet with the liquid 
 employed, as was done in the case of water. 
 
 A strip of plain sheet-metal may be used instead of the 
 graduated paper scale. The position of the lowest point of 
 the meniscus might then be carefully marked on it with a 
 sharp-pointed instrument, and the distance afterwards meas- 
 ured with the dividers and scale. 
 
 Enter the results in the note-book as follows : 
 
 CAPILLARY MEASUREMENTS. 
 
 Problem. Determination of laws governing capillary action. Sept. 
 20, 1888. 
 
 Method. [To the pupil. Give brief summary of the process 
 used.] 
 
 Results. 
 
 
 
 
 
 
 a 
 
 
 
 
 
 
 & 
 
 jj 
 
 
 
 >> 
 
 3 
 
 1 
 
 8 
 
 4 
 I 
 
 s 
 
 V 
 
 1 
 
 
 2 
 
 
 il 
 
 r 
 
 Weight of Vess 
 
 > 3 
 U 
 
 11 
 
 bflT3 
 
 | S 
 
 Weight of Merc 
 
 Area of Cross-S( 
 
 Diameter of Tu 
 
 Height Water ri 
 
 Height correctec 
 Meniscus. 
 
 Product of Dian 
 by Height. 
 
 First tube .... 
 
 
 
 
 
 
 
 
 
 
 Second tube . . . 
 
 
 
 
 
 
 
 
 
 
 Third tube .... 
 
 
 
 
 
 
 
 
 
 
THE PROPERTIES OF MATTER. 61 
 
 X. SOLUBILITY. 
 
 86. Apparatus. Small Flasks, Test-Tubes, Thermom- 
 eter, and Balance. 
 
 87. Exercise. Determine the solubilit}^ of a substance, 
 that is, the number of grammes which one gramme of the 
 solvent will dissolve, the solution to be saturated. 
 
 Fill a small flask, or a large test-tube, half full of the solvent. 
 Add, in a powdered state, a quantity of the substance to be 
 dissolved, being sure to add more than will dissolve. Now 
 raise the temperature somewhat higher than that at which the 
 solubility is to be determined ; if water, it may be brought 
 to the boiling-point. When the undissolved part no longer 
 diminishes in quantity, remove from over the source of heat, 
 and cool it to the required temperature by placing the vessel in 
 melting ice. When the required temperature is reached, drop 
 in the solution a crystal of the substance, and there will be 
 precipitated all the salt in solution over and above that held in 
 solution at the saturation point. Pour off into a small Florence 
 flask of known weight some of this solution, weigh it accurately, 
 and then, by placing it on a sand-bath, over a lamp or steam- 
 coil, evaporate all the water, even that of crystallization, being 
 careful not to hasten too rapidly the evaporation for fear of 
 loss of material through " spitting." When thoroughly dry, 
 weigh the residue, and obtain the weight of the substance 
 dissolved. Divide the weight, in grammes, of the amount of 
 the substance dissolved, by the amount of the solvent 
 evaporated out of the solution, and the solubility of the 
 substance is obtained. 
 
62 PRACTICAL PHYSICS. 
 
 88. Exercise. Find the solubility of alum in water at 
 C., 20 C., 40 C., etc., to 100 C. Construct the curve of 
 solubility. See Art. 598. 
 
 89. Exercise. Find the solubility of potassium chloride 
 in water at C., 20 C., 40 C., etc., to 100 C. Construct the 
 curve of solubility. 
 
 90. Exercise. Determine the solubility of potassium ni- 
 trate in water at 0C., 20 C., 40 C., etc., to 100C. Construct 
 the curve of solubility. 
 
 91. Exercise. Determine the solubility of common salt 
 in water at C., 20 C., 40 C., etc., to 100 C. Construct the 
 curve of solubility. 
 
 92. Exercise. Determine the solubility of alum, potas- 
 sium chloride, potassium nitrate, and common salt, in alcohol 
 (95 per cent), at 20 C. 
 
 93. Exercise. Determine the solubility of potassium 
 sulphate in water at the temperature of the room ; also of 
 sodium nitrate. Finally, determine the solubility of sodium 
 nitrate in the saturated solution of potassium sulphate. 
 
THE PROPERTIES OF MATTER. 
 
 63 
 
 XI. DIFFUSION. 
 
 94. Apparatus. Test-Tubes, Thistle-Tubes, Battery-Jar, 
 Four-Ounce Bottle, Parchment Paper, Dialyzer, Porous Cup, 
 Large Glass Tube, Sheet Rubber, etc. 
 
 full of 
 in the 
 
 95. Exercise. Fill a large test-tube two-thirds 
 water colored with blue litmus. Place a thistle-tube 
 test-tube (Fig. 40), having it reach to the bot- 
 tom, and pour into it a few drops of sulphuric 
 acid. A reddish color will be seen at the 
 bottom of the test-tube. Set the test-tube to 
 one side, and record, from time to time, the 
 position of the upper surface of the red-colored 
 liquid. 
 
 Into a common test-tube, pour a little blue 
 litmus solution, and add to it a drop of sulphuric 
 acid by stirring, observing the effect on the 
 color. Apply the truth taught by this to the ex- 
 planation of the first. Account for the surface 
 which separates the colored liquids not being 
 stationary. 
 
 96. Exercise. Measure the Tate of diffu- 
 sion of a substance in water. 
 
 Obtain a cylindrical vessel of about 2 litres 
 capacity, a common battery-jar will answer; a 
 wide-mouthed bottle of about 4 ounces capacity, to be known 
 as the diffusion-bottle ; and a solution of the salt under investi- 
 gation of some known strength, say, 6 parts by weight in 100 
 parts of water. 
 
64 PRACTICAL PHYSICS. 
 
 Fill the diffusion-bottle with the solution to be tested up to 
 the brim, and place it on the bottom of the large cylindrical 
 jar. Then pour water into this jar till it rises about 3 mm. 
 above the top of the diffusion-bottle (Fig. 41). Let the 
 apparatus remain undisturbed for twenty- 
 four hours, and at a constant temperature. 
 Then, by means of a siphon, run off the 
 contents of the jar into a basin, in which 
 wash off the outside of the diffusion-bottle 
 by means of a little jet of pure water, first 
 taking the precaution to place a small plate 
 of glass over the mouth so as not to spill 
 any of its contents into the basin. Evaporate 
 to dry ness the solution in the basin, and determine the weight 
 of the residue. Comparing this with the result obtained by 
 using a solution of some other salt of the same strength will 
 give their relative diffusion. 
 
 97. Exercise. Compare the rates of diffusion of potassium 
 chloride and potassium sulphate. 
 
 98. Exercise. Ascertain if the strength of the solution in 
 any way affects the rate of diffusion by using four solutions of 
 common salt made by dissolving 1, 2, 3, and 4 parts of salt in 
 100 parts of water by weight. 
 
 These four solutions may be tested simultaneously by select- 
 ing jars and bottles of the same size. The diffusion-bottles 
 especially must have the same capacity, and the openings must 
 be of the same size. 
 
 99. Exercise. Wet a piece of parchment paper, and tie 
 it across the top of a large thistle-tube. Pour down the stem 
 
THE PROPERTIES OF MATTER. 
 
 65 
 
 of the thistle- tube a concentrated solution of copper sulphate, 
 spilling none on the outside of it. Now support the tube by 
 means of a burette-holder in a beaker of water, so as to have 
 the liquids at the same level on both sides of the tube to prevent 
 hydrostatic pressure. Set aside for a few hours, occasionally 
 observing the relative levels of the two liquids. Explain. 
 
 100. Exercise. Set up an apparatus similar to that of 
 the last experiment, and substitute a thin starch paste for the 
 salt solution. Ascertain whether any of the starch passes 
 through the parchment by testing the water on the outside 
 with iodine water. A blue color would indicate that there was 
 starch present. Iodine water is made by dissolving iodine in 
 water. 
 
 101. Exercise. Separate a mixed solution of common 
 salt and starch. 
 
 Make a wooden hoop about 8 cm. 
 in diameter and 5 cm. deep. Stretch 
 across it a piece of parchment paper, 
 making a shallow tray. Such an ap- 
 paratus is known as a Dialyzer. Pour 
 the given mixture into this tray, and 
 float it on pure water in a large battery- 
 jar or suitable vessel. Set aside for a 
 few da} r s, and then test the liquid in 
 the jar for starch, as in Art. 100, and 
 also for salt, by adding a little of it to 
 a dilute solution of silver nitrate. A flocculent white precipitate, 
 changing, when exposed to light, to a dirty pink color, would 
 indicate the presence of salt. Pure distilled or rain water must 
 be used. 
 
 FIG. 42. 
 
66 
 
 PRACTICAL PHYSICS. 
 
 A good form can be made by cutting off a large bottle 
 (see Appendix, p. 354) about 5 cm. below the neck (Fig. 
 42). 
 
 102. Exercise. Cement a small porous battery-cup to a 
 funnel-tube with sealing-wax, making it 
 
 air-tight at the line of junction. Attach 
 the diffusion-tube to a two-necked flask 
 which has a jet- tube extending through 
 the second neck, and reaching below the 
 surface of some water contained in the 
 flask (Fig. 43). Fill a large bell-jar 
 with hydrogen, and invert it over the 
 porous cup. Account for what takes 
 place. Now remove the jar from over 
 the porous cup, and note the effect. 
 Explain. 
 
 For method of preparing hydrogen, 
 consult " Shepard's Chemistry," Exp. 
 24. 
 
 103. Exercise. Determine the rate FIG. 43. 
 of diffusion of a gas. 
 
 Select a glass tube about 20 cm. long and 25 mm. internal 
 diameter. By means of emery-powder and water on an old 
 stove-lid or piece of flag-stone, grind one end so that a glass 
 plate will close it gas-tight. Mix plaster-of -Paris with water 
 to a thin paste, and out of it, on a glass plate, cast a disk 
 about 3 mm. thick. When thoroughly dry, cut it with a 
 sharp knife to fit the ground end of the tube, cementing it 
 in with sealing-wax applied to its edges. The outer surface 
 of the plaster plug should be about 2 mm. below the edge of 
 
THE PROPERTIES OF MATTER. 67 
 
 the tube. Avoid getting any wax on the face of the plug. 
 Paste a millimetre scale lengthwise of the tube, having its zero 
 at the inner surface of the plaster plug, and give it a coat of 
 thin varnish to protect it from water. It would be preferable 
 to etch a scale on the glass. (See Art. 14.) Over the closed 
 end of the tube, place a glass plate coated with a film of lard 
 to close it gas-tight; then, holding the open end of the tube in 
 the water of the pneumatic trough with one arm of a U-shaped 
 glass tube passing up within the tube nearly to the plug, lower 
 the cylinder slowly into the water. The air will escape through 
 the U-tube, and the cylinder will be nearly full of water. If the 
 plaster disk should get wet, it will have to be dried before 
 proceeding further with the experiment. Remove the U-tube 
 by dropping it down into the water- tank. Now take the 
 reading of the water-level in the tube to obtain the amount of 
 air left in it. Then, with a rubber tube, introduce the gas to 
 be examined, filling the tube down to the level of the water in 
 the tank. Take the reading again ; the difference of the two 
 will be a measure of the amount of gas. Now remove the 
 glass cap, and, as the water rises in the tube, lower the tube to 
 keep the level the same without as within to avoid hydrostatic 
 pressure. When the water ceases to rise, take the reading of 
 the water-level. 
 
 Let us suppose that the first reading was 2, and the second 
 100; then 98 measures the amount of gas introduced, and 2 
 measures the amount of air left in. If the last reading taken 
 was 25, then 25 2, or 23, measures the air which passed 
 through the porous plug, as against 98, which measures the 
 amount of gas which passed out in the same time. Hence 
 ff = 4.26 is the ratio of the diffusion of the gas under 
 examination to that of air. 
 
68 
 
 PRACTICAL PHYSICS. 
 
 104. Exercise. Determine the rate of diffusion of hydro- 
 gen ; also of oxygen. 
 
 For method of preparing oxygen, consult " Shepard's Chem- 
 istry," Exp. 7. 
 
 105. Exercise. Tie a rubber membrane 
 over the mouth of a glass vessel filled with 
 oxygen gas, and place it under a bell-jar filled 
 with hydrogen gas, standing on a glass plate. 
 Account for what takes place. Try air and 
 common illuminating gas. 
 
 106. Exercise. Fill two wide-mouthed bot- 
 tles with hydrogen and oxygen respectively, having 
 previously fitted to them perforated corks through 
 which passes a glass tube about 60 cm. long. 
 After connecting these two bottles by the glass 
 tube, set them in a vertical position (Fig. 44), 
 with the one containing the hydrogen uppermost. FIG. 44. 
 After half an hour, remove the corks, and apply 
 a lighted taper. If a loud explosion follows, it indicates 
 that the gases have mixed. Why place the hydrogen-jar 
 uppermost? 
 
MECHANICS OF SOLIDS. 69 
 
 CHAPTER II. 
 
 MECHANICS OF SOLIDS. 
 I. LAWS OF MOTION. 
 
 107. Apparatus. Wooden, Lead, and Glass Balls, Air- 
 Fump, Spring-Balances, Electro-Magnet, and certain special 
 appliances to be made in accordance with directions given 
 hereafter. 
 
 108. Exercise. Procure two balls of light wood of about 
 25 mm. diameter, place one of them near one end of a strip of 
 common hemp matting stretched on the floor, and suspend the 
 other by a string from some suitable support so placed that 
 the ball just touches the one resting on the matting at a point 
 a little above the extremity of a horizontal diameter ; that is. 
 the suspended ball must swing clear of the floor. Now pull to 
 one side the suspended ball till it is, say, 15 cm. from the floor, 
 and let it fall toward the other ball, striking it, and setting it 
 in motion. Measure the distance the ball rolls on the matting 
 before stopping. Obtain the average of several trials. 
 
 Repeat the experiment, substituting a piece of carpet for the 
 matting. The suspended ball must be raised the same distance 
 as before, in order that the force of the blow given to the ball 
 may be the same as before. 
 
 Repeat the experiment on the floor; also try as smooth a 
 surface as may be available. Tabulate all the results. 
 
70 
 
 PRACTICAL PHYSICS. 
 
 On comparing the distances the ball moves in the different 
 cases, under equal impulses, with the character of the surfaces 
 on which it rolls, to what conclusion do you come? What 
 would you infer would be the result if a surface offering no 
 resistance were used? 
 
 109. Exercise. Find the resultant of two forces acting 
 at an angle on a body at a point. 
 
 Procure two good spring-balances graduated to quarter- 
 pounds, and a weight of about 10 pounds. Insert screws, at 
 
 FIG. 45. 
 
 Intervals of 3 or 4 inches in the frame, about one of the upper 
 corners of the blackboard, for the attachment of wires to which 
 the balances are to be fastened. The hooks of the balances 
 are fastened to a small ring to which is also attached the known 
 weight (Fig. 45) . Trace lines of direction along the wires with 
 a pencil. If accurately drawn, these will pass through the centre 
 of the ring on being produced. After reading the indications of 
 the balances, remove them, extend the lines, and lay off on 
 
MECHANICS OF SOLIDS. 71 
 
 them as many units of length as there are units of weight 
 indicated by the balances respectively. Through the points 
 thus located, draw parallels, making a parallelogram of which 
 the line of direction of the weight will be the diagonal. On 
 measuring this diagonal, it will be found to be 10 units long, 
 thus showing, that, if we represent by lines the directions and 
 the intensities of two forces acting at an angle, the diagonal 
 of the parallelogram of which these lines are adjacent sides 
 represents both the direction and the intensity of the result- 
 ant. 
 
 Attach the balances at different points in the frame of the 
 board, and test the law stated above. Ascertain the effect of 
 making the angle between the directions of the supporting wires 
 very small. What do the balances indicate when both are 
 attached to the same point, that is, the supporting wires are 
 parallel ? What does this show to be the value of the resultant 
 of parallel forces? Increase the angle between the lines of 
 direction of the two supporting wires, and determine the effect 
 on the readings of the balances. Make the angle as large as 
 possible. What would you infer from the last experiment 
 would be the effect if the supporting wires could be made to 
 act in exactly opposite directions? 
 
 110. Exercise. Procure three balls of wood of about 
 25 mm. diameter each, and perforated with a small hole. 
 Attach each to a cord about 60 cm. long, and then suspend the 
 balls from a piece of board supported in a clamp by inserting 
 the cords through holes drilled in the board, the distances 
 between them being such that each suspended ball just touches 
 the other two. Now draw off two of the balls to equal 
 distances, and let them fall at the same instant against the 
 ball at rest. Observe the direction of its motion. For one 
 
72 PRACTICAL PHYSICS. 
 
 of the balls, substitute an iron one of the same size, and 
 repeat the experiment. Compare the direction in which the 
 third ball moves, with that obtained in the first case. Ascer- 
 tain the effect of changing the angle between the lines 
 traversed by the falling balls. What is the teaching of this 
 experiment? 
 
 Glass balls may be substituted for the wooden ones, the cord 
 being attached to the ball by tying it into a stout cloth 
 loop cemented to the ball by means of a pitch cement. See 
 p. 357. 
 
 111. Exercise. Cut out of a board a circular piece 30 cm. 
 in diameter, and divide it by radii into five-degree sections 
 (Fig. 46), and mount it on a wooden 
 support. Make four wooden blocks 
 of the form shown in Fig. 47, each 
 carrying a pulley about 3 cm. in diam- 
 eter. With small iron clamps, attach 
 the four pulleys at different places 
 on the circular board. Knot together 
 four flexible cords, and place them so 
 as to draw over the pulleys. To the 
 free end of 
 
 FIG. 46. , 
 
 these cords, 
 
 attach weights, adjusting both the 
 weights and the position of the pul- 
 leys so that the knot rests over the 
 centre of the board. Tapping the ap- FDS - 47> 
 
 paratus with the finger will assist in overcoming friction. The 
 weights may be cut out of sheet lead, and have the form shown 
 in Fig. 48, or scale-pans can be used, equal lead balls serving as 
 weights. 
 
MECHANICS OF SOLIDS. 
 
 73 
 
 FIG. 48. 
 
 Fiu. 49. 
 
 Now draw a circle on a piece of paper, lay off on it the 
 
 position of the cords, and on each 
 
 line measure off as many units of 
 
 distance as there are unit-weights 
 attached (Fig. 
 49). Find by 
 the rules given 
 for the compo- 
 sition of forces 
 the resultant 
 of any three of 
 the forces rep- 
 resented, and 
 
 compare this resultant with the fourth force as to direction 
 
 and intensity. Inference. 
 
 Vary the positions of the pulleys, and the ratios of the 
 
 weights. 
 
 112. Exercise. Determine the resultant of two or more 
 parallel forces acting in the 
 same direction. 
 
 Prepare a rectangular bar 
 27 cm. long, and having the 
 uniform cross-section of 1 
 by 2 cm. At the middle, 
 and at intervals 3 cm. each 
 side of the middle, insert 
 equal pieces of brass wire 
 of about 2 mm. diameter 
 and 3 cm. long (Fig. 50). 
 
 In each end, insert a piece of brass wire on which a small 
 lead ball screws, to serve as adjusting weights to correct for 
 
74 PRACTICAL PHYSICS. 
 
 inequalities in the wooden bar. Construct a small clevis out of 
 brass wire to be used as a support to the bar. With common 
 bullet-moulds, cast a quantity of lead balls. Drill small holes 
 through them, and attach small wire hooks so that the balls 
 may be attached to the bar. or to each other, as desired. A 
 small pulley, a stout cord with a small ring or scale-pan 
 attached to one end, and a suitable support, will be needed to 
 complete the apparatus. Now, with the clevis, hang the bar 
 by the middle pin, and counterpoise it over the pulley by means 
 of weights. Move the adjusting weights till the bar is hori- 
 zontal. Add weights at two points on opposite sides of the 
 clevis, and place a sufficient number in the pan to balance the 
 loaded bar. Compare the number added to the pan with 
 the number attached to the bar. Observe the position of the 
 clevis, as well as the positions of the pins to which the weights 
 are attached, and then frame a law expressing these relations. 
 Test the law by varying the positions and values of the weights. 
 
 A second device for determining the resultant can be con- 
 structed as follows : 
 
 Procure a rectangular bar 1 metre by 5 cm. by 3 cm., of pine, 
 graduate it to centimetres, screw on each end an ear made of 
 sheet brass or iron, and suspend it by these ears in a horizontal 
 position from the hooks of two spring- balances secured to some 
 suitable support, as the edge of the laboratory table. Take 
 the reading of each balance, so as to know what allowance to 
 make for the weight of the bar. Now place on the bar a 
 sliding-weight of known value, sa} T 5 kg., and take the readings 
 of the balances for different positions of the weight on the bar. 
 Correct the readings for the weight of the bar. Examine the 
 results for evidence of any relation between the corrected 
 readings and the position of the weight. Compare the readings 
 with the value of the weight. 
 
MECHANICS OF SOLIDS. 75 
 
 113. Exercise. Make two lead balls of about 3 cm. 
 diameter. To do this, make a plaster-of-Paris mould, using 
 a wooden ball as a pattern. 
 
 Suspend them by cords from 
 a horizontal bar so as just to 
 touch (Fig. 51). Now draw 
 one of them to one side, and 
 let it fall against the other. 
 How much matter moves 
 after the impact, and how far 
 does it move as compared 
 with the distance the ball 
 moved before the impact? 
 Has the amount of motion 
 been altered by the impact? 
 What has been changed? 
 What principles are sug- 
 gested by this experiment? 
 
 Raise both balls equal dis- 
 tances in opposite direction, FIG. 51. 
 and let them collide, recording the effect. Is this result 
 inconsistent with the laws of motion? Explain. 
 
 Bags of sand can be used as substitutes for the lead 
 balls. 
 
 114. Exercise. Suspend two elastic balls, ivory, wood, 
 or glass, by cords, so as to swing in front of a graduated arc 
 (Fig. 51) for convenience in comparing distances the balls 
 move through. The balls, when at rest, should just touch 
 each other. This arc may be cut out of cardboard, and equal 
 distances measured off on it with a pair of compasses. Raise 
 one of the balls through any number of spaces, and let it fall 
 
76 PRACTICAL PHYSICS 
 
 against the other. Observe the motion of the balls after 
 impact. Harmonize the result with the third law of motion. 
 Raise both balls through equal distances in opposite directions, 
 and let them strike. Explain the result. Raise one through 
 twice the distance of the other. Explain. 
 
 Repeat these experiments after fastening neatly around each 
 ball a piece of flannel. Explain. Try lead balls. Try iron 
 balls. 
 
 Are the balls perfectly elastic? What effects would be 
 produced by perfectly elastic balls? What facts support this 
 conclusion? 
 
 For a method of attaching cords to glass balls, see Art. 110. 
 It is preferable to suspend each ball by two cords, the ball 
 forming the point of a V, as the balls will then swing in a 
 plane. 
 
 115. Exercise. Suspend four or five highly elastic balls 
 by cords, from a frame, in a manner similar to that described 
 in Art. 114. Raise one of the balls through an observed 
 distance on the scale, and let it fall against the adjacent one. 
 Describe and account for the effect produced. 
 
 Substitute lead balls for the ones just used, or else cover 
 them neatly with flannel or cotton-wool, and repeat the 
 experiment. Why the difference? What would you infer 
 would be the result if perfectly elastic balls were em- 
 ployed ? 
 
 Consecutive balls must just touch each other when at 
 rest. 
 
 116. Exercise. Cut out of a board a semicircular piece 
 having a radius of about 24 cm. At the centre of the 
 semicircle, fasten with its face in the diameter a small 
 
MECHANICS OF SOLIDS. 
 
 11 
 
 T 
 
 rectangular piece of polished marble. Draw radial lines divid- 
 ing the circle into ten-degree spaces. ! i 
 Suspend from a wire an ivory or other 
 highly elastic ball, as glass, of about 
 2 cm. diameter, so as just to touch the 
 marble surface exactly at the centre of 
 the semicircular board (Fig. 52) . Stand 
 a common crayon near the outer end of 
 any of the radial lines ; draw off the 
 ball, and release it over different radial 
 lines till you find one by trial so situ- 
 ated, that, after the ball is reflected 
 from the marble, it overturns the crayon. 
 What law expresses the relation you find 
 existing between the angles of incidence and reflection ? Try a 
 lead ball. Inference. 
 
 FIG. 52. 
 
 II. CENTRE OF MASS. STABILITY. 
 
 117. Apparatus. Cardboard, Round-bottomed Flask, 
 Double Cone, Cube, Prism, Pyramid, Pulley, etc. 
 
 118. Exercise. Find the centre of mass of a cardboard 
 figure. 
 
 Cut a slot in a lead bullet with a knife ; in the slot place a 
 thread, and then close it up with a blow from a hammer. Cut 
 from a sheet of cardboard a piece of any desired shape, and 
 then suspend it from the edge of the table by inserting a fine 
 needle through the cardboard as close as possible to the edge. 
 Be sure that the figure is free to turn freely about the support. 
 Now hang the bullet alongside of this cardboard figure, letting 
 
78 
 
 PRACTICAL PHYSICS. 
 
 FIG. 53. 
 
 the string press gently against the needle (Fig. 53). Mark 
 with a sharp-pointed pencil a point below the needle, and 
 alongside of the thread. Through this point 
 and the point of suspension, draw a straight 
 line. In the same manner, locate a second 
 line by suspending the cardboard from an- 
 other point. Balance the cardboard figure 
 on the point of a needle stuck into a cork 
 for a base, and compare the position of the 
 point when equilibrium is secured with 
 the point of intersection of the two lines 
 drawn. What position does the centre of 
 mass sustain to the point of suspension 
 when the cardboard hung from the needle 
 in the edge of the table? 
 
 119. Exercise. Find the centre of mass of the following 
 cardboard figures : Square, rhombus, rectangle, circle, and 
 triangle. What simple relation does this point sustain, in each 
 case, to the form of the figure, enabling one to locate it by the 
 aid of the ruler alone ? 
 
 If the rectilinear figures are suspended by their corners, the 
 law in each case will be readily seen. 
 
 120. Exercise. Put a quantity of shot in a round- 
 bottomed flask. Then fill the flask up with paper so that the 
 shot will not move around on tipping the flask. Now overturn 
 the flask, comparing its action on being released with that of 
 one not so loaded. How is the centre of mass affected on 
 overturning the flask? Where is the centre of mass when the 
 flask is at rest? 
 
MECHANICS OF SOLIDS. 79 
 
 121. Exercise. Thrust a darning-needle, eye first, into a 
 large cork, and try to make the apparatus maintain a vertical 
 position, the needle-point resting on the point of a pencil. 
 Account for the failure. Now thrust the 
 
 blades of two heavy-handled knives into 
 
 the cork (Fig. 54) on opposite sides, so as 
 
 to form with each other an inverted V. 
 
 Ascertain if the apparatus will now stand 
 
 on the end of the pencil. Explain. Would 
 
 it answer as well to have the knives perpen- FlG - 54 - 
 
 dicular to the needle ? Why ? Whenever the apparatus stands 
 
 alone, where is the centre of mass? 
 
 122. Exercise. Turn out of wood a double cone 20 cm. 
 long and 8 cm. in diameter. Make a V-shaped track (Fig. 55) 
 out of two thin strips of board for the cone to roll on, giving 
 it a length of about one metre, with the point 3 cm. lower than 
 
 the wide end. Now place 
 the double cone at the 
 point of the track, and it 
 will slowly roll toward the 
 higher end. Does the cone 
 roll up hill? Where is the 
 
 FIG. 55. 
 
 centre of mass of the cone ? 
 
 Find, by measurement, whether the centre of mass has been 
 raised or lowered by the motion. 
 
 123. Exercise. Determine the law governing the stability 
 of bodies. 
 
 Cut out of hard wood, the heavier the better, a cube 1 dm. 
 on each edge, a rectangular prism 1 by 1 by 2 dm., and a right 
 pyramid whose base is 1 dm. square, and whose altitude is 
 
80 
 
 PEACTICAL PHYSICS. 
 
 2 dm. Insert a small screw-eye in a face of each solid opposite 
 the centre of mass, and to it fasten a stout flexible cord. 
 Stretch the cord over a pulley clamped to some adjustable 
 vertical support, attach a scale-pan of known weight, and then 
 add weights till the solid begins to overturn. In this way, 
 compare the stability of these several solids as they rest on 
 different faces successively, and generalize a law from the 
 results. The height of the pulley should be such as to 
 make the cord horizontal between the pulley and the solid ; 
 likewise, the base of the block must be secured against 
 slipping. 
 
 III. CURVILINEAR MOTION. 
 
 124. Apparatus. The Whirling-Machine and its Attach- 
 ments. 
 
 125. Exercise. Attach to a whirling-machine (Fig. 56) a 
 strong frame, across which is stretched a wire carrying two 
 equal balls free to slide on it, and connected by a thread. 
 
 FIG. 56. 
 
 Find, by trial, a position for these balls on the wire, such that, 
 when the apparatus is rapidly rotated, the balls do not slide 
 toward the end of the wire. 
 
MECHANICS OF SOLIDS. 81 
 
 Repeat the experiment, using two unequal balls of known 
 weights. How does the relation of the weights of the balls 
 compare with that of their distances from the axis of rotation? 
 What law of curvilinear motion is here illustrated ? 
 
 126. Exercise. Determine the laws for curvilinear motion. 
 
 Get a good mechanic to construct an attachment for the 
 whirling-machine, of the form shown in the figure (Fig. 57), in 
 which a ball is arranged so as to be clamped to a string which 
 draws under a pulley, and thus lifts a weight whenever the ball 
 moves away from the centre of rotation. The weights are lead 
 disks of equal weight, provided with a slot, so that they can be 
 placed on the platform attached to the cord. The 
 weight of this platform may be taken as the unit 
 weight. The centre of the weights must be exactly 
 over the centre of rotation. Let us suppose that 
 the ball is clamped at 20 cm. from the axis, and a 
 load of 3 units is placed on the platform, making 
 4 units in all. Determine the 
 number of revolutions the drive- 
 wheel of the machine makes in, 
 
 FIG. 57. 
 
 say, 10 seconds, in order just to 
 
 raise the load. As soon as the weight is seen to lift, then 
 maintain a constant speed, and determine the rate. Use the 
 average of several trials. Now replace the ball by one twice 
 as heavy, and at the same distance from the axis ; make the 
 total load to be moved 8 of the unit- weights, and find the speed 
 necessary to lift it. The number of revolutions will be found 
 to be the same in each case. Repeat, using other distances 
 and other weights, tabulating the results. Express as a law 
 the relation between mass and centripetal force exhibited by 
 these experiments. 
 
82 PRACTICAL PHYSICS. 
 
 Again, set the small ball at 8 cm. from the axis, and deter- 
 mine, as before, the speed of the drive- wheel necessary to lift 
 a load of 2 units. Compare it with that necessary to lift a 
 load of 4 units when the ball is 16 cm. from the centre. Also 
 compare it with that necessary to lift a load of 6 units when 
 the ball is 24 cm. from the centre. How do the number of 
 revolutions compare? Express as a law the relation shown 
 to exist between the radius of the circle traversed by the ball, 
 and the centripetal force or tension on the cord. 
 
 Again, set the small ball at 15 cm. from the axis, and 
 determine the speed necessary to lift a load of 2 units. 
 Compare this speed with that required to lift a load of 8 
 units. What measures the centripetal force in each case? 
 Express as a law the relation existing between speed, or time 
 of rotation, and centripetal force. 
 
 127. Exercise. Attach to the whirling-machine a heavy 
 ring having a diameter of about 30 cm. Suspend by a stout 
 cord from the top of the ring, so as to hang in the axis of 
 rotation, a small globe (Fig. 58), such as is 
 used for aquariums, in which has been placed 
 some mercury and some colored water. Rotate 
 the apparatus, and observe the behavior of the 
 liquids. Explain. 
 
 Suspend in a similar manner, in succession, 
 
 Fio. 58. 
 
 the following : A skein of thread, a loop formed 
 of a short chain, a prolate spheroid of wood, an oblate 
 spheroid, a sphere, a double cone, and a cylinder. 
 
 Suspend these geometrical solids from the extremities of 
 different axes, and ascertain if it makes any difference. Is 
 there any law regulating their behavior ? 
 
MECHANICS OF SOLIDS. 
 
 83 
 
 IV. ACCELERATED MOTION. GRAVITATION. 
 PROJECTILES. 
 
 128. Apparatus. Smooth Plank, Atwood's Machine, 
 Iron Balls, Electro-Magnets, Spring-Gun, etc. 
 
 129. Exercise. Determine the laws of accelerated motion. 
 Take a straight plank about 5 metres long, and tack along 
 
 the centre of it two strips, each having a cross-section of 
 1 cm. square, forming a narrow straight groove with sharp even 
 edges not over 1 cm. wide. Graduate one of these strips in 
 centimetres. Raise one end of the plank 40 cm. higher than 
 the other (Fig. 59). 
 Suspend a heavy ball 
 by a thread 1 metre 
 long, for a measurer 
 of time. With a little 
 adjusting, this pendu- 
 lum will vibrate sec- 
 onds. Now set the 
 pendulum in vibra- 
 tion, and at the instant the ball reaches the lowest point 
 of its arc, let an iron ball of about 3 cm. diameter roll down 
 the groove on the plank, starting from the zero of the scale 
 on the plank. Mark the point reached by the ball at the 
 end of the first second. Make several determinations of this 
 distance. In like manner, find the distance passed over in 2, 
 3, and 4 seconds respectively. What is the relation between 
 the distance passed over in successive seconds? How is the 
 total distance passed over at the end of any second related to 
 the number of that second? How much is the acceleration? 
 
 Fia. 59. 
 
84 
 
 PRACTICAL PHYSICS. 
 
 By what number would you multiply the acceleration in this 
 case to give that for a body falling freely in space ? Compare 
 the result with the true value. Point out any source of error 
 in the above method of determining the acceleration. 
 
 A stout wire stretched tightly across the room (Fig. 60) may 
 be substituted for the plank. A simple way to stretch the wire 
 is to fasten the upper end of it to the appliance commonly used 
 in tightening the saw in the ordinary buck-saw frame. Place 
 on this wire a pulley carrying a weight suspended from the 
 under side. Parallel to the wire, and at a few centimetres 
 
 /&\ above it, stretch a stout 
 ^ cord. Pieces of paper 
 *- suspended from this so 
 
 as to be moved by the 
 pulley as it runs down 
 the inclined wire will 
 serve to measure dis- 
 tance. 
 
 A metronome, such 
 as musicians emplo} 7 in 
 measuring time, will be 
 found very serviceable in this experiment. 
 
 As it is rather difficult to start the ball and pendulum 
 simultaneously, it is recommended to hold the ball at the top 
 of the inclined plane by means of an electro-magnet, with a 
 piece of paper over the pole, the battery-circuit being closed 
 by the iron bob of the pendulum being held in contact 
 with the battery-poles when at the highest point of its path 
 or swing. Then, on releasing the pendulum, the circuit will 
 be broken, and hence the ball on the plane will be released 
 at the same moment. The electro-magnet may be made 
 by winding two or three layers of insulated copper wire 
 
 FIG. 60. 
 
MECHANICS OF SOLIDS. 
 
 85 
 
 No. 16, on a piece of annealed iron 8 cm. long and 2 cm. in 
 diameter. 
 
 The accuracy of the distance traversed by the ball can be 
 tested by placing a ruler in the groove at the point, and then 
 ascertaining if the click of the ball against the ruler is 
 coincident with the expiration of the time as indicated by 
 the pendulum. 
 
 130. Exercise. Determine the laws of accelerated motion 
 
 b} 7 means of an At wood's machine. 
 
 A very efficient Atwood's machine may be made by a careful 
 
 mechanic as follows : 
 
 Mount an accurately balanced metal or wooden wheel of 
 
 20 cm. diameter on the top of a heavy wooden column 
 
 (Fig. 61) set firmly into a tri- 
 angular piece of plank, through 
 which pass three wood or iron 
 screws to serve as levelling- 
 screws. A fine silk cord passes 
 over the wheel, carrying two 
 weights at its extremities. On 
 the face of the column, graduate 
 a centimetre scale 1.5 metre 
 long, with the zero about 2 cm. 
 below the lowest point of the 
 wheel. Construct out of brass 
 or iron a ring and a shelf, each 
 provided with a clamp, so that 
 they may be fastened to the 
 column at any desired point in 
 the path traversed by one of the 
 
 weights. The weights can be made of lead or brass, and 
 
86 PRACTICAL PHYSICS. 
 
 should be slotted disks of known weight. The platform of 
 one of the weights must be made of iron in order that it may 
 be attracted by the electro-magnet placed directly under it on 
 the base. A metronome or clock beating half-seconds, so 
 arranged that it can be put in circuit with a battery and the 
 electro-magnet, will be found very desirable, as it will enable 
 the experimenter to release the weight at the exact beginning 
 of the interval of time marked by the clock. An iron ball 
 suspended by a cord of a length to vibrate half-seconds can be 
 used as a substitute, as in the last experiment. Slotted bars 
 of lead or brass of known weight, called " riders "or " over- 
 weights," to be removed by the ring-rest at any desired point, 
 complete the apparatus. 
 
 First. Put equal loads on the two sides of the pulley. Set, 
 by trial, the ring for arresting the over-weight so that the ring- 
 is reached by the descending weight in one second. Set the 
 arresting-shelf so that it is reached at the end of the second 
 second. The lower end of the descending weight starts from 
 zero ; hence its length must be added to the distance that the 
 ring is below zero, to give the distance traversed in the first 
 second. The distance between the ring and the shelf decreased 
 by the length of the weight will be the velocity at the end of 
 the first second. Why? Compare this distance with that passed 
 over in the first second. Make several trials. 
 
 Secondly. Set the arresting-ring so that it is reached by the 
 descending weight at the end of two seconds. Set the arrest- 
 ing-shelf so that it is reached at the end of the third second. 
 What is the velocity at the end of the second second ? Why ? 
 After determining, by repeated trials, the position of the 
 arresting-ring and arresting-shelf, see if you can discover any 
 fixed relation between the velocity at the end of any second of 
 time and the number of the second. 
 
MECHANICS OF SOLIDS. 87 
 
 Thirdly. Place weights on the pulley so as to differ by some 
 known quantity ; for example, use 275 grammes and 325 
 grammes, a difference of 50 grammes. Then the moving- force 
 is due to this excess, and the mass moved is 275 + 325 -f- such 
 a part of the mass of the pulley as, placed on the rim, would 
 be equivalent to the whole mass distributed as now from the 
 axis to the rim. In the case of a solid cylindrical pulley, this 
 quantity is half of the total mass of the pulley. In the case 
 of an open wheel, it is approximately the mass of the rim 
 increased by the mass of the outer half of the spokes. This 
 can be found by computing the volume in cubic centimetres, 
 and multiplying it by the density of the substance. 1 Let the 
 pulley be represented by 150 grammes. Then the total mass 
 moved will be 275 -f- 325 -f 150 = 750 grammes. Now deter- 
 mine, by trial, the position of the arresting-shelf so that it is 
 reached in one second. Also determine the position of the 
 arresting-shelf when it is reached in two seconds. Also find 
 the position when reached in three seconds. What is the ratio 
 of each of these distances to the first ? If the total distance 
 passed over is represented by s, and the time by , what 
 formula will represent the value of s in terms of t? 
 
 Fourthly. Find, as in the last case, the distance passed over 
 by the descending weight in one second, two seconds, three 
 
 1 The value of the pulley can be determined experimentally as follows: Let 
 a = velocity generated in unit of time, w and w' = masses attached to the cord, 
 w" = mass of pulley when considered as placed at the circumference. Then 
 
 a = g w ^"^ . Let * = space passed over by the descending weight in t seconds ; 
 w + w' + w" 
 
 then s = w ~ ^ . \g&. Place on the pulley the weights w and w'. Set w at the 
 
 w + w' + w'' 
 
 zero of the scale, and adjust by trial the arresting-ring to take off the overweight 
 (w u/) coincidently with any subsequent beat of the clock. The distance of the 
 arresting-ring below zero will be the value of *, and the number of seconds elapsed 
 from the beginning of motion till the ring is reached is the value of t. By substituting 
 these values in the formula the value of w" can be determined. 
 
88 PRACTICAL PHYSICS. 
 
 seconds, etc. Then, by taking their difference, we have the 
 distance passed over during the first second, second second, 
 third second, etc. Find the ratio that each of these distances 
 sustains to the first. 
 
 131. Exercise. Determine the increment of gravity, using 
 Atwood's machine. 
 
 Let us suppose' that a weight of 275 grammes is placed on 
 each side of the pulley, and an overweight of 50 grammes 
 on one side. If the pulley can be represented by 150 
 grammes, then the mass moved will equal 275 -f- 275 -f- 150 
 -|- 50 = 750 grammes, and the moving-force will be clue to 
 50 grammes. The ratio of 50 to 750 equals the ratio of the 
 moving-force to the force of gravity, and hence equals the ratio 
 of the velocity the moving-force produces in a second to that 
 
 7, 
 
 gravity produces, that is, -ff^ = -, in which k is twice the 
 
 i7 
 
 space the 750 grammes move in one second. Now determine, 
 by repeated trials, the position of the arresting-ring when 
 reached in one second. Hence g = 
 
 132. Exercise. Find the measure of the effect of a force. 
 
 First. Using an Atwood's machine, put on one side of the 
 pulley, say, 287.5 grammes, on the other 312.5 grammes. 
 Hence, if the pulley is represented by 150 grammes, there is 
 moved 750 grammes by a force due to the excess of 25 
 grammes of one weight over the other. This force acting on 
 25 grammes would produce a velocity of 9.8 m. in a second, 
 and the momentum would be 25 x 9.8 = 245. This force 
 moves 750 grammes, and as there must be an equality of 
 momenta, then 25 x 9.8 = 750 x velocity acquired. Hence 
 the velocity acquired by the 750 grammes will be f-JJ = .326, 
 and the space passed over during the first second will be 
 
MECHANICS OF SOLIDS. 89 
 
 o o /* 
 
 - = .163 metre; that is, if the arresting-shelf is placed at 
 
 2 
 
 .163 metre below the bottom of the weight, it should be reached 
 by the weight in one second. Test it. 
 
 Secondly. Using the weights 275 grammes and 325 grammes, 
 giving a total mass of 750 grammes, and a moving-force double 
 of the first, being due to 50 grammes, we have 50 X 9.8 
 
 = 750 X velocity acquired, velocity = - - = .653 metre, 
 
 You 
 
 /> ^o 
 
 and space passed over in one second = '- - = .326 metre. 
 
 Therefore the arresting-shelf placed at .326 metre should 
 be reached in one second by the descending weight. Test 
 it. 
 
 It is now seen that a force due to 50 grammes imparts to 
 750 grammes twice the velocity that a force due to 25 grammes 
 does ; that is, while the mass remains constant, the velocity 
 generated in a unit of time varies as the force. 
 
 Thirdly. Keeping the force which causes the motion the 
 same as in the first case, by putting 100 grammes on one side, 
 and 125 grammes on the other, making a total load of 375 
 grammes, one-half of the first load employed, we have 25 
 X 9.8 = 375 X velocity acquired, from which the velocity 
 
 25 x 9 8 
 
 acquired = = .653 metre, and the space passed over 
 
 o /o 
 
 = .326 metre. Test it. 
 
 Now the ratio of the masses moved in the first case and in 
 the last is f|f = 2, and the ratio of the velocities produced is 
 
 QO 
 
 ' = 4. Hence, while the moving-force remains constant, 
 
 .653 
 
 the velocity generated in a unit of time varies inversely as the 
 mass moved. Change the loads, and ascertain if this statement 
 is general. 
 
90 PRACTICAL PHYSICS. 
 
 From these considerations, it is evident that the effect of a 
 force may be measured by the product of the mass moved 
 by the velocity produced, that is, may be measured by the 
 momentum acquired in a second. 
 
 133. Exercise. Ascertain if mass affects the velocity of 
 falling bodies. 
 
 Procure two or three iron balls of different sizes, and as 
 many U-shaped electro-magnets. Tie the electro-magnets to a 
 stout stick so that they may be held out of an upper window of 
 some high building. These electro-magnets should all be in 
 circuit with a battery of sufficient strength to cause them to 
 hold up the balls. By breaking the circuit, the balls will all 
 be released at the same moment, and one standing on the 
 ground can determine if there is any difference of time in their 
 reaching the ground. Does a difference of weight perceptibly 
 affect the time of falling ? 
 
 Drop from your hand, at the same instant, an iron ball 
 and a cork one, and ascertain if the conclusion in this case 
 harmonizes with that previously reached. Then make a paper 
 cone out of light cardboard, and of sufficient size to hold both 
 balls. After placing the balls in the cone, the iron one first, 
 drop it point first. Are the results the same as before? 
 Explain. 
 
 Drop a coin and a paper disk of the same size simultaneously, 
 comparing the result with that obtained by placing the paper 
 disk on top of the coin, and dropping them from the hand. 
 Now place the coin and the paper disk in a long glass tube 
 sealed at one end, and having a stop-cock fitted to the other. 
 Such an apparatus is supplied by dealers under the name of 
 Guinea and Feather Tube. Connect the tube with the air- 
 pump, and exhaust the air as perfectly as possible. Close 
 
MECHANICS OF SOLIDS. 91 
 
 off the tube, remove it from the pump, invert quickly, and 
 ascertain if the relative time of falling of the two objects is 
 affected in any way. 
 
 Prepare a set of propositions embodying the truths exhibited 
 by these experiments. 
 
 134. Exercise. Support a pail of water at an elevation 
 of two or more metres above the floor. Place in the pail one 
 end of a rubber tube of sufficient length to reach to the floor. 
 In the other end of the tube, insert a short piece of glass tubing 
 drawn out to a jet-point. See p. 356. Secure this tube in the 
 jaws of a suitable clamp so that any desirable direction may 
 be given to it. Start the water flowing through the tube by 
 suction, and then observe the shape of the path of the stream, 
 and the horizontal distance reached by it, as the direction of 
 the jet-tube is changed. Inference. Ascertain the effect of a 
 change in the height of the pail above the end of the jet-tube. 
 What forces determine the path of the stream ? 
 
 135. Exercise. Determine the path of a projectile. 
 Construct a spring-gun after the pattern shown in Fig. 62. 
 
 The horizontal and vertical pieces are 2.5 cm. thick ; N is a 
 cylinder with tenons of equal length sliding freely through 
 round holes in the vertical pieces ; K is a pin to serve as a 
 handle ; L and M are elastics or spiral springs firmly fastened 
 to N and the vertical CD. Two wooden balls of the same 
 diameter are needed. Through each, drill a hole of such a size 
 that either will slide easily on the tenon F. The tenons on N 
 should be of such a length, that, when N is drawn back, the 
 right-hand one will be flush with the face of CD, and the left- 
 hand one will project a distance equal to the diameter of the 
 ball. Now draw N back, place one ball on F, and the other 
 
92 PRACTICAL PHYSICS. 
 
 on the ledge CB opposite the hole at H ; then release N, and 
 it will be seen that both balls will be set in motion at the same 
 time, one falling vertically, and the other moving as a projectile. 
 AB must be held in a horizontal position. Compare the mo- 
 tions of these balls, and the times required to reach the floor. 
 
 To picture the path of the projectile, hold the spring-gun so 
 that the path of the ball will be parallel to a vertical wall, and 
 distant a few centimetres from it. By watching carefully the 
 
 ball, it will be found 
 possible to insert a 
 pin in the wall op- 
 posite some position 
 of the ball in its 
 flight, new points 
 being marked each 
 FIG. 62. * trial, as well as 
 
 those just located 
 
 verified. A line traced through these points will represent 
 closely the path of the projectile. This can be transferred to a 
 sheet of paper by ascertaining, first, the vertical distance of 
 each of these points from the horizontal line passing through 
 the highest point of the curve, as well as the horizontal 
 distance from the initial point of the curve ; and secondly, 
 locating them with reference to a corresponding line drawn 
 on a sheet of paper, reducing each measurement on the same 
 scale. 
 
 V. THE PENDULUM. 
 
 136. Apparatus. A number of Balls to use in con- 
 structing pendulums. 
 
 137. Exercise. Determine the laws for the vibrations of 
 pendulums. 
 
MECHANICS OF SOLIDS. 
 
 93 
 
 Fasten to each of a number of lead balls, of about 15 mm. 
 diameter, a stout cotton thread, by cutting in each a slot with 
 a knife, inserting one end of the thread, and closing it up by a 
 blow from a hammer. Drill a number of holes, 5 cm. apart, 
 through a piece of board about 60 cm. long, 5 cm. wide, and 
 15 mm. thick. Pass the strings through these holes, securing 
 each in its place with a small 
 wooden wedge. Support this 
 board in a horizontal position 
 in some suitable way (Fig. 63). 
 These suspended balls will serve 
 as pendulums, the lengths being 
 the distances respectively from 
 the under side of the support 
 to the centre of the balls, and 
 easily varied by pulling the strings 
 through the holes in the support. 
 Marbles may be substituted for 
 the lead balls, the strings being 
 attached by some very adhesive 
 cement. See p. 357. 
 
 First. -Set one of these pendulums swinging through a small 
 arc, about five degrees, and determine the number of vibrations 
 made in thirty seconds by averaging several trials. Now set 
 the pendulum vibrating through a much larger arc, and deter- 
 mine the number of vibrations made in thirty seconds. Does 
 the size of the arc affect the time? Test the conclusion by 
 extending the time of observation, as well as increasing still 
 more the size of the arc. 
 
 Secondly. Adjust, by trial, the length of one of the pendu- 
 lums so that its time of vibration is one second. How long is 
 the pendulum? Adjust another to vibrate in half-seconds; 
 
 FIG. 63. 
 
94 PBACTICAL PHYSICS. 
 
 another in one-third of a second. Compare the lengths of 
 these several pendulums, ascertaining if there is any simple law 
 connecting the lengths of the pendulums with their times of 
 vibration. 
 
 Thirdly. Set up two pendulums of the same length, using a 
 wooden ball for the bob of one, and a metal ball for the other. 
 Compare carefully their times of vibration. Inference. 
 
 Fourthly. Using an iron ball as a bob for a pendulum, 
 determine carefully its time of vibration. Now place just 
 below the lowest point traversed by the ball, a pole of an 
 electro-magnet, and again determine the time of vibration. 
 Would you infer from the comparison of these times, that an 
 increase in the force of gravity would affect the time of 
 vibration of a pendulum? 
 
 138. Exercise. Fasten six lead or iron balls on a stout 
 string at intervals of 15 cm., forming a compound pendulum 
 about 105 cm. long. Set the pendulum in vibration, and 
 determine its time. Find the time of vibration of a pendulum 
 whose length is the distance of the centre of the lowest ball 
 of the six from the point of support. In like manner, find the 
 times of pendulums whose lengths are the distances respectively 
 of the other balls from the point of support. Set up a pendu- 
 lum whose time is that of the compound pendulum. Notice 
 the shape of the compound pendulum when vibrating, and 
 apply the facts ascertained above to account for it. Which 
 ball would you remove to shorten the time, and which to 
 lengthen? Add another ball to the number without affecting 
 the time. Explain. 
 
 139. Exercise. Suspend from a suitable frame a uniform 
 strip of wood about 1 metre long, 5 cm. wide, and 1 cm. thick, 
 
MECHANICS OF SOLIDS. 
 
 95 
 
 by driving into the end of it a small wire staple, forming an 
 eye through which a knitting-needle can be passed to serve as 
 an axis of oscillation (Fig. 64) . Adjust a pendulum, as in the 
 last experiment, to 
 vibrate in the same 
 time as the wooden 
 bar. Compare the 
 length of the pen- 
 dulum with that of 
 the bar. Now cut 
 from a sheet of lead 
 a piece weighing 
 half a kilogramme. 
 Bend this into a 
 clasp that will slide 
 along the bar with 
 sufficient friction to 
 
 stay wherever placed. Having measured off on the bar the 
 length of the pendulum vibrating in the same time, place the 
 sliding-clasp below that point on the bar, and note the effect 
 on its time of vibration. Note the effect when the weight is 
 at the point, and also when above the point. 
 
 140. Exercise. Suspend a wooden bar as in the last 
 experiment, and adjust a pendulum to vibrate in the same 
 time. Bore a hole through the wooden strip at the point 
 marked in that experiment, and support the bar by passing 
 the needle through it. How does its time of vibration 
 compare with its previous time? State as a proposition the 
 relation found to exist between this point and the centre of 
 suspension. 
 
 FIG. 64. 
 
96 PRACTICAL PHYSICS. 
 
 141. Exercise. Suspend a common lath by a cord 10 or 
 15 cm. longxso as to swing as a pendulum. Adjust a ball- 
 pendulum to vibrate in the same time. Mark a point on the 
 lath distant from the suspension-point the length of the ball- 
 pendulum. Now set the lath in vibration by striking it with 
 a ruler opposite this point. Compare the effect with that 
 produced when the lath is put in vibration by a blow delivered 
 at some other point on the bar. Inference. 
 
 VI. FRICTION. 
 
 142. Exercise. Measure the friction between two surfaces 
 when one moves over the other. 
 
 Procure a board about 1 metre long and 25 cm. wide, dressed 
 to a plane, and a rectangular block 12 x 6 x 4 cm. In the 
 centre of each of any three faces about a corner, insert a screw- 
 eye for convenience in attaching a cord. Weigh the block, 
 place on it any convenient number of grammes, attach a 
 spring-balance by means of a cord ; then, keeping the cord 
 horizontal, apply sufficient force to move the block, reading the 
 balance just as the block starts to move, and also after motion 
 has begun. Make several determinations of both the starting 
 and the moving force. 
 
 Repeat the tests to ascertain if the area of the face of the 
 block resting on the board affects the results. 
 
 Ascertain the effect of using a greater weight. 
 
 Determine the effect of varying the character of the sub- 
 stances by placing a plate of glass, iron, brass, etc., on the 
 board, and cementing to the face of the block a thin sheet or 
 plate of the same substance. 
 
 Measure the friction between the surfaces when coated with 
 some kind of lubricator. 
 
MECHANICS OF SOLIDS. 
 
 97 
 
 Make several determinations in each case, and, using the 
 mean as the most probable value of the force applied, divide 
 it by the mass moved, to obtain the coefficient of friction. 
 
 As a substitute for the balance, the string may be stretched 
 over a pulley by weights placed in a scale-pan. 
 
 VII. THE SIMPLE MACHINES. 
 
 143. Apparatus. A Lever, several Pulleys, a Wheel 
 and Axle, an Inclined Plane, and a Set of Weights. 
 
 144. Exercise. Determine the law of equilibrium for the 
 lever. 
 
 The apparatus employed 
 in Art. 112 will be found 
 useful for this one. When 
 any other point than the 
 centre of the bar is taken 
 as the fulcrum, the weight 
 of the bar can be neutral- 
 ized by means of a lead 
 ball made to screw on the 
 end of the wire inserted in 
 the end of the bar. A Y- 
 shaped support (Fig. 65) 
 
 will be found convenient, but it is not indispensable, as the 
 
 wire clevis can be used to support the bar. 
 
 PIG. 65. 
 
98 
 
 PRACTICAL PHYSICS. 
 
 Set the fulcrum at any point, and counterpoise the bar. 
 Suspend any number of weights from a point on one side of 
 the fulcrum, and a sufficient number from a point on the 
 opposite side to cause the bar to assume a horizontal position. 
 Compare the ratio of these weights with that of the spaces 
 between their points of attachment and the fulcrum. Vary the 
 weights and their points of attachment. Arrange the apparatus 
 so that one weight is between the fulcrum and point of appli- 
 cation of the other weight. What law do you find expresses 
 the relation between the weights and the arms of the lever ? 
 
 145. Exercise. Secure in a vertical position a board 
 about 1 metre long and 40 cm. wide. Mount on this board a 
 
 circular wooden disk of about 20 
 cm. diameter, so that it can turn 
 freely about a fixed axis through 
 the centre. Attach at any two 
 points of the disk cords which 
 pass over pulleys (Fig. 66) which 
 can be given any desired position 
 on the supporting board by hav- 
 ing, as their axes, bolts moving 
 in vertical slots, and fastened by 
 nuts. To the ends of these 
 cords, attach scale-pans cut out 
 of tin plate. Now place known 
 weights in these pans, and when 
 the apparatus assumes a position 
 of rest, measure the perpendicular 
 
 distance from the centre of the disk to the line of direction of 
 each cord, and compare their ratio with that of the weights. 
 The weights should include the pans, and the position of the 
 
 FIG. 66. 
 
MECHANICS OF SOLIDS. 
 
 99 
 
 cords should be such that the direction does not pass through 
 the centre of the disk. Make a number of experiments in 
 which the weights and the positions of the pulleys are changed. 
 Express as a law the relation found to exist. 
 
 146. Exercise. Determine the law for the movable 
 pulley. 
 
 With three small pulleys, some 
 flexible cord, and two small scale- 
 pans, set up successively the 
 arrangements shown in Fig. 67. 
 Place shot in one of the pans to 
 counterbalance the weight of the 
 pulleys, then place known weights 
 in the two pans, and ascertain 
 the ratio between them whenever 
 equilibrium is secured. Account 
 for the value of the ratio in each 
 case. 
 
 FIG. 67. 
 
 147. Exercise. Determine the law of equilibrium for the 
 
 wheel and axle. 
 
 A suitable apparatus for 
 this experiment may be made 
 by a good mechanic as fol- 
 lows : 
 
 Procure a piece of hard wood about 15 
 cm. long, and of about the same diameter. 
 Turn it down in a lathe so as to have a 
 succession of disks with diameters as the 
 numbers 1, 2, 3, etc. These disks need not be more than 2.5 
 cm. thick. Fasten to the circumference of each disk a cord for 
 
 FIG. 68. 
 
100 PRACTICAL PHYSICS. 
 
 the attachment of weights. The axis, consisting of a piece of 
 brass or iron rod driven into the ends of the piece of timber, 
 can be supported from two brackets firmly screwed to the edge 
 of a piece of plank (Fig. 68) . Attach scale-pans to the cords ; 
 place shot in one till equilibrium is secured, then, employing 
 known weights in the pans, ascertain the law of the machine. 
 
 148. Exercise. Determine the law for the inclined 
 plane. 
 
 Construct an apparatus for this experiment as follows : 
 
 Hinge together two pieces of board, each about 15 cm. wide 
 
 and 50 cm. long. On the under side of the one to be used as 
 
 the inclined plane, fasten thin strips across it at intervals of 
 
 2 cm. Then, by means of a prop moved along between the 
 
 boards, kept from slipping by 
 the strips on the upper one, any 
 desired elevation may be given 
 FIG 69 to the plane. Fasten a pulley at 
 
 the opposite end from the hinge, 
 
 so that a cord attached to a car moving along the plane, and 
 drawing over the pulley, will be parallel to the plane. Place 
 weights in the scale-pan to counterpoise the car, then add weights 
 to both the car and the scale-pan, comparing them, when equi- 
 librium is secured, with the dimensions of the plane. 
 Fig. 69 illustrates a modified form of this apparatus. 
 
MECHANICS OF 
 
 CHAPTER III. 
 
 MECHANICS OF FLUIDS. 
 
 [. PRESSURE IN FLUIDS. 
 
 149. Apparatus. Large Glass Tube, Two-litre Bottle, 
 Metal Tube, Bladder-Glass, Weight-Lifter, Magdeburg Hemi- 
 spheres, Air-Pump, Glass Tubing, Barometer-Tube, Aneroid 
 Barometer, small Rubber Foot-Ball, Glass Bolt-Head, Model 
 of Sprengel Pump, etc. 
 
 150. Exercise. Close with a cork one 
 end of a brass or tin tube about 1 metre 
 long and 3 cm. in diameter, and set it 
 into a wooden block for a base. In the 
 side of the tube, drill five holes 5 mm. 
 in diameter, at equal distances apart, and 
 placed so that the third hole is at the 
 middle of the tube (Fig. 70). Close these 
 apertures with corks, and fill the tube with 
 water. On uncorking the apertures, com- 
 pare the ranges of the streams, and also 
 ascertain if they differ in force. Inference. 
 The water in the tube should be kept at a 
 
 constant level while these comparisons are being made, by 
 pouring water from a suitable vessel. 
 
 FIG. 70. 
 
102 
 
 PRACTICAL PHYSICS. 
 
 151. Exercise. Ascertain if the atmosphere exerts 
 pressure. 
 
 Tie firmly a piece of sheet-rubber over one end of a large 
 tube, tin or glass, about 30 cm. long and 5 cm. in diameter. 
 After filling it with water, invert it in a vessel of water, 
 keeping the mouth just below the surface. Observe the shape 
 of the rubber surface. Ascertain the cause of it by substituting 
 a carefully fitted glass plate for the rubber, and comparing the 
 force needed to pull it off when the tube is full of water with 
 that when free from water. 
 
 152. Exercise. Tie a piece of sheet-rubber or tough 
 paper over one end of a bladder-glass, place it on the table 
 of the air-pump, and exhaust the air. What fact is proved? 
 
 To make a bladder-glass, cut off the bottom of a common 
 glass fruit-jar (see p. 354), and grind down the edges on a 
 piece of flat sandstone. g=s 
 
 Coat with lard the edges of the glass 
 resting on the air-pump table. 
 
 153. Exercise. Connect the Weight- 
 Lifter (Fig. 71) to the air-pump by a piece 
 of heavy rubber tubing. Account for the 
 upward movement of the piston with the 
 heavy weight attached as the air is ex- 
 hausted from the cylinder. Measure the 
 cylinder, and compute how great a weight 
 can be lifted by the machine. Remove the 
 piston, and tie a rubber membrane across 
 
 the end of the cylinder. Observe the effect on the membrane 
 on exhausting the air as different positions are given to the 
 cylinder, varying from vertical to horizontal. Inference. 
 
 Fm. 71. 
 
MECHANICS OF FLUIDS. 
 
 103 
 
 154. Exercise. Connect the Magdeburg Hemispheres 
 (Fig. 72) with the air-pump. Exhaust the air, remove them 
 
 from the pump, and then try to separate them. 
 While thus fastened together, place them under 
 a bell- jar on the table of the air-pump, exhaust 
 the air, and observe the effect. What do yon 
 find held the hemispheres together? Ascertain 
 if the hemispheres can be pulled apart in any 
 one position more easily than in another. In- 
 FIG. 72. ference. 
 
 155. Exercise. Compare the 
 pressure exerted by fluids in different 
 directions. 
 
 Bend a stout glass tube about 75 
 cm. long into the form shown in 
 Fig. 73 (a), and also three shorter 
 pieces into the forms shown in (b), 
 (c), and (d). In the U-shaped part 
 of (a), pour enough mercury to rise 
 about 1 cm. in each arm. Attach 
 the tube (b) to the lower end of (a) 
 with a rubber connector, and hold the 
 apparatus vertically in a vessel of 
 water, observing the distance of the 
 mouth of (b) below the surface of 
 the water, and also the effect on the 
 level of the mercury in (a). Now 
 substitute the tube (c) for (b), sub- 
 merging the apparatus to the same depth as before, as 
 indicated by the mouth of the tube. Note the change in 
 the mercury level. Try (d). What causes the change of 
 
 FIG. 7 
 
104 PRACTICAL PHYSICS. 
 
 level? What is the evidence? What truth is proved by 
 this experiment? 
 
 The tubes (b), (c), and (d) must be filled with water as 
 high as the mouth, to insure success. 
 
 156. Exercise. Cut a board about 75 cm. long, 15 cm. 
 wide, and 15 mm. thick. Place it on a table so that it projects 
 25 cm. over the edge. Spread a large newspaper over the end 
 on the table, making it as smooth as possible. Now strike the 
 projecting part of the board with the hand, comparing the blow 
 necessary to raise the other end of the board with that required 
 when the paper is removed, or a smaller paper is used. 
 Explain. 
 
 157. Exercise. Select two test-tubes, such that one 
 slides easily within the other. Fill the larger one with water, 
 insert the closed end of the smaller tube, and quickly invert. 
 Account for the upward movement of the small tube in opposi- 
 tion to the force of gravity. What is the office of the water in 
 this experiment? 
 
 158. Exercise. Measure the atmospheric pressure. 
 
 Fill a heavy glass tube about 80 cm. long, and closed at one 
 end, with mercury. To do this, connect to the tube a small 
 glass funnel by means of a rubber connector. Invert it in a 
 cup of mercury (Fig. 74) by placing the finger firmly over the 
 end of the tube to keep the mercury from running out during 
 the operation. Why does not the mercury all run out of the 
 tube? Devise some way of showing that it is atmospheric 
 pressure on the mercury in the cup that supports the column 
 in the tube. Measure the height of the column m the tube 
 above the level of the mercury in the cup. Incline the 
 
MECHANICS OF FLUIDS. 
 
 105 
 
 tube, and again determine the difference of level. Why 
 the same? 
 
 Measure the cross-section of the tube, and then compute the 
 volume of mercury in cubic centimetres. 
 Multiply this volume by 13.6, and you 
 have the weight of mercury in grammes. 
 Compute what the weight would be if the 
 cross-section of the tube were 1 scm., 
 and the mercury column 76 cm. long. 
 
 In filling the tube with mercury, re- 
 move air-bubbles by sliding down the 
 tube a slender iron wire. 
 
 159. Exercise. Measure the height 
 
 of a building or hill by means of a 
 
 barometer. 
 
 For this purpose, use an Aneroid 
 
 Barometer (Fig. 75), as it is more 
 
 portable and 
 
 more sen si- FlG - 74> 
 
 tive than the mercurial. Note the 
 rise or fall of the barometer in hun- 
 dredths of an inch in passing from 
 one station to the other, multiply by 
 9, and the product is the difference 
 in altitude expressed in feet. If the 
 pressure is below 26 inches, or the 
 temperature above 70 F., use 10 for 
 a multiplier. Many readings at both 
 stations should be taken, extending 
 
 over a period of several days, the averages being used in the 
 
 computation. 
 
 FIG. 75. 
 
106 
 
 PRACTICAL PHYSICS. 
 
 The readings should be taken with the aneroid in a horizontal 
 position, tapping the face slightly with the finger before taking 
 them in order to bring the needle into equilibrium. Guard 
 against parallax in taking the readings, and estimate all 
 fractions of spaces. 
 
 For more accurate methods of measuring heights, consult 
 Plympton's "Aneroid Barometer," published by D. Van 
 Nostrand, New York. 
 
 160. Exercise. Fill a small rubber foot- 
 ball half full of air, and place it under a 
 bell-jar on the air-pump table. Exhaust the 
 air from the jar ; notice the effect on the ball. 
 Explain. 
 
 Substitute a dish of soap-bubbles for the 
 ball, or an empty bottle with its mouth opening 
 under water in a tumbler. 
 
 What property of air do these experiments 
 show? 
 
 161. Exercise. Procure a bolt-head, that 
 is, a stout glass tube with a large bulb on one 
 end. A strong glass tube fitted air-tight to 
 a bottle by means of a perforated cork will 
 make a good substitute. Close the top of an 
 open-top bell-jar with a good cork, through FIG. 76. 
 which passes this glass tube reaching to the 
 
 bottom of a vessel of water within it (Fig. 76). Place the 
 apparatus on the table of an air-pump, exhaust the air, and 
 watch the effect. Also observe the effect of admitting the air. 
 Explain. 
 
MECHANICS OF FLUIDS. 
 
 107 
 
 162. Exercise. Fit to a flask or bottle a good cork, 
 through which passes a jet-tube. Connect this tube to an 
 air-pump by means of a rubber tube, and exhaust the air. 
 Close the connection between the flask and the pump with a 
 pinch-cock, disconnect the tube from the pump, and open 
 the pinch-cock after placing the mouth of the rubber tube in 
 a vessel of water. Explain. 
 
 163. Exercise. Connect with rubber tubing, as shown in 
 Fig. 77, a glass funnel, a T-tube, a stout glass tube one metre 
 long, and a flask to be exhausted. 
 
 On the rubber connector, between' 
 the T-tube and the funnel, place 
 an adjustable pinch-cock. Secure 
 the apparatus in a vertical position, 
 with the lower end of the tube 
 fitting into a vessel which has an 
 opening on the side a little higher 
 than the end of the tube. Now 
 close the pinch-cock, pour mercury 
 into the funnel, and open the pinch- 
 cock on the tube leading to the 
 vessel to be exhausted. Then open 
 the pinch-cock so that the mercury 
 falls in a rapid series of drops, 
 closing the tube, and preventing, 
 air from entering from below. As 
 the mercury flows down, the ex- 
 haustion begins, the air of the tube being carried down by the 
 mercury drops, and the air of the flask expanding to fill its 
 place. The mercury can be poured back into the funnel from 
 time to time, care being exercised to prevent the funnel's 
 
 FIG. 77. 
 
108 PRACTICAL PHYSICS. 
 
 becoming empty, as then air would immediately enter the flask. 
 Search for evidence in the working of this mercury-pump, 
 showing that the degree of vacuum is improving. 
 
 II. LAW OF BOYLE. 
 
 164. Apparatus. Heavy Glass Tubing, Mercury, etc. 
 
 165. Exercise. Determine the law of the compressibility 
 of gases. 
 
 First. Close one end of a stout glass tube in a gas-flame, 
 and then bend it into the shape of the letter J, the short 
 arm bsing the closed one, and about 25 cm. long (Fig. 78). 
 Lengthen the long arm to 2 metres, using a heavy rubber 
 connector, and winding it with fine copper wire. Fasten the 
 completed tube with metal straps to a board set into a block 
 for a base. Attach metric scales to the arms, placing the zero 
 of each one on the same level, and just above the bend in the 
 tube. Now pour in enough mercury just to close the bend up 
 to the zero of the scales, bringing the mercury to the same 
 level by jarring the tube. Under what pressure is the air in 
 the short arm ? After this adjusting has been carefully done, 
 pour in mercury till a reading of about 20 cm. is secured in the 
 long arm. Record the height of the mercury column in each 
 arm. Add more mercury and record the readings, proceeding 
 in this way till the long arm is full of mercury. The difference 
 of any two corresponding readings, plus the barometer reading 
 at the time of conducting the experiment, will measure the pres- 
 sure on the confined air-column. Why ? Compute the pressure 
 for each observation and multiply it by the length of the con- 
 fined air-column corresponding to it. If the experiment is care- 
 fully conducted these products will be found to be nearly equal. 
 
MECHANICS OF FLUIDS. 
 
 109 
 
 Tabulate the results. 
 
 Express as a law the relation between volume and pressure 
 exhibited by the experiment. Represent this relation by a 
 curve (598). 
 
 The mercury must be poured in the tube very gently, and 
 with the tube in an inclined position at first, so that the mercury 
 stream will not act as a piston, and drive air 
 ahead of it into the short arm. 
 
 Secondly. Fill with mercury to within 20 
 cm. of the end a stout glass tube 80 cm. long, 
 closed at one end. Under what pressure is 
 the 20 cm. of air in the tube? Close the end 
 of the tube with the finger, and invert it in a 
 vessel of mercury. Accurately measure the 
 length of the air-column, and also the height 
 of the mercury-column, above the level of 
 the mercury in the vessel. What supports the 
 mercury in the tube? Observe what the 
 barometer-reading is. Why is the mercury- 
 column less in height than that in the barom- 
 eter? Under what pressure must the air in 
 the top of the tube be ? How does the ratio 
 of the initial and present volume of the air in 
 the tube compare with that of the pressures it 
 is under in the two cases? Make several 
 experiments with different initial volumes of 
 air, and ascertain if the same relation holds 
 good. Express as a law the relation discovered. 
 
 In order to subject the same volume of air to different 
 pressures less than one atmosphere, a deep cistern of mercury 
 will be required. To provide this, close one end of a heavy 
 glass boiler-tube about 75 cm. long and 2.5 cm. diameter, and 
 
 FIG. 78. 
 
110 
 
 PRACTICAL PHYSICS. 
 
 insert it in a heavy wooden block for a base. Then, instead of 
 closing one end of the barometer-tube used by fusion, it would 
 be better to cement on the end a metal ferrule, into which is 
 fitted a screw for closing the end. With such an arrangement, 
 it will be easy to regulate the amount of air enclosed. 
 
 III. LAW OF PASCAL. 
 
 166. Apparatus. Brass Tube, Haldat's Apparatus, Equi- 
 librium Vases, Glass Tubing, etc. 
 
 167. Exercise. Procure a piece of brass tubing 25 mm. 
 in diameter and 25 cm. long. Fit to it a piston made by 
 
 winding candle-wick around one end of a piece 
 of barometer-tube 20 cm. long (Fig. 79). Close 
 one end with a perforated cork. Drill holes 
 through the side of the tube at different dis- 
 tances from the open end, and insert perforated 
 corks. Fit neatly in all these corks glass tubes 
 of such a length, and so bent, that their free 
 ends are all on the same level, and at least 5 
 cm. above the open end of the brass tube. Re- 
 move the piston, fill the apparatus nearly full of 
 water, and then insert the piston, holding the 
 tube in a vertical position. Compare the heights 
 of the water in all the tubes as pressure is 
 applied to the piston. Why does the water rise 
 in each tube? How does the direction of the 
 applied pressure compare with that of the motion observed in 
 the different tubes ? What is to be learned from the comparison 
 of the heights of the water in the tubes ? Express as a prop- 
 osition the truth developed by this experiment. 
 
 FIG. 79. 
 
MECHANICS OF FLUIDS. 
 
 Ill 
 
 168. Exercise. Bend a stout glass tube twice at right 
 angles, making the arms 25 cm. and 12 cm. long respectively, 
 and the distance between them 50 cm. Set this in a frame so 
 that these arms are vertical and well supported. Take a glass 
 tube 25 mm. diameter and 25 cm. long, a lamp-chimney of 
 about the same length, and a two-litre bottle with the bottom 
 removed (see p. 354) ; fit to each of these a cork with two 
 holes, through which pass two pieces of tubing of the same 
 bore, so arranged that one of 
 
 them can be attached to the 
 short arm of the U-shaped 
 tube, and the other can be 
 closed with a small cork, and 
 be used as an emptying-pipe 
 (Fig. 80). Pour mercury in 
 the U-shaped tube till it rises 
 8 or 10 cm. in the long arm. 
 Now attach one of these 
 vessels by a short rubber con- 
 nector to the U-shaped tube, 
 
 and pour in water till nearly full. Mark the height of the 
 water, and also of the mercury, in the long arm. Then replace 
 this vessel by one of the others, and fill it with water to the 
 same height as in the first case. In like manner, use the third 
 vessel. What causes the mercury to rise in the long arm each 
 time ? Is there any evidence to show that it is connected with 
 the quantity of water in the vessel attached to the short arm ? 
 Any evidence that it is connected with the height? What truth 
 is taught by the experiment? 
 
 169. Exercise. Cut out of wood a rectangular block 
 25 cm. long, 10 cm. wide, and 5 cm. thick. Bore a hole length- 
 
 FIG. 80. 
 
112 PRACTICAL PHYSICS. 
 
 wise through the stick 2 cm. in diameter. Likewise bore 
 several holes, 5 cm. apart, through the side of the piece, so as 
 to connect with the first one. Close the holes with perforated 
 stoppers, rubber ones if you have them, through which pass 
 glass tubes bent into various forms, but all terminating in a 
 line parallel to the stick (Fig. 81). Pour water through one 
 
 FIG. 81. 
 
 of them till it rises several centimetres in that tube. Compare 
 the level of the water in the various tubes. What causes the 
 water to rise in the other tubes ? Account for the height 
 attained in each tube. What truth is taught? 
 
 170. Exercise. Bore a hole in the side of a wooden pail 
 near the bottom, and insert a stop-cock. A perforated cork, 
 through which passes a glass tube, may be used as a substitute, 
 by slipping over the end a short piece of rubber tubing closed 
 with a pinch-cock. Fill the pail with water, place it on a chair 
 on the table, and attach a piece of rubber tubing 2 or 3 metres 
 long to this stop-cock. In the other end of this tube, insert a 
 jet-tube secured in a vertical position by means of a support 
 standing on the floor. Open the stop-cock, and observe closely 
 the attending phenomenon. Explain. 
 
 Substitute for the jet-tube a glass tube of sufficient length to 
 reach to the level of the water in the pail. Note the height 
 
MECHANICS OF FLUIDS. 118 
 
 to which the water rises. Account for the difference between 
 the height reached b} T the water in the tube, and that when 
 escaping as a jet. Ascertain what the height of the jet 
 depends on, by comparing the conditions under which different 
 heights are obtained. 
 
 f 
 IV. THE SIPHON AND PUMP. 
 
 171. Apparatus. Glass and Rubber Tubing, several 
 large Bottles, small Suction-Pump, Air-Pump, etc. 
 
 172. Exercise. Bend into a U -shape a glass tube about 
 50 cm. long. Fill the tube with water, close one end with the 
 finger, and invert it. Why does not the water run out of 
 the tube ? Now let each end dip into a cylindrical jar partly 
 filled with water. Place one of the jars on a block of wood, 
 and observe the motion of the liquid. Is the velocity of flow 
 constant? When greatest? When least? 
 
 Make a second siphon by connecting together two L-shaped 
 glass tubes with a rubber connector. Ascertain if the apparatus 
 will work when a small hole is made in the side of the rubber 
 tube between the two glass tubes. Explain. 
 
 Make a third siphon similar to the first, using tubing of 
 about 1.5 mm. bore to diminish the rate of flow. Connect two 
 flasks with it, place the apparatus beneath the bell-jar of an 
 air-pump, and then quickly exhaust the air. 
 
 Examine these different experiments, and frame an explana- 
 tion of the action of a siphon. 
 
 173. Exercise. Make a siphon out of a rubber tube. 
 Let the outer arm be a few centimetres longer than the inner 
 one, and measure the amoant of flow during five minutes. 
 
114 PRACTICAL PHYSICS. 
 
 Increase the length of the outer arm, leaving the inner arm 
 unchanged, and again measure the flow during five minutes. 
 Again increase the length, and measure the flow. On what 
 does the velocity of flow depend ? 
 
 174. Exercise. Determine the law which regulates the 
 height over which a liquid can be carried by a siphon. 
 
 Use a long rubber tube of small bore for a siphon, and 
 mercury for the fluid. Fill the tube with mercury, and tie up 
 the ends securely with wire. After placing the tube in 
 position, with its ends opening in dishes having different levels, 
 the higher containing mercury, open the ends, and gradually 
 raise the bend of the tube till a position is reached in which the 
 flow ceases, but is resumed on lowering it in the least. Compare 
 the height of this above the surface of the mercury in the higher 
 vessel, with the barometer reading at the time. 
 
 A glass siphon of small bore could be substituted for the 
 rubber, and the experiment made under the bell-jar of an 
 air-pump, the reading of the pump-gauge being taken at the 
 instant the mercury-column breaks in the siphon, and this 
 compared with the height of this column. 
 
 175. Exercise. Devise a fountain by conducting the 
 water from a vessel to a jet-tube by means of a siphon. On 
 what does the height of the jet depend? Why? 
 
 176. Exercise. Construct an intermittent fountain. 
 
 Cut off the bottom of a large bottle. See p. 354. Cork the 
 mouth of the bottle with a perforated cork through which 
 passes a glass tube, reaching to within 2 or 3 cm. of the end of 
 the bottle. Support the bottle, mouth downward, in the ring 
 of the iron stand ; place a long test-tube over the glass tube, 
 
MECHANICS OF FLUIDS. 
 
 115 
 
 such, that, when the bottle is full of water, the upper surface 
 is above the test-tube. Arrange a siphon with an adjustable 
 pinch-cock to convey water from some large vessel to the bottle 
 at a rate somewhat less than the outlet-tube can empty it. Set 
 the siphon in operation, and notice the character of the flow 
 from the bottle. Explain. 
 
 177. Exercise. Select three bottles of about one litre 
 capacity each, and fit to them corks with 
 two holes. Only the best corks can be 
 used. Place two of the bottles on the 
 table, and the third one on 
 the floor. Using rubber and 
 glass tubing, connect them 
 as shown in Fig. 82. Now 
 fill the bottles on the table 
 with water, leaving the one 
 on the floor filled with air, 
 and set the apparatus in op- 
 eration by blowing through 
 the short tube of the farther 
 bottle. Explain. Why must 
 the corks be tight? Find, 
 by varying the connections, 
 upon what the height of the 
 jet depends. 
 
 FIG. 82. 
 
 FIG. 83. 
 
 178. Exercise. Fit a good cork to an 
 open-top receiver. Through this cork, pass, 
 air-tight, a glass tube reaching to the bottom of 
 a tumbler of water within the receiver. Connect with this 
 tube a small suction-pump (Fig. 83). Ascertain whether water 
 
116 PRACTICAL PHYSICS. 
 
 can be pumped out of the tumbler. Then place the apparatus 
 on the table of an air-pump, exhaust the air, and ascertain the 
 effect on the working of the pump. Inference. 
 
 V. THE PRINCIPLE OF ARCHIMEDES. 
 
 179. Apparatus. Balance, Bucket and Cylinder Appara- 
 tus, Cylindrical Graduate, Cylindrical Jar, Air-Pump, etc. 
 
 180 Exercise. Ascertain the effect on the weight of a 
 substance produced by an enveloping fluid. 
 
 Attach a heavy weight, stone or metal, to an accurate spring- 
 balance, and take the reading. Lower the weight into a vessel 
 of water, and again take the reading. Inference. 
 
 Repeat the experiment, using a block of wood. Inference. 
 Under what condition does a substance appear to lose all of its 
 weight? 
 
 Now place the vessel of water on the platform of a balance, 
 and find its weight. Suspend each of the above articles ID 
 succession from the hook of the spring- balance, submerging it 
 in the water if possible, and compare the difference in the 
 weight of each substance caused by being placed in water, with 
 the change produced in the weight of the vessel of water as 
 shown by the balance. Account for the apparent loss of weight 
 in the first two experiments. 
 
 Repeat all these experiments, substituting strong brine for 
 the water. Compare the weight apparently lost with that appar- 
 ently lost when water was used. Compare the weight apparently 
 lost by a large piece of metal with that apparently lost by a 
 small piece of the same substance. Compare the loss appar- 
 ently suffered by a block of lead with that apparently suffered 
 
MECHANICS OF FLUIDS. 
 
 117 
 
 by a block of any other metal of the same size, 
 the amount of apparent loss depend ? 
 
 On what does 
 
 181. Exercise. Find the measure of the buoyant force. 
 Dealers in physical apparatus furnish a piece known as the 
 
 Bucket and Cylinder. It consists of a cylindrical brass 
 bucket, to which is accurately fitted a 
 brass plug (Fig. 84). Hang the bucket 
 from one arm of a balance, with the 
 plug attached below it by means of a 
 hook and thread. Counterpoise the 
 two cylinders by weights in the other 
 scale-pan. Now place a vessel of 
 water beneath the apparatus, so that 
 the solid cylinder will be submerged 
 when the beam is horizontal. Why 
 is the equilibrium destroyed? Pour 
 water into the bucket till the equilib- 
 rium is restored. How much water is 
 displaced by the plug? Compare this 
 amount with that found necessary to FlG - 84 - 
 
 restore equilibrium. How much weight do you find that a 
 submerged body apparently loses ? 
 
 182. Exercise. A second method of finding the measure 
 of the buoyant force. 
 
 Tie a fine thread or hair to a piece of metal or stone, and 
 suspend it from one end of a balance-beam. Many balances 
 have a hook provided for attaching any substance in this way. 
 Weigh the substance ; then bring a vessel of water beneath it, 
 arid find its weight when submerged. The vessel of water can 
 be supported on a small wooden stool placed over the scale-pan 
 
118 PRACTICAL PHYSICS. 
 
 so as not to interfere with the movement of the balance. 
 Determine how much water the substance will displace by 
 proceeding as in Art. 20. Allowing each cubic centimetre of 
 water to weigh a gramme, how does the weight apparently lost 
 compare with the weight of the water displaced? State as a 
 proposition the truth proved. 
 
 183. Exercise. Determine the principle of flotation. 
 Weigh a piece of paraffine or varnished wood, then, employing 
 
 a graduated cylinder containing water, determine the amount 
 of water displaced by it when floating. If each cubic centi- 
 metre of water displaced weighs one gramme, how does the 
 total weight of water displaced by a floating body compare with 
 the weight of that body in air? Infer from this when a body 
 will float in a fluid. Can the form of a body affect the 
 displacing power ? Make a piece of lead float on water without 
 attaching any thing to it. 
 
 184. Exercise. Weight a small test-tube, so 
 that, when placed in a vessel of water, mouth 
 downward, it will float, maintaining a vertical 
 position (Fig. 85). Fill a cylindrical jar with 
 water to within a few centimetres of the top, place 
 in it the test-tube, and set the apparatus beneath a 
 bell-jar on the table of the air-pump. Gradually 
 exhaust the air, letting it re-enter the bell-jar quite 
 frequently, to determine whether that point has yet 
 been reached at which the test-tube is nearly on the 
 point of sinking owing to air having been removed: 
 from it. When that point is reached, remove 
 
 rIG. so. 
 
 the jar from the air-pump, and tie over the top 
 
 a piece of sheet-rubber. Now, by pressing on the top of 
 
MECHANICS OF FLUIDS. 
 
 119 
 
 the rubber, the tube can be made to sink to any desired point 
 within the jar. Observe the level of the water in the tube as 
 it is made to occupy different positions by varying the pressure. 
 Explain the action of the apparatus, pointing out all the prin- 
 ciples illustrated by it. 
 
 In case a sufficiently tall bell-jar is not at hand, the necessary 
 amount of air can be removed by means of a J-shaped tube, 
 the short arm of which is about as long as the test-tube. By 
 holding the test-tube over the short arm of the J-tube as 
 you let it down into the water, the air will escape through 
 this tube, water taking its place. After a few trials, it will 
 be found easy to remove the proper amount. 
 
 185. Exercise. Ascertain if 
 air affects the apparent weight of 
 substances. 
 
 Place beneath a large bell-jar 
 on the table of an air-pump a 
 short - beam jeweller's balance, 
 having, in place of the scale-pans, 
 a large cork or glass float and a 
 piece of lead accurately balanced 
 (Fig. 86). Exhaust the air, and 
 note the effect on the balance. 
 Repeat several times to make it 
 certain that the phenomenon at- 
 tending the exhaustion is not 
 
 accidental. Explain. How can the weight of an object 
 obtained in air be reduced to that in a vacuum? 
 
 FIG. 86. 
 
120 
 
 PRACTICAL PHYSICS. 
 
 VI. DETERMINATION OF DENSITY. 
 
 186. Apparatus. Balance, Cylindrical Graduate, Spe- 
 cific-gravity Bottle, Hydrometers, Florence Flask, Air-Fump, 
 Glass Tubing, etc. 
 
 187. Exercise. Determine, by means of a balance, tha 
 density of a solid insoluble in water. 
 
 Suspend the substance, by means of a fine thread or hair, 
 from the hook on the bail of the scale-pan provided for that 
 purpose, and determine carefully its weight. As in Art. 182, 
 find its weight in water. From these data determine the volume 
 of water displaced by the solid. Divide the weight in the air 
 by the volume, and the density is obtained. This result needs 
 correcting for temperature, pressure, etc., when great accuracy 
 is required. 
 
 As a check, divide the weight in air expressed in grammes 
 by the volume in cubic centimetres, as determined by the 
 method of Art. 20. 
 
 Tabulate results as follows : 
 
 Name of 
 Substance. 
 
 Weight 
 in Air. 
 
 Volume, 
 ccm. 
 
 Density. 
 
 Weight 
 in Water. 
 
 Density. 
 
 Average. 
 
 Glass . . . 
 
 
 
 
 
 
 
 Iron . . . 
 
 
 
 
 
 
 
 Lead . . . 
 
 
 
 
 
 
 
 Marble . . 
 
 
 
 
 
 
 
 Copper . . 
 
 
 
 
 
 
 
 etc. 
 
 
 
 
 
 
 
MECHANICS OF 'FLUIDS. 121 
 
 188. Exercise. Determine the density of a substance 
 lighter than water. 
 
 As in the last experiment, determine the weight in air, and 
 also the weight of a piece of lead or other metal of sufficient 
 mass to sink the specimen in water. Then determine the 
 weight of the sinker in water, and also of the specimen and 
 sinker combined. From these data, the volume of the water 
 displaced by the substance is easily obtained. How? Divide 
 the weight in air by the volume, and the required density is 
 obtained. 
 
 Check this in the same manner as in the last experiment. 
 
 189. Exercise. Determine the density of a substance 
 soluble in water. 
 
 As in Art. 182, find the weight of an equal volume of some 
 liquid of known density in which it is insoluble. This divided 
 by the density of that liquid will give the volume of the 
 substance. Why? Now proceed as in Art. 187. 
 
 Rock-salt is insoluble in naphtha, rock-candy and saltpetre in 
 strong alcohol, alum and blue vitriol in oil of turpentine, etc. 
 
 190. Exercise. Determine the density of a liquid. 
 
 For accurate work, use the specific-gravity bottle. It is a 
 small flask holding usually 10, 25, 50, or 100 ccm., closed with 
 an accurately fitting glass stopper, through which is a small 
 capillary opening. Thoroughly clean the bottle, rinsing it out 
 finally with strong alcohol, and dry by forcing into it a stream 
 of air passing through a heated tube. After weighing the 
 bottle, ascertain its capacity if not already known, then fill it 
 with the liquid whose density is sought, wiping the exterior of 
 the bottle dry, and removing the excess of the liquid that 
 escapes through the hole in the stopper, and find its weight. 
 
122 PRACTICAL PHYSICS. 
 
 Deducting the weight of the empty bottle, divide the remainder 
 by the volume of the bottle, and you have the density. This 
 result, when great accuracy is required, must be corrected for 
 temperature, etc. Consult Stewart and Gee's " Practical 
 Physics," vol. i. 
 
 For approximate work, a small Florence flask may be used, 
 filling it with water up to a line marked on the neck. 
 
 191. Exercise. Determine the density of a liquid by 
 weighing a solid in it. 
 
 Make a sinker out of a thick piece of glass rod. Fasten it 
 by a fine thread to the hook on the frame of the scale-pan. 
 Find the apparent loss of weight of the sinker in water, and 
 in the liquid whose density is sought. What does this 
 apparent loss represent? Divide the apparent loss in the 
 liquid by the apparent loss in water, and the quotient will be 
 the density. 
 
 192. Exercise. Determine the density of a substance in 
 a state of powder. 
 
 Use the flask of Art. 190, find its weight, then re-weigh it 
 after filling it part full of the powder. Now cover it with water, 
 place it beneath the bell- jar of the air-pump, and exhaust the 
 air, the water taking the place of the air within the powder. 
 If the substance is soluble in water, some other liquid must be 
 used. On removing the flask from the pump, ascertain the 
 weight after filling it full of water. Let / = weight of 
 the flask, w = weight of substance after deducting weight 
 of the flask, w r = weight of substance when covered with 
 water, w" = weight of water required to fill the flask when the 
 substance is removed. Then w' w = weight of water 
 added to fill the flask when the substance was in it, and 
 
MECHANICS OF FLUIDS. 
 
 123 
 
 w " _ ( w ' _ w) = weight of water whose volume is that of the 
 substance. Therefore the density = 
 
 w" w' 
 
 193. Exercise. Determine the density of a solid with 
 Nicholson's hydrometer. 
 
 This instrument usually consists of a metal cylinder with 
 conical ends, to the vertices of which are soldered stout wires. 
 On the end of one wire is soldered a small 
 scale-pan, and on the other a perforated 
 pan (Fig. 87). The lower end of the 
 cylinder is loaded with shot so that, when 
 the apparatus is placed in water, it takes 
 a vertical position with the cylindrical part 
 nearly submerged. 
 
 To use this apparatus, place on the 
 upper pan a sufficient number of known 
 weights to sink it to a mark on the stem 
 just below the scale-pan. Let a represent 
 the number of grammes required. Then 
 place on the pan the substance whose density is required, and 
 add weights till the instrument sinks to the mark on the 
 stem. Let b represent the number of grammes added. Then 
 a b = the weight of the substance. Now transfer the 
 substance to the lower pan, tying it on if necessary, and 
 observe how many weights must be added to the b weights to 
 sink the instrument to the mark on the stem. Let c represent 
 
 the number of grammes necessary. Then 
 Why? 
 
 a - b 
 
 density. 
 
 194. Exercise. Determine the density of a substance 
 with the Jolly balance. 
 
124 
 
 PR A C TIC A L PH YSICS. 
 
 Solids are weighed as directed in Art. 24, but with the lower 
 pan attached, and immersed in water. The weight in water is 
 obtained by placing the substance on the lower pan. 
 
 To find the density of a liquid, weigh a solid insoluble in it, 
 first on the upper pan, then on the lower pan when immersed 
 in water, and finally on the lower pan when immersed in the 
 liquid. Then proceed as in Art. 191. 
 
 195. Exercise. Determine the density of a liquid by 
 means of a Nicholson's hydrometer. 
 
 Weigh the instrument, then place it in water, adding weights 
 to the upper pan till it sinks to the mark on the stem. The 
 weight of the water displaced by the instrument will be the sum 
 of the weights on the pan and that of the instrument. Why? 
 In like manner, determine the weight of the liquid 
 displaced, whose density is required. From these 
 data, the density is easily determined. How? 
 
 For corrosive liquids, a glass hydrometer must 
 be used. In such instruments, the lower pan is 
 usually omitted. 
 
 196. Exercise. Make out of light wood a 
 bar of uniform size throughout, having a length 
 of 30 cm. and a cross-section of 1 scm. Bore a 
 hole several centimetres deep into one end, and 
 put in pieces of lead sufficient to maintain the bar 
 in a vertical position when floating in water, closing 
 the hole with cement. Lay off on the bar a decimal 
 scale, the zero at the loaded end. Give the apparatus a thin 
 coat of paraffine. Now float the instrument in a vessel of 
 water, and note the division of the scale to which it sinks ; 
 then place it in the liquid whose density is sought, and take the 
 
 FIG. 88. 
 
MECHANICS OF FLUIDS. 
 
 125 
 
 reading. The quotient of the former by the latter is the density 
 of the liquid. Why? 
 
 For accurate determinations, especially of corrosive liquids, 
 glass hydrometers (Fig. 88) with graduated stems are usually 
 employed. The method of use is similar to that illustrated 
 above. 
 
 Make a five-per-cent, a ten-per-cent, and a twenty-per-ceut 
 solution of common salt, and determine, by 
 means of the hydrometer of constant weight, 
 the density of each. Verify the results by 
 some one of the methods already given. 
 
 197. Exercise. Fit a rubber stopper with 
 two holes to a small Florence flask. In this 
 stopper, insert, air-tight, two glass tubes, each 
 75 cm. long, and bent twice at right angles at 
 the end next the cork (Fig. 89), so that the 
 tubes will not stand so close together. Sup- 
 port the apparatus in a vertical position, 
 with the end of one tube dipping into a 
 beaker of water, and the other into a vessel 
 containing the liquid whose density is sought. 
 Carefully measure the capillary effect. Now 
 gently warm the flask till part of the air is ex- 
 pelled. When cold, the liquids having ceased 
 
 to rise, measure the height of each liquid Fie< 89 - 
 
 above that in the vessel. The ratio of these heights corrected 
 for capillarity will be the inverse ratio of their densities. 
 
 198. Exercise. Determine the density of air. 
 
 Fit to a stout Florence flask of about one litre capacity a 
 rubber stopper through which is inserted a good stop-cock. 
 
126 PRACTICAL PHYSICS. 
 
 Dry the flask, and determine its weight. Then exhaust the air 
 as completely as possible, reading the pressure-gauge on the 
 pump as well as the barometer. Weigh the exhausted flask, 
 then measure its capacity, and compute from these data the 
 weight of one cubic centimetre of air, that is, its density. 
 The capacity of the flask can be found by weighing it full 
 of water. 
 
 For more accurate methods, consult Roscoe and Schorlem- 
 mer's " Chemistiy," vol. iii. pt. i. 
 
HEAT. 127 
 
 CHAPTER IV. 
 
 HEAT, 
 I. HEAT, AND MECHANICAL MOTION. 
 
 199. Apparatus. Flint and Steel, Fire-Syringe, Tinder, 
 Bottles, Thermometer, Metal Rod, Tumblers, Mercury, Whirl- 
 ing-Machine, Air-Thermometer, Condensing-Pump, Air-Pump, 
 Florence Flasks, Pyrometer, Radiometer, etc. 
 
 200. Exercise. Hold a piece of hardened steel, as the 
 back of the blade of a large pocket-knife, between the thumb 
 and forefinger of the right hand, and strike a glancing blow 
 against the sharp edge of a piece of flint. Observe any 
 attending phenomena. Examine the substances after 
 striking them together a few times. Is there any evi- 
 dence of any quantitative connection between the energy 
 expended and the heat obtained ? 
 
 201. Exercise. Place a small piece of German 
 tinder in the cavity at the end of the piston of a Fire- 
 Syringe (Fig. 90) , and force it quickly into the cylinder. 
 Remove the piston as soon as possible, and examine 
 the tinder. After each introduction of the piston, 
 fresh air must be introduced into the tube to supply 
 
 If the syringe has a glass cylinder, introduce within 
 it a pellet of cotton-wool moistened with carbon disulphide. 
 
128 PRACTICAL PHYSICS. 
 
 Remove it after it has remained a few moments, and force in 
 the piston, keeping a close watch on the tube. 
 
 Account for the phenomenon attending this experiment. 
 
 202. Exercise. Fill a bottle of about four ounces capacity 
 half full of water, and take the temperature with a thermometer. 
 The water should be at the temperature of the room. Now 
 cork the bottle, wrap it up in several thicknesses of paper to 
 keep heat from being communicated to it from the hand, shake 
 vigorously for an observed number of minutes, and again take 
 the temperature. Ascertain the effect of increasing the time 
 of shaking. Is there any evidence of any connection between 
 the amount of motion and the heat? Devise some way of 
 showing that the rise in temperature was not due to heat 
 communicated to the water from the hand. 
 
 203. Exercise. Rub a metal rod vigorously with a piece 
 of leather for a few minutes, protecting the rod from the 
 heat of the hand by a paper holder. Touch the rod to a 
 piece of phosphorus. Inference. Have you any equivalent 
 for the energy expended in rubbing the rod? Is there any 
 evidence of any quantitative relation between the heat devel- 
 oped and the energy expended? If energy is indestructible, 
 what would you infer is the nature of heat ? 
 
 Caution. Always cut phosphorus under water, and never handle it 
 with dry fingers. 
 
 204. Exercise. Wrap each of two tumblers with several 
 thicknesses of paper to keep from them the heat of the 
 hand. Fill one of the tumblers one-third full of mercury, 
 and determine its temperature by inserting a thermometer. 
 Then, pour the mercury rapidly, in a stream as large as a 
 
HEAT. 
 
 129 
 
 slate-pencil, back and forth between the tumblers for five 
 times, letting the mercury fall from a height of about 25 cm. 
 Take the temperature. Ascertain the effect of ten pourings ; 
 twenty. Repeat these tests, letting the mercury fall 50 cm. 
 Inference. 
 
 The mercury should be at the temperature of the room at the 
 beginning of each set of pourings. 
 
 205. Exercise. Attach to a whirling-machine a brass 
 tube about 15 cm. long and 15 mm. diameter (Fig. 91). Fill 
 it half full of alcohol, and close the end with a cork. Rotate 
 
 c-w 
 
 FIG. 91. 
 
 the apparatus rapidly, applying a brake made of two pieces 
 of board hinged at one end with a strip of leather, and also 
 Covered with leather at the places of contact with the tube. In 
 a few minutes, the alcohol can be made to boil vigorously, as 
 the experimenter will find ample evidence. Account for the 
 heat. 
 
130 
 
 PRACTICAL PHYSICS. 
 
 206. Exercise. Blow a stream of air with a small bellows 
 against the bulb of a sensitive thermometer, or the face of a 
 thermopile (Fig. 114), and record the effect. Explain. 
 
 207. Exercise. Compress air within the copper reservoir of 
 the condensing-pump, obtaining as high a pressure as possible. 
 After the apparatus has stood long enough to acquire the tem- 
 perature of the room, turn the stop-cock, directing the escaping 
 air against the bulb of a thermometer, or the face of the thermo- 
 pile, and record the effect. Whence does the 
 
 air, on escaping, acquire its kinetic energy? 
 Devise some way of proving your answer. 
 
 Suspend a thermometer within the receiver 
 of the air-pump, observing the effect as the 
 exhaustion proceeds. Explain. 
 
 208. Exercise. Fit, air-tight, to a Flor- 
 ence flask a cork through which passes a 
 J-shaped tube reaching nearly to the bottom 
 of the flask, and a thermometer with the bulb 
 at the centre of the flask (Fig. 92). Fill the 
 flask a little less than half full of water at 
 the temperature of the room, and hold it sub- 
 merged in a vessel of boiling water for 30 
 seconds. Note carefully the effect produced on 
 both the water of the flask and the thermometer. 
 Now remove the J-tube, and close, air-tight, 
 the opening in the cork. Change the water in 
 
 the flask for an equal amount of water of the temperature of the 
 room. Again hold the flask, for 30 seconds, in a vessel of 
 boiling water, and record the reading of the thermometer. 
 Account for the difference of temperature in the two cases. 
 
 FIG. 92. 
 
HEAT. 
 
 131 
 
 It will be necessary to hold the cork in the flask, or the elastic 
 force of the air will throw it out, and break the thermometer. 
 
 209. Exercise. Fasten a metal rod about 30 cm. long to 
 
 a wooden block by means 
 of small wire staples, the 
 block to be attached to a 
 board for a base. To the 
 opposite end of the board, 
 tack a thin piece, to sup- 
 port an index against 
 which rests the free end 
 FIG - 93 - of the rod (Fig. 93). The 
 
 pointer may be cut out of tin or brass, 
 
 and should have the pivot distant but a 
 
 couple of millimetres from the end of the 
 
 rod. Place a spirit or gas flame under 
 
 the rod for a few minutes, and watch the 
 
 effect. 
 
 Fasten the end of the pointer, by an 
 
 elastic, to a pin, and see if the expanding 
 
 rod does work by stretching the elastic. 
 
 Whence the energy expended in doing this 
 
 worK ? 
 
 210. Exercise. Place a Radiometer 
 (Fig. 94) in a beam of sunlight, or in the 
 light from a gas-jet admitted through an 
 opening cut in a large sheet of cardboard, 
 and notice the effect on the instrument. 
 Try a Bunsen or spirit flame which emits 
 
 heat and but little light. Interpose between the radiometer 
 
 FIG. 94. 
 
132 PRACTICAL PHYSICS. 
 
 and the source of light a chemical tank (Fig. 234) or flat bottle 
 filled with alum-water, a substance which cuts off but little light 
 and most of the heat. Substitute a solution of iodine in carbon 
 disulphide in place of the alum- water, thus cutting off the light, 
 and but little of the heat. Inference. 
 
 II. HEAT, AND CHEMICAL ACTION. 
 
 211. Apparatus. Test-Tube, Thermometer, Saucer, Mor- 
 tar, etc. 
 
 212. Exercise. Fill a test-tube one-third full of water, 
 and take its temperature with a thermometer. Fill a second 
 one one-third full of sulphuric acid, and likewise take its 
 temperature. Now pour the acid in a fine stream into the 
 water, and record the temperature. Inference. 
 
 213. Exercise. Place in a common saucer a lump of 
 freshly burned quicklime as large as a hen's egg. Ascertain 
 its temperature by placing the bulb of the thermometer in 
 contact with it for a few minutes. Now fill the saucer with 
 water, and, after a few minutes, take the temperature of the 
 lime. Explain. 
 
 214. Exercise. Powder in a mortar some crystals of 
 cupric nitrate. Spread the powder thickly on a piece of 
 tin-foil about 10 cm. square. Sprinkle on the powder a 
 small quantit} T of water, and quickly wrap it up in the foil, 
 pressing down the edges. Notice the changes which follow. 
 Explain. 
 
HEAT. 133 
 
 III. CONDUCTION OF HEAT. 
 
 215. Apparatus. Thermometer, Conductometer, Rods 
 of different kinds of material, Cylinder of Brass, and one of 
 Wood, Lead Balls, Brass Wire-Cloth, Wooden Cube, Air- 
 Thermometer, etc. 
 
 216. Exercise, Take the temperature of several different 
 articles in a room, at about the same distance from the floor, 
 by holding the bulb of the thermometer in contact with each 
 successively for a few minutes. Now test the same substances 
 as to temperature by touching them with the hand. Which 
 substances feel cold, and which do not? Account for the 
 differences between the conclusions based on the sense of 
 touch, and those on the indications of the thermometer. 
 
 217. Exercise. Compare the conductivity of several 
 substances. 
 
 Get a tin-smith to construct a tin dish with small tubes on the 
 side, in which can be cemented rods of different substances, as 
 iron, copper, zinc, brass, 
 etc. (Fig. 95). Coat 
 these rods with a thin 
 layer of beeswax ; then | 
 fill the tank with hot 
 water, and compare the 1 
 rates at which the wax 
 melts on the rods. FIG g . 
 
 As the four substances 
 
 mentioned differ but little in their capacity for heat, the rates 
 of transference of temperature will not differ much from those 
 for transference of heat. 
 
134 
 
 PRACTICAL PHYSICS. 
 
 218. Exercise. Wrap firmly around a brass cylinder a 
 layer of writing-paper, hold it in the flame of a lamp, and 
 record the time required to set the paper on fire. Then wrap a 
 similar piece around a wooden cylinder of the same size, and 
 hold it in the flame till the paper burns. Account for the 
 difference in the times. 
 
 219. Exercise. Compare the thermal conductivity of iron 
 and copper. 
 
 Select a stout wire of each, 35 cm. long, twist them together 
 for about 10 cm., and then insert the twisted end through a 
 
 wooden frame, the untwisted 
 parts being separated (Fig. 
 96). Attach lead balls or 
 marbles to the wires at reg- 
 ular intervals between the 
 supports, using shoemaker's 
 wax for the purpose. Place a 
 spirit-lamp under the twisted part, and record the effect on the 
 balls. Inference. 
 
 220. Exercise. Support a 
 piece of brass wire-cloth on the 
 ring of the iron stand, place a 
 gas-flame beneath it, and record 
 the effect on the flame (Fig. 97). 
 Test for gas above the gauze by 
 applying a lighted match. Ac- 
 count for the flame's not ex- 
 tending through the gauze at 
 first. Now let the wire-cloth 
 
 cool, then turn on the gas, and light it above the cloth. 
 
 FIG. 96. 
 
 FIG. 97. 
 
HEAT. 135 
 
 Account for its burning above the wire-cloth, and not below. 
 Observe the manner in which gum-camphor burns when placed 
 on the wire-cloth. 
 
 221. Exercise. Compare the conductivity of wood with 
 the grain, with that across the grain. 
 
 Coat uniformly with paraffine three of the faces about one 
 corner of a wooden cube 5 cm. on the edge. Heat a metal ball 
 of 2.5 or 3 cm. diameter in boiling water, and place it as 
 quickly as possible on one of the waxed faces of the cube. 
 Compare the shapes of the melted spots formed on the different 
 sides, and account for the difference. The ball must remain 
 on the block the same length of time in each case. Try cubes 
 made from pine, oak, maple, etc. 
 
 Wipe the water off of the ball before placing it on the 
 wax. 
 
 222. Exercise. Test the conductivity of water. 
 
 Place in a long test-tube some fragments of ice. Fill the 
 tube nearly full of water, keeping the ice from floating by 
 means of a small marble or stone. Hold the tube in an 
 inclined position in a Bunsen or spirit flame, heating the part 
 near the surface. Compare the temperature of the water at 
 the bottom with that at the top on its coming to a boil. 
 Inference. 
 
 In heating the tube, pass it slowly backward and forward 
 through the flame, as a sudden application of heat is liable to 
 break the tube. Why? 
 
 223. Exercise. Cork the neck of a large funnel, and 
 through it pass the stem of an air-thermometer, bringing the 
 bulb below the surface of the funnel. Support the apparatus 
 
136 
 
 PRACTICAL PHYSICS. 
 
 as shown in Fig. 98. Fill the funnel with water till the bulb 
 of the air-thermometer is covered to the depth of a 
 centimetre. Pour a spoonful of ether on the water, 
 set it on fire, and record the effect on the thermom- 
 eter. Inference. 
 
 The lower end of the thermometer- tube should 
 dip into colored water. By warming the bulb 
 with a gas-flame before introducing water into 
 the funnel, some of the air can be expelled 
 from the bulb, so that, on cooling, water will 
 FIG. 98. stand at an elevation of a few centimetres in 
 
 the tube. 
 
 IV. CONVECTION OF HEAT. 
 
 224. Apparatus. Florence Flasks, Glass Tubing, Lamp- 
 Chimneys, tall Bell-Jar, large Bottle, etc. 
 
 225. Exercise. Fill a large Florence flask two-thirds full 
 of water, introduce a little powdered cochineal or paper 
 raspings, and apply heat by placing it on a sand-bath on the 
 iron stand. Make a careful study of the action of the par- 
 ticles, to ascertain if any law governs their movements. 
 Explain. 
 
 226. Exercise. Construct out of glass tubing a rectangle 
 about 12 cm. long by 50 cm. wide, making the connections 
 with rubber tubing. A T-tube should be inserted at one corner 
 for convenience in filling, and to provide for the expansion of 
 the water. Fill the apparatus with water freed from air by 
 boiling, and introduce a little powdered cochineal. Now hold 
 one corner of the apparatus in a vessel of hot water, and 
 
HEAT. 
 
 137 
 
 observe the effect on the water in the tube. Apply ice or snow 
 to the upper corner of the rectangle, and record the effect. 
 Make the application at other points. Account for the results. 
 
 227. Exercise. Support a short piece of candle in a 
 vertical position in the bottom of a common plate. Light the 
 candle, and place over it a wide cylindrical lamp-chimney. 
 Pour water into the plate to prevent air entering the chimney 
 at the bottom. Note the effect on the flame. Insert a 
 cardboard partition in the chimney, reaching nearly to the 
 Hame, and note the effect. Soak some porous paper in a 
 solution of saltpetre, and dry it thoroughly. This is known 
 as touch-paper, and burns with the emission of considerable 
 smoke. Hold a piece of burning touch-paper over the top of 
 the chimney, and make a study of the air circulation. 
 
 228. Exercise. Paste paper over the cracks of a common 
 chalk-box to make it air-tight. Near one end of the cover, 
 make a number of small holes in a 
 
 circle somewhat smaller than the base 
 of a lamp-chimney (Fig. 99). In the 
 centre of this ring, place a lighted 
 taper. Near the other end of the 
 cover, cut a hole 25 mm. in diameter. 
 Place a lamp-chimney over each of 
 these openings, coating the edge of 
 each with paraffine to produce an air- 
 tight joint. Study the air currents 
 through the apparatus by holding 
 burning touch-paper over the tops of 
 
 the chimneys. Ascertain the effect of closing the top of the 
 chimney not containing the taper. 
 
 FIG. 99. 
 
138 
 
 PRACTICAL PHYSICS. 
 
 229. Exercise. To a tall wide-mouthed jar, fit a cork 
 ring supporting a wide glass chimney. Place the jar over a 
 candle standing in a plate of water. After observing the 
 effect on the flame, insert in the chimney 
 
 a smaller one extending down nearly to 
 the flame, supporting it by a wire frame 
 (Fig. 100). Study the air-currents with 
 touch-paper. 
 
 Paper cylinders may be substituted for 
 the chimneys. 
 
 230. Exercise. Invert a tall jar, at 
 least 50 cm. high, over a stand support- 
 ing several tapers 
 
 <^~^ (Fig. 101). The 
 
 stand may be made 
 by inserting a stout 
 wire into a circular 
 piece of board for 
 
 ^ O a base, supporting 
 
 !p the tapers on wire FIG. 100. 
 
 arms made to re- 
 tain their places on the standard by 
 the friction of the spiral formed on 
 one end. Observe the order in which 
 the tapers are extinguished. Why do 
 the tapers go out? What is implied 
 by the order in which they are ex- 
 tinguished? Ascertain the effect of 
 introducing fresh air by means of a 
 
 tube reaching to the top of the standard, and connected to 
 
 a bellows. 
 
 FIG. 101. 
 
HEAT. 
 
 139 
 
 231. Exercise. Test different parts of the schoolroom 
 for carbonic acid. 
 
 Prepare a number of litres of lime-water by stirring quicklime 
 in distilled water, and, after standing a few hours, filtering 
 it through porous paper (Fig. 102). Select a clear white glass 
 bottle, holding, when full, 10J fluid ounces of water. Dry it 
 thoroughly, and fill it with the air to be tested by taking the 
 bottle to that part of the room, and sucking out the air in it by 
 means of a glass tube. Avoid breathing through the tube into 
 the bottle. Now introduce half a fluid 
 ounce of clear lime-water, cork the bottle, 
 and shake vigorously for several seconds. 
 If, after the air-bubbles have disappeared, 
 the liquid is not clear, the air examined 
 contains at least 0.06 per cent of car- 
 bonic acid. If an eight-ounce bottle 
 is used, turbidity indicates at least 0.08 
 per cent. A six-and-a-half-ounce bottle 
 will show 0.1 percent; a five-and-a-half- 
 ounce bottle will show 0.12 per cent. If 
 one ounce of lime-water is used, a seven 
 
 ounce bottle will show 0.2 per cent; a five-ounce bottle will 
 show 0.3 per cent ; a four-ounce bottle will show 0.4 per cent. 
 Compare the air of a room which has recently been occupied 
 by a large class with that of one which has been vacant for 
 several hours. Test the air at the top, at the middle, and at 
 the bottom of the room. 
 
 Breathe through a glass tube, holding the end in a vessel of 
 lime-water, and note the effect. Also let a candle burn for a 
 short time in a large bottle, then remove it, pour in lime-water, 
 shake the bottle, and mark the effect. Account for the air of 
 rooms becoming vitiated. 
 
 FIG. 102. 
 
140 PRACTICAL PHYSICS. 
 
 V. EXPANSION BY HEAT. 
 
 232. Apparatus. Heavy Wire, Pyrometer, Metal Ball, 
 Caliper, Compound Bar, Florence Flasks, Glass Tubing, Ther- 
 mometer, etc. 
 
 233. Exercise. Ascertain whether heat affects the length 
 / \ of a wire. 
 
 f \J Bend a thick brass or iron wire about 25 cm. 
 
 long into a rectangular figure ; cut out of one side 
 a piece 5 cm. long, and adjust the link so that 
 this piece fits exactly the place from which it 
 was taken when at the temperature of the room 
 (Fig. 103). The ends of the parts must be planes 
 perpendicular to the axis of the wire. Hold the 
 FIG. 103. straight piece with a pair of tongs in a flame, and, 
 when hot, try to insert it in its place in the link. Inference. 
 
 234. Exercise. Determine the coefficient of expansion of 
 a metallic rod. 
 
 Employ an apparatus of the form shown in Fig. 104, in 
 which, by means of a compound lever, the expansion is 
 magnified. HK is a copper tank 30 cm. long, 5 cm. deep, 
 and 3 cm. wide. This rests on the base of the instrument, and 
 is prevented from moving towards K by a brace L. In this 
 tank, place the rod, rest it on short pieces of glass tubing 
 placed across the bottom. One end of the rod must press 
 firmly against the end K of the tank ; the other end must 
 press against the flat vertical rod D which is soldered at right 
 angles to the rod BF supported by the block P, and free to 
 turn about its axis without play. The bearing at A is made 
 in two parts, and works in a groove in the rod BF, preventing 
 
HEAT. 
 
 141 
 
 motion lengthwise. The pointer CE is soldered at right angles 
 to BF at B, the part BE being heavy enough to cause D to 
 press firmly against the end of the rod in the tank. The ex- 
 pansion of the rod will cause the pointer to move over the 
 scale M, and the space traversed divided by the ratio of BC to 
 the arm D will be the expansion of the rod. It should be 
 
 FIG. 104. 
 
 observed that the arm D extends from the centre of the end of 
 BF to the point of contact of the upper edge of the rod in the 
 tank with D. 
 
 To use the apparatus, measure accurately the rod by laying 
 it on a finely divided steel scale, then place it in the tank and 
 record the reading of the pointer and the temperature of the 
 rod. Now fill the tank with boiling water, and again record 
 the reading of the pointer and the temperature of the rod or 
 water. From these data compute the rod's change in length, 
 and also its change per unit of length for one degree. 
 
 235. Exercise. Determine the effect of heat on a metal 
 ball. 
 
 Adjust a pair of calipers so that an iron or brass ball will 
 
142 PRACTICAL PHYSICS. 
 
 just pass between the points. Again caliper the ball after it 
 has stood for a few minutes in hot water. What fact regarding 
 the effect of heat on substances is shown by this experiment 
 different from that shown in the last experiment? Compute 
 the change in volume per degree from the change in diameter. 
 
 236. Exercise. Select two pieces of brass tubing about 
 8 cm. long each, such that one will just telescope the other. 
 Fit to each a wooden handle. Heat the smaller tube in a gas- 
 flame, and try to insert it within the larger one. Heat both 
 tubes, and then try to insert one within the other. Inference. 
 
 237. Exercise. Fasten together by rivets, at intervals of 
 2 cm., a strip of sheet-iron, and one of copper or brass, each 
 15 cm. long and 2 cm. wide. Place this bar on the supports 
 A and B of the apparatus shown in Fig. 36. Place a spirit- 
 lamp beneath the centre of the bar. What is implied by the 
 movement of the indicator ? Ascertain the effect of placing ice 
 on the upper side of the compound bar. 
 
 238. Exercise. Determine the effect of heat on the 
 volume of a liquid. 
 
 Fit a perforated cork to a Florence flask, and insert a glass 
 tube about 30 cm. long, just reaching through the cork. Fill 
 the flask and part of the tube full of water, excluding all air- 
 bubbles. The cork and tube must fit water-tight. Place 
 the apparatus on the sand-bath of the iron stand. Mark the 
 position of the water in the tube. Apply heat, and note 
 the effect. Inference. 
 
 239. Exercise. Determine the coefficient of expansion of 
 a liquid. 
 
HEAT. 143 
 
 Close one end of a glass tube 15 cm. long and about 5 mm. 
 in diameter, by heating the end in a gas-flame. Select one of 
 uniform bore. Fill the tube part full of some liquid, as water, 
 alcohol, glycerine, ether, or naphtha, and then tie it to a 
 chemical thermometer, so that the thermometer-scale may be 
 used in measuring the liquid in the tube. Support the appara- 
 tus in a beaker of ice-water, and, when it has acquired the 
 temperature of the water, ascertain the length of the liquid 
 column in terms of the spaces of the attached thermometer- 
 scale. Then plunge the apparatus into a vessel of hot water, 
 and note the thermometer reading, and the length of the liquid 
 column after the liquid has ceased rising in the tube. The part 
 of the tube containing the liquid must be kept in the water so 
 that all the liquid may be at the same temperature. Compute, 
 from the data, the expansion per unit of volume for one degree, 
 neglecting the effect of the heat on the capacity of the tube. 
 
 240. Exercise. Determine the effect of heat on the 
 volume of air. 
 
 Procure a heavy glass tube about 30 cm. long and 2 mm. 
 internal diameter, one end terminating in a bulb of about 
 5 cm. diameter. A small Florence flask closed with a good 
 cork, through which passes a glass tube, will make a fair 
 substitute. Support the tube in a vertical position, with the 
 end dipping into a shallow vessel of colored water. Apply 
 heat to the bulb by either a gas-flame, or by pouring on hot 
 water. Note the effect. Inference. 
 
 241. Exercise. Determine the coefficient of expansion of 
 air. 
 
 Procure a glass tube about 20 cm. long and 1 mm. internal 
 diameter. Introduce into it an index of mercury 5 mm. long 
 
144 PRACTICAL PHYSICS. 
 
 by plunging it into a bottle of mercury, and then holding the 
 finger firmly over the outer end of the tube as you remove it 
 from the bottle. By inclining the tube, move the index along 
 to the middle of the tube, and then close one end of the tube 
 by holding it, in a horizontal position, in a gas or alcohol 
 flame. Tie the tube to a chemical thermometer so that the 
 thermometer-scale may be used as one of equal parts in 
 measuring the length of the confined air-column in the tube. 
 Place the apparatus in melting ice, and determine the length of 
 the air-column when the thermometer-reading is zero. Before 
 taking the readings, tap the tube with the finger to facilitate 
 the movement of the mercury index. Now place the apparatus 
 in a vessel of water so arranged that the temperature can be 
 increased at pleasure, and determine the length of the air- 
 column for 10 C., 20 C., 30 C., etc. A long shallow dish 
 should be employed in order that the apparatus may be placed 
 in nearly a horizontal position to remove the pressure on the 
 air produced by the index. Such a dish can be easily made 
 out of sheet-lead, closing the joints with plaster-of-Paris. Heat 
 the tube by pouring hot water into the dish. Compute, 
 from the data, the expansion per degree of the air per unit 
 of volume at C., between degree and 10 degrees, 10 
 degrees and 20 degrees, 20 degrees and 30 degrees, etc., 
 neglecting the errors arising from the effect of heat on the 
 volume of the tube, and from the lack of uniformity in the bore 
 of the tube. 
 
 242. Exercise. Fit a perforated cork, through which 
 passes a glass tube, to a test-tube. As a test-tube will stand 
 but little pressure, soft and elastic corks must be employed. 
 Fill the tube with water, recently boiled to expel the air, 
 half-way up the inserted tube. Pack the apparatus in 
 
HEAT. 145 
 
 finely broken ice, and watch the water-column for some 
 time. Remove from the ice, and, with as little delay as 
 possible, plunge the tube into hot water, recording the effect 
 on the column. Inference. 
 
 243. Exercise. Close one end of a piece of lead pipe 
 about 30 cm. long and 15 mm. in diameter by flattening it, on 
 an anvil, by a blow from a hammer. To the 
 
 other end, fit a perforated cork, through which 
 passes a glass tube about 20 cm. long. Bend 
 the lead into a coil, the plane of which is per- 
 pendicular to the glass tube (Fig. 105). Now 
 fill the apparatus with water till it stands at a 
 height of 4 or 5 cm. in the glass tube. Care 
 must be taken to exclude all air-bubbles from 
 the coil. Then pack the apparatus in a freezing 
 mixture made of three parts of pounded ice, and ." FlG 105 
 one of common salt. Mark the level of the 
 water in the tube when first placed in the freezing mixture. 
 Observe the change in level during the following twenty 
 minutes. Explain. 
 
 
 244. Exercise. Prepare an apparatus similar to that 
 used in Art. 242. Introduce several pieces of dry ice, then 
 fill the apparatus with kerosene till the column reaches within a 
 few centimetres of the top of the tube. Observe the change 
 of level as the ice melts. Measure the amount of change of 
 volume ; measure the amount of water produced by the ice. 
 From these data, compute the density of ice. 
 
146 
 
 PRACTICAL PHYSICS. 
 
 VI. THERMOMETBY. 
 
 245. Apparatus. Thermometer, Funnel, Florence Flasks, 
 Air-Pump, Condenser, Test-Tubes, etc. 
 
 246. Exercise. Test the accuracy of the location of 
 the freezing and the boiling points on a thermometer- 
 stem. 
 
 To ascertain if the zero-point is accurately located, support 
 the thermometer in a burette-holder, and pack around the bulb 
 
 pounded ice as far up the 
 stem as the zero -point. 
 The vessel containing the 
 ice should have a hole in 
 the bottom for drainage. 
 A common funnel will an- 
 swer (Fig. 106). Wash the 
 ice thoroughly before using, 
 so that the melting-point 
 will not be interfered with 
 by the presence of foreign 
 substances. After the ther- 
 mometer has remained a 
 
 FIG. 106. few minutes in the melting 
 
 ice, observe the reading of 
 
 the thermometer, using a magnify ing-glass to estimate fractions 
 of a degree. 
 
 To test the accuracy of the location of the boiling-point, 
 fit into a wide-mouthed Florence flask a large glass tube, as 
 a lamp-chimney, placing candle-wick around the base of the 
 tube, so that steam from the water in the flask escapes only 
 
HEAT. 
 
 147 
 
 from the top (Fig. 107). Hang the thermometer within this 
 tube, with the bulb 2 or 3 em. above the water in the flask, 
 and the boiling-point on the stem just above 
 the top of the tube. On boiling the water 
 in the flask, the mercury-column is enveloped 
 in steam, and will be heated quite uniformly. 
 After the lapse of several minutes, the ap- 
 paratus having time to become thoroughly 
 heated, read the height of the mercury- 
 column, and also observe the barometric 
 pressure. As the boiling - point is affected 
 by changes in the atmospheric pressure, to 
 obtain the true boiling-point for the pressure 
 at the time of the experiment, apply the 
 formula t = 100 + 0. 0375 (b 760), in 
 which b is the observed barometric reading 
 expressed in millimetres. 
 
 The record may be kept as follows : 
 
 FIG. 107. 
 
 Freezing-point. . . . 
 True boiling-point . . 
 Boiling-point observed . 
 
 Error of instrument . . 
 
 , as computed for pressure of mm. 
 
 . Error of instrument 
 
 247. Exercise. Compare the temperature of boiling water 
 with that of the steam given off. 
 
 Boil some water in a flask. Compare the reading of the 
 thermometer when suspended within the flask, with the bulb 
 about two centimetres above the boiling water, with that when 
 the bulb is in the water. Ascertain the effect of placing 
 rough pieces of glass or stone in the flask. Account for 
 the difference. 
 
148 PRACTICAL PHYSICS. 
 
 248. Exercise. As in Art. 246', locate the freezing-point 
 on the thermometer-stem. Now hold the thermometer for 
 some moments in boiling water, and then replace it in the 
 vessel containing the melting ice, observing again the freezing- 
 point. Account for the difference. 
 
 249. Exercise. Fill a vessel of about one litre capacity 
 half full of cold water. Pour into it nearly as much more 
 boiling water, letting the stream strike a floating cork to break 
 the fall. Then observe the temperature at the top, at the 
 bottom, and midway. Now stir the water with the thermom- 
 eter, and again observe the temperature. Account for the 
 differences. What precaution does this experiment suggest 
 should be taken in obtaining the true temperature of a liquid? 
 
 250. Exercise. Assuming that one thermometer is cor- 
 rect, compare a second one with it, and make out a table of 
 corrections to be applied to its readings. 
 
 Suspend the two instruments side by side with the two bulbs 
 on the same level. Pack the bulbs in melting ice, and record 
 the reading of each. On removing the ice, place beneath the 
 thermometers a beaker of water so arranged that its temperature 
 can be varied at pleasure by introducing ice or applying heat. 
 Beginning with ice-water, apply heat, stirring constantly with 
 a glass rod, and record the readings of the thermometers, as 
 they hang with their bulbs immersed in the water, for every 
 change of 10 degrees in the standard, till the boiling-point is 
 reached. Conclude the observations by returning the standard 
 to the melting ice, and recording the reading. Correct the 
 standard by the deviation of this last reading from zero. 
 Reduce all the readings to the same thermometric scale, and 
 obtain the differences between corresponding ones. These 
 
HEAT. 
 
 149 
 
 differences will be the corrections to be applied to the ther- 
 mometer under examination to make its readings standard. 
 Enter results as follows : 
 
 Standard 0, 10, 20, 30, 40, 50, 60, 70, 80, etc. 
 
 Standard corrected .... 
 
 The one being tested . . . 
 
 Keduced to scale of standard, 
 
 Corrections to be applied . 
 
 251. Exercise. Determine the general effect of changes 
 in the atmospheric pressure on the boiling-point. 
 
 Fill a small beaker half full of water, and heat it over a lamp 
 till it nearly reaches the boiling-point. Take the temperature, 
 and then place the beaker under 
 the receiver of an air-pump. As 
 you exhaust the air, note from 
 time to time the temperature of the 
 boiling water as shown by a ther- 
 mometer suspended m it, at the 
 same time reading the pressure- 
 gauge of the pump. Inference. 
 
 Try alcohol, ether, naphtha, etc. 
 
 252. Exercise. Fill a round- 
 bottomed Florence flask half full 
 of water, and heat it over a lamp. 
 After the boiling has continued for 
 
 some minutes, and the air has been expelled, remove the flask 
 from over the lamp, cork tightly, support it in an inverted 
 position (Fig. 108) on a ring of the iron stand, and pour over 
 it cold water. Account for the result. 
 
 FIG. 108. 
 
150 PRACTICAL PHYSICS. 
 
 253. Exercise. Determine the melting-points of such 
 substances as tallow, lard, paraffine, beeswax, etc. 
 
 Fill, by suction, with the melted substance, a capillary glass 
 tube having thin walls, and close the end by fusing it in a lamp. 
 On cooling, you will have a fine opaque thread of the substance 
 in the tube. Fasten this tube alongside the thermometer so 
 that the bulb and the substance to be melted will be side by 
 side. Place a small glass beaker nearly full of water on the 
 sand-bath over the lamp. As the water approaches the melting- 
 point of the substance, stir it gently with the thermometer, 
 watching closely for any change in the appearance of the 
 contents of the tube. On melting, it loses its opacity; and, 
 just as soon as that change is observed, the reading of the 
 thermometer must be taken. Now let the water cool, and 
 record the temperature at which opacity returns. Repeat the 
 experiment several times, and use the average of the results. 
 
 Suitable capillary tubes can be easily made by drawing out, 
 in a flame, a piece of soft glass tubing till the diameter is about 
 one millimetre. 
 
 254. Exercise. Determine the boiling-point of a liquid, 
 as ether, naphtha, alcohol, turpentine, etc. 
 
 Fit to a test-tube of 25 mm. diameter a cork with two 
 holes. In one of these openings, insert a thermometer, and, 
 in the other, a glass tube bent at right angles to serve as an 
 escape for the vapor of the liquid to be tested (Fig. 109). 
 Fill the test-tube one-third full of the liquid, and insert the 
 cork, with the thermometer-bulb two centimetres above the 
 liquid. Apply heat, and, on vapor escaping freely from 
 the bent tube, take the reading of the thermometer. If the 
 vapor of the liquid is combustible, apply the heat by means 
 of an oil or water bath. 
 
HEAT. 151 
 
 Why not have the thermometer-bulb in the liquid ? Try it, 
 comparing results with those obtained 
 by the above process. Repeat the 
 experiment with the thermometer in 
 the liquid, having first placed in the 
 test-tube some fragments of some 
 substance not acted on by the liquid. 
 Inference. 
 
 For most liquids, the temperature 
 increases 0.0375 C. for an increase of 
 one millimetre in the atmospheric 
 pressure. Hence, to reduce the tem- 
 perature of the boiling-point obtained 
 above to that for a pressure of 760 
 mm., add to it 0. 0375 (760 6), in 
 which b is the barometric pressure 
 
 at the time when the observation was made on the temper- 
 ature. 
 
 255. Exercise. Determine the boiling-point of a satu- 
 rated solution of some substance, as common salt, saltpetre, 
 etc. 
 
 Proceed as in the last experiment. The thermometer-bulb 
 must be in the liquid. Why? Pieces of broken glass, or some 
 substance on which the liquid does not act, must be placed in 
 the tube. Why? 
 
 256. Exercise. Separate a mixture of two liquids having 
 different boiling-points, as alcohol and water. 
 
 Set up an apparatus like that shown in Fig. 110. In the 
 first flask, put the mixed liquids. This flask is connected to 
 the second one by a bent tube of glass, and, in a similar 
 
152 
 
 PRACTICAL PHYSICS. 
 
 FIG. 110. 
 
 manner, the second one is joined to the third. The first flask 
 is directly over the lamp, the second one stands on a water- 
 bath, and the third one stands in a vessel of cold water to keep 
 
 it at a low temper- 
 ature. The liquid 
 in the first flask is 
 made to boil gently, 
 .while that in the 
 second one is kept 
 at a temperature 
 intermediate be- 
 tween the boiling- 
 points of the two 
 liquids, a condition 
 easily determined 
 
 by having a thermometer inserted through the cork into the 
 flask. After a quantity of liquid 
 has been collected in the third 
 flask, examine it to ascertain 
 whether the experiment has been 
 successful. 
 
 A very convenient form of 
 condenser is shown in Fig. Ill, 
 known as Liebig's. It con- 
 sists of a large tube kept filled 
 with cold water flowing from 
 some convenient reservoir, 
 through which passes the deliv- FlG - 11L 
 
 ery-tube from the flask containing the liquids to be separated. 
 The cold water enters the enveloping- tube at the lower end, 
 and escapes from the upper end. 
 
HEAT. 
 
 153 
 
 VII. RADIANT HEAT. 
 
 FIG. 112. 
 
 257. Apparatus. Air-Thermometer, Leslie's Cubes, Flor- 
 ence Flasks, Differential Thermometer, etc. 
 
 258. Exercise. Determine how the temperature of a 
 substance affects its power to radiate heat. 
 
 Construct of tin or copper a cubical box one 
 decimetre on each edge, with an 
 opening in one side for the intro- 
 duction of water (Fig. 112) . Fill 
 it with water, bring its tempera- 
 ture to 10 C., and place it at 
 a distance of, say, 3 cm. from a 
 Differential, or Air, Thermome- 
 ter (Fig. 113), observing the effect. Raise 
 the temperature to 20 C., and again read 
 the thermometer. Similarly test 30 C., 
 40 C., etc. Compare the indications of FIG. 11:3. 
 
 the air-thermometer with the readings of the mercurial one 
 in the tank to see if there is any law connecting the two. 
 All air-currents must be carefully excluded. 
 
 259. Exercise. Ascertain how distance affects the inten- 
 sity of radiant heat. 
 
 Construct of tin or copper a tank 5 cm. thick by 50 cm. square. 
 Fill this with boiling water, and place it at a distance of a few 
 centimetres from the face of a Thermopile (Fig. 114), having 
 a conical mouth-piece to concentrate the heat rays on the 
 face. Observe the deflection of the galvanometer connected 
 with the thermopile. Test the effect of increasing the distance 
 
154 
 
 PRACTICAL PHYSICS. 
 
 of the tank from the thermopile. Is the surface which sends 
 its heat to the pile the same for all distances of the tank? 
 How does increasing the distance of the pile from the tank 
 affect the area of the surface radiating its heat to the pile? 
 What law for intensity of radiant heat can be inferred from the 
 results ? 
 
 The greatest distance that the tank should be placed from 
 the pile is that at which the sides of the conical reflector, 
 
 FIG. 114. 
 
 on being extended, just touch the edges of the face of the 
 tank. A sensitive air-thermometer can be substituted for 
 the thermopile by adapting to it a funnel-shaped reflector 
 such as accompanies the pile, supporting it in a burette- 
 holder. 
 
 260. Exercise. Employing the apparatus of the last 
 experiment, place a large sheet of cardboard between the tank 
 of water and the thermometer, and record the effect on the 
 latter. What inference as to direction of radiation can be 
 made? 
 
HEAT. 155 
 
 26L Exercise. Ascertain if air is essential to the trans- 
 mission of radiant heat. 
 
 Fit a cork with two holes to a large Florence flask. Insert a 
 thermometer in one of these openings so that the bulb is near 
 the centre of the flask. In the other opening, fit a glass tube, 
 connecting it by rubber tubing to a good air-pump. Exhaust 
 the air as complete!} 7 as possible, record the reading of the ther- 
 mometer, then plunge the flask into hot water, and again read 
 the thermometer. Ascertain how much the thermometer would be 
 affected if the air were not exhausted from the flask. Inference. 
 
 262. Exercise. Determine the law for the reflection of 
 heat. 
 
 Place a tank like the one employed in Art. 258, filled with 
 hot water, on a proper support, adjusting the height to that 
 
 FIG. 115. 
 
 of the bulb of a differential thermometer. Half-way between 
 Jie thermometer and the face of the tank, place a mirror hori- 
 zontally. Between the mirror and the tank, support a sheet of 
 cardboard in which a hole 3 cm. in diameter has been cut at 
 the point where a line joining the centre of the face of the cube 
 and the centre of the mirror intersects it (Fig. 115). What must 
 
156 
 
 PRACTICAL PHYSICS. 
 
 be the course of the heat rays which reach the thermometer? 
 Ascertain if moving either the radiator or the thermometer 
 affects the readings of the thermometer. What law expresses 
 the facts observed? 
 
 Ascertain if different kinds of reflectors are equally good. 
 
 Test the effect of fineness of polish. 
 
 Test the effect of increasing the size of the incident angle. 
 
 263. Exercise. Compare the absorptive powers of differ- 
 ent substances. 
 
 Coat with lamp-black one of the bulbs of a differential ther- 
 mometer by mixing the lamp-black with thin shellac varnish. 
 
 FIG. 116. 
 
 Place the blackened bulb in the focus of a concave reflector 
 such as is frequently placed behind wall-lamps (Fig. 116). At 
 a short distance in front of the reflector, place the cubical tank 
 of Art. 258, filled with hot water. Compare the effects of the 
 heat on the plain bulb and the blackened one. 
 
 Try, in succession, the following substances as coverings for 
 one of the bulbs : India-ink, tin-foil, foil of other metals, etc. 
 
HEAT. 157 
 
 Arrange the substances tried, in the order of their absorptive 
 power as shown by these experiments. 
 
 A differential thermometer, which will serve for these experi- 
 ments, may be made as follows : 
 
 Take two small flasks, and join them by a stout glass tube 
 about 30 cm. long and 1 mm. bore, with its ends bent at right 
 angles. Seal the flasks with wax to make them air-tight after 
 introducing within the tube two or three drops of colored 
 water. Attach a scale of equal parts to the horizontal portion 
 of the connecting-tube, and mount the apparatus on a support. 
 
 A simple way of comparing the absorbing power of substances 
 is the following : 
 
 Cut two pieces of bright tin plate 10 cm. square. Saw in a 
 narrow board two slits 10 cm. apart, and mount the plates in 
 them, having first coated the inner face of one of them with the 
 substance to be tested. Stick with wax, using as little as 
 possible, balls of equal size on the outside of each at about the 
 centre of the face. Now place a hot iron, as a soldering-iron, 
 midway between the two plates. The better absorbent will be 
 indicated by the melting of the wax holding the ball. 
 
 264. Exercise. Fill the chemical tank (Fig. 234) with 
 alum-water, place it between the sun and a large reading-glass, 
 and focus the rays on a sheet of paper. Compare the effect 
 with that obtained when the alum- water is omitted. Try the 
 effect of a solution of iodine in carbon disulphide. 
 
 265. Exercise. Ascertain if the radiating surface affects 
 the rate of cooling. 
 
 Take two tanks similar to that of Art. 258, and blacken the 
 faces of one with lamp-black, leaving the other bright. Fill 
 each with water at, say, 80 C. ; insert in each a thermometer, 
 
158 PRACTICAL PHYSICS. 
 
 and record the readings every five minutes for half an hour. 
 Inference. 
 
 Two bottles of the same shape and size may be used as 
 substitutes. 
 
 266. Exercise. Compare the radiating power of sub- 
 stances. 
 
 Using the apparatus of Art. 265, coat one face of the tank 
 with lamp-black, a second with white lead, a third with white 
 paper, and the fourth with cotton cloth. Fill the tank with 
 boiling water, and compare the radiating power of the four 
 faces by observing the effects produced on the thermometer as 
 each face is turned successively toward it for five minutes. 
 The initial temperature of the water in the tank must be the 
 same for each face. 
 
 Four equal bottles coated with the above substances respec- 
 tively may be used as substitutes. 
 
 A radiometer may be substituted for the thermometer in 
 many of these experiments in radiant heat, the intensity of 
 radiation being indicated by the speed with which the vanes 
 rotate. 
 
 267. Exercise. Determine if the rate of cooling of a 
 body is affected by the amount by which its temperature 
 exceeds that of the surrounding air. 
 
 Take a cylindrical tin can of about one litre capacity, such 
 as is used in preserving fruit, remove one end by unsoldering 
 it, and fit to it a wooden cover, through the centre of which is 
 a small hole of sufficient size to admit the bulb of a thermometer 
 (Fig. 117). Blacken thoroughly the inside of the can, as well 
 as the under side of the cover, by holding it in the smoke from 
 burning gum-camphor. Select a thermometer having a large 
 
HEAT. 
 
 159 
 
 bulb as the object whose rate of cooling is to be studied. Slide 
 over its stem a cork selected to fit the hole in the cover of the 
 can, that the thermometer may be supported with its bulb at 
 about the centre of the vessel. The tin can is designed to 
 exclude air-currents from the cooling body. To maintain the 
 surrounding air at a practically constant temperature, sink the 
 vessel nearly to its top in a large vessel of water. Take 
 the temperature, which will be that 
 of the chamber, then introduce 
 within the chamber the thermom- 
 eter heated to, say, 80 C., by ci 
 dipping it into hot water, care- 
 fully drying it with a cloth before 
 putting it in place. Record the 
 reading of the thermometer for 
 every half-minute. In a parallel 
 column, write the differences be- 
 tween these readings and the tem- 
 perature of the water. These will 
 be the excess of the temperature of the object over that of the 
 surrounding air for each half -minute. In a third parallel 
 column, write the number of degrees the temperature of the 
 object has fallen each half-minute. Finally, ascertain the ratio 
 of the excess of the temperature of the cooling body above the 
 temperature of the chamber, for each half-minute, to the fall of 
 temperature during each corresponding half-minute, and place 
 the results in a fourth parallel column. A comparison of these 
 ratios will enable you to decide whether the rate of cooling is 
 in any way connected with the temperature of the surrounding 
 medium. 
 
 FIG. 117. 
 
160 PRACTICAL PHYSICS. 
 
 VIII. CALORIMETBY. 
 
 268. Apparatus. Beakers, Thermometer, Florence Flasks, 
 Metal Balls of different substances and of the same diameter, 
 
 etc. 
 
 269. Exercise. Show that the capacity of water for heat 
 is nearly constant ; that is, the heat required to raise a given 
 quantity of water a given number of degrees in one part of the 
 thermometric scale is able to raise the same quantity nearly the 
 same number of degrees in any other part of the scale. 
 
 Balance two thin glass beakers of about one litre capacity 
 each, on the opposite pans of a balance, and pour into each 
 400 grammes of water. Let one be brought to the temperature 
 of the room, and the other heated to about 60 C. Replace 
 the beakers on the balance, and adjust the weights which have 
 been disturbed by evaporation. Now take the temperature of 
 each, observing the heated one last. Why? Then, without 
 delay, pour the heated one into the other, stirring constantly 
 with the thermometer for a few seconds, and record the temper- 
 ature of the mixture. The difference between the temperatures 
 of the mixture and the hot water will be the number of degrees 
 lost by the hot water. Likewise the difference between the 
 temperatures of the mixture and the cold water will be the num- 
 ber of degrees gained by the cold water. The average of the 
 initial temperatures will nearly equal that of the mixture ; the 
 discrepancy being due to the heat absorbed by the cold beaker, 
 that lost by radiation, and possibly that the amount of heat 
 required to raise cold water one degree is different from that 
 required to produce the same change in hot water. 
 
 Repeat the experiment, with the change that the cold water 
 is poured into the hot, to ascertain how much the heat in the 
 
HEAT. 161 
 
 warmer beaker influences the result. Then the heat in the glass 
 will go to raise the temperature of the cold water, and hence 
 increase the temperature of the mixture. 
 
 In subsequent experiments, methods of correcting for absorp- 
 tion and radiation are given. These corrections carefully 
 applied to this problem have shown that the capacity of water 
 for heat is not strictly constant, but increases slightly with the 
 temperature. 
 
 270. Exercise. Mix unequal quantities of water at differ- 
 ent temperatures, and ascertain the temperature of the mixture. 
 Compare the result with that obtained by computation on the 
 supposition that all the heat lost by the hot water went to 
 the cold water. 
 
 To compute the temperature, divide the total number of heat 
 units in the two quantities of water by the total quantity of 
 water. 
 
 271. Exercise. Determine the water-equivalent of a 
 vessel ; that is, find how much water will equal it in capacity 
 for heat. 
 
 Dry the vessel thoroughly, and let it come to the temperature 
 of the room, which will be indicated when a thermometer 
 suspended in it registers the same as when without it. Then 
 pour in it a known quantity of water, as .4 kg., at a known 
 temperature, say, 40 C., and record the temperature after the 
 lapse of about thirty seconds. The fall in temperature is due 
 to heat having been absorbed by the vessel, and to radiation, 
 while pouring in the water and stirring. This may be allowed 
 for as follows : Before pouring the water into the vessel, ascer- 
 tain the fall of temperature in one minute, then observe the fall 
 in one minute following the period of thirty seconds allowed for 
 
162 PRACTICAL PHYSICS. 
 
 the heat to be communicated to the vessel. Then the radiation 
 rate may be taken as the average of these two losses. One- 
 half of this will be the loss from radiation during the thirty 
 seconds, and will be the amount to be added to the observed 
 temperature of the water in the vessel to give the correct 
 temperature for the water, and hence of the vessel. The 
 number of calories Of heat consumed by the vessel will be 
 the loss of temperature on the part of the water, times the 
 amount of water. This divided by the gain of the vessel will 
 give the number of calories required to change the temperature 
 of the vessel one degree, and hence will be the number of 
 kilogrammes of water to which the vessel is equivalent. 
 
 272. Exercise. Determine the thermal capacity of a 
 substance, as lead, copper, etc. 
 
 Make a loose coil of a known weight of the metal in sheet 
 form, and suspend it, by a thread, in boiling water for a 
 sufficient time to acquire the temperature of the water. The 
 temperature of the boiling water must be observed. Why? 
 Pour into a beaker, whose water-equivalent has been deter- 
 mined as in Art. 271, a known weight of water of the tem- 
 perature of the room, and of sufficient amount to cover the coil 
 entirely when placed within it. Now transfer to it the heated 
 coil, stir the water around thoroughly with a thermometer, and 
 record the reading when it ceases to rise, and also the time 
 occupied in thus equalizing the temperatures. Keep up the 
 stirring for one minute longer, that the effect of radiation may 
 be observed. Half of this loss multiplied by the time occu- 
 pied in securing equalization must be added to the observed 
 temperature, to give the correct temperature produced in the 
 water by the heated coil. Now add to the weight of water 
 used, the water-equivalent of the beaker, and multiply this by 
 
HEAT. 163 
 
 the gain in temperature to obtain the number of calories of heat 
 imparted by the coil to the water and beaker. This product 
 divided by the number of degrees lost by the coil will give its 
 capacity for heat. 
 
 273. Exercise. Compare, by Tyndall's method, the ther- 
 mal capacities of several metals. 
 
 Make a ball out of each of the metals lead, tin, zinc, bismuth, 
 antimony, etc., by the aid of a pair of large bullet-moulds, and 
 an iron spoon in which to melt the metal. Reduce them to 
 the same weights by cutting off a part of the ball. Solder a 
 fine wire handle to each. Mould, 
 in a shallow pan, a cake of wax 
 about 5 mm. thick. Support the 
 cake in a horizontal position by 
 its edges. Heat the balls in boil- 
 ing water till they have acquired 
 the temperature of the water. FIG ug 
 
 Place them simultaneously on the 
 
 wax, several centimetres apart, and observe the time occupied 
 by each in melting through the cake (Fig. 118). Some of the 
 balls may not get through ; in that case, the depth the ball 
 melts into the cake must be noted. The drop of water adhering 
 to each ball must be removed before placing the ball on the 
 wax cake. The handles should be attached at the point where 
 the weight-adjustment was made, so that like surfaces, in every 
 case, will be in contact with the wax. Only approximate 
 results can be secured by this method. 
 
 274. Exercise. Determine the specific heat of a liquid. 
 First Method. Make a loose coil of some metal, as lead, 
 
 whose specific heat is known, and then, proceeding as in 
 
 ^^^^ 
 
 FTfa 
 
 
164 PRACTICAL PHYSICS. 
 
 Art. 272, find its thermal capacity with reference to the liquid in 
 question by substituting the liquid for the water. The quotient 
 of the heat capacity when compared with water, by that when 
 compared with the liquid, will give the thermal capacity of the 
 liquid with reference to water. 
 
 Second Method. Procure two test-tubes of the same size ; 
 in one of them pour a few grammes of water, and, in the 
 other, an equal volume of the liquid under examination. In 
 each test-tube, insert a thermometer ; then place the tubes 
 in a vessel of water, at, say, 70 C., as indicated by a third 
 thermometer, and note the time required for the contents of the 
 tubes to acquire^ that temperature. As these substances differ 
 in density, it will be necessary to reduce these times to those 
 for equal weights by dividing each by the density of the corre- 
 sponding liquid. The ratio of these times will be the specific 
 heat of the liquid. Compare the results given by this method, 
 with those given by the first. 
 
 Try turpentine, ether, kerosene, benzine, glycerine, etc. 
 
 275. Exercise. Determine the latent heat of water ; that 
 is, find the number of calories of heat disappearing during the 
 melting of one kilogramme of ice. 
 
 Pour into a beaker a known quantity of water, say 500 
 grammes, and raise its temperature to, say, 70 C. Set the 
 beaker on a board, and observe the fall in temperature during 
 one minute. Now add ice in small pieces till about 200 
 grammes have been introduced, constantly stirring the water 
 with the thermometer. Each piece of ice should be wiped with 
 a dry cloth before putting it in the beaker, to avoid introducing 
 any water in the liquid form. The time occupied in putting in 
 the ice should be as short as possible. As soon as the ice is 
 melted, take the temperature of the water, and record the time 
 
ttEAf. 165 
 
 occupied. Also obtain the fall due to radiation during the 
 next minute. The amount of ice introduced is the increase in 
 weight of the beaker and contents. The following example 
 will show the method of making the computation : 
 
 Amount of water in beaker 500 grammes. 
 
 Temperature of water 75 C. 
 
 Fall in temperature during one minute 1| C. 
 
 Temperature of water taken as soon as ice melted . 32 C. 
 
 Fall in temperature during next minute | C. 
 
 Time required to melt ice 3 minutes. 
 
 Amount of ice introduced 179 grammes. 
 
 Water-equivalent of beaker previously determined . 34 grammes. 
 
 Data corrected for radiation and absorption : 
 
 Amount of water, 500 + 34 = 534 grammes. 
 Temperature of water before introducing ice, 73^ C. 
 Temperature of water after introducing ice, 32 + s( * 2 2 J = 35 C. 
 
 .534(734 35) = 20.559 calories of heat consumed; 
 
 .179 X 35 = 6.265 calories of heat consumed in raising the ice 
 froinO to 35; 
 
 . . 20.559 6.265 = 14.294 calories of heat consumed in melting . 179 kg. 
 
 of ice, 
 
 .-. 14.294 ~r .179 = 79.9 calories of heat consumed in melting 1 kg. of 
 
 ice. 
 
 276. Exercise. Determine the latent heat of steam. 
 
 Fit to a Florence flask of about one litre capacity a delivery- 
 tube of the form shown in Fig. 119. Fill the flask half full of 
 water, and support it on the iron stand. The delivery-tube 
 should reach nearly to the bottom of a beaker containing a 
 
166 
 
 PRACTICAL PHYSICS. 
 
 known quantity of water, say 400 grammes, at the temperature 
 of the room. Apply heat to the flask, and, as soon as a 
 
 strong jet of steam issues from 
 the delivery-tube, let it enter the 
 water in the beaker. Stir the water 
 constantly and gently with the ther- 
 mometer ; and, when the tempera- 
 ture has risen a certain number of 
 degrees, as 20 C., record the time 
 occupied, and also the fall from 
 radiation during the next minute. 
 Then ascertain the increase in 
 weight, and also the temperature of 
 steam. The following example will 
 show the method of making the computation : 
 
 FIG. 119. 
 
 Amount of water in beaker 400 grammes. 
 
 Water-equivalent of beaker previously determined . 34 grammes. 
 
 Temperature of water in beaker 21. 75 C. 
 
 Temperature of water after steam ceases to enter . 41. 75 C. 
 
 Loss in one minute from radiation 0.25 C. 
 
 Time occupied in admitting steam 4.25 minutes. 
 
 Amount of steam introduced 14 grammes. 
 
 Temperature of steam 99. 25 C. 
 
 Temperature of water in beaker corrected for radiation, 
 
 25 
 41.75 + V X 4.25 = 42.28 C. 
 
 Zi 
 
 Amount of water corrected for beaker-equivalent, 434 grammes. 
 
 .434 X 20.53 8 91 calories of heat imparted to the water. 
 .014(99.25 42.28) = .8 calories of heat derived from the water produced 
 by the steam in condensing and cooling from 
 99. 25 C. to 42.28 C. 
 
 .*. 8.91 .8 = 8.11 calories of heat derived from .014 kg. of steam 
 condensing to water at the boiling-point. 
 
HEAT. 167 
 
 Hence 
 
 8.11 -r .014 = 579.3 calories of heat latent in 1 kg. of steam. 
 
 It will be observed that the large piece of tubing inserted in 
 the delivery-tube will retain the water produced by steam 
 condensing before reaching the water in the beaker. To admit 
 this would introduce serious error. Why? 
 
 IX. ARTIFICIAL COLD. 
 
 277. Exercise. Dissolve in three parts, by weight, of 
 water not warmer than 10 C., a mixture of two parts of pul- 
 verized ammonium nitrate and one part -of ammonium chloride. 
 Stir the mixture with a test-tube containing water, observing 
 the reading of a thermometer placed in the tube. Account 
 for the low temperature. 
 
 278. Exercise. Dissolve common salt in water, and see 
 if it affects the temperature of the water in any way. Try 
 potassium nitrate, ammonium nitrate, etc. Try some substance 
 not having a crystalline character, as dextrine, gum-arabic, etc. 
 Account for the difference in the results. 
 
 279. Exercise. Tie a piece of cotton-wool about the bulb 
 of a mercurial thermometer. Wet the wool with ether, and 
 note the effect. Explain. 
 
 280. Exercise. Pour water at the temperature of the 
 room into a porous cup, such as is used in the construction of 
 galvanic batteries. A new unglazed flower-jar will answer the 
 purpose if the drainage-hole is closed up. Take the tempera- 
 
168 PRACTICAL PHYSICS. 
 
 tu re every five minutes for half an hour, and also that of the 
 room at the same time. Account for the difference. 
 
 281. Exercise. Place a bell-jar on the table of the 
 air-pump, observe closely the degree of transparency, then 
 exhaust the air, watching for any change in the appearance of 
 the jar. Now admit the air, introduce a thermometer, take the 
 temperature, and, after exhausting the air, again take the tem- 
 perature. Why is it lower? Account for the phenomenon 
 seen during the first exhaustion. What applications can you 
 find in the theory of clouds, of the truth brought out in this 
 experiment ? 
 
 282. Exercise. As in Art. 278, dissolve sodium sulphate 
 in water, determining the effect on the temperature. Now 
 prepare a saturated solution of sodium sulphate by dissolving 
 a few grammes of the substance in an equal weight of hot 
 water. Set the solution aside in a vessel to cool, having first 
 poured a thin layer of oil over the top. If not disturbed, it 
 will cool to the temperature of the room without crystallizing. 
 After waiting long enough to be certain that the solution has 
 reached the temperature of the room, introduce a thermometer, 
 and observe the effect. Explain. 
 
 Try sodium acetate in the same manner. 
 
 283. Exercise. Test some of the following freezing- 
 mixtures : 
 
 1st, Common salt, by weight, one part ; snow or pounded 
 ice, two parts. The temperature will sink to 20 C. 
 
 2d, Common salt, by weight, five parts ; ammonium nitrate, 
 five parts ; snow or pounded ice, twelve parts. The temperature 
 will sink to -31 C. 
 
HEAT. 169 
 
 3d, Crystallized calcium chloride, by weight, two parts ; 
 snow or pounded ice, two parts. The temperature will sink 
 to -40 C. 
 
 4th, Sodium phosphate, by weight, nine parts ; dilute nitric 
 acid, four parts. The temperature will sink to 29 C. 
 
 5th, Sodium sulphate, by weight, six parts ; ammonium 
 nitrate, five parts ; dilute nitric acid, four parts. The temper- 
 ature will sink to 26 C. 
 
 In these mixtures, the substances are supposed to be at the 
 temperature of 10 C. If, however, they are previously cooled 
 down, a lower temperature still can be obtained in most cases. 
 
170 PRACTICAL PHYSICS. 
 
 CHAPTER V. 
 
 MAGNETISM AND ELECTRICITY. 
 I. MAGNETS. POLARITY. INDUCTION. 
 
 284. Apparatus, Bar-Magnets, Needles, Thin Plates of 
 Different Substances, Short Rod of Soft Iron, Carpet-Tacks, 
 etc. 
 
 285. Exercise. Touch one end of a bar-magnet to a pile 
 of carpet- tacks, and record the effect. Try the other end of the 
 magnet. Count the number of tacks adhering in each case, and 
 obtain the average of a number of trials. Inference. Ascer- 
 tain if any piece of steel will affect the tacks in the same way. 
 
 Make a paper stirrup, place the bar-magnet in it, and suspend 
 the bar-magnet by a thread, thus giving the magnet freedom of 
 motion. Now bring near each end, in succession, an iron nail. 
 Repeat the experiment, the nail and magnet having changed 
 places. Does the magnet attract the nail, or does the nail 
 attract the magnet? 
 
 Magnets for the purpose of this experiment, as well as the 
 following ones, may be made by stroking, from end to end, 
 and always in the same direction, large steel nails, or short 
 steel rods, with one pole of an electro-magnet (Art. 382). 
 
 286. Exercise. Float a common darning-needle on a 
 piece of cork in a glass vessel of water, and ascertain, by 
 making several trials, if, after coming to rest, it points in any 
 
MAGNETISM AND ELECTRICITY. 171 
 
 one way in preference to another. Now stroke the needle, 
 from end to end, with one pole of a magnet, and repeat the 
 tests. Inference. 
 
 287. Exercise. Magnetize a large sewing-needle by strok- 
 ing it a few times with one pole of a magnet. Pull a silk fibre 
 several centimetres long out of silk floss, by untwisting it, and 
 attach it, by a very little wax, to the needle, so that, on holding 
 it up, the needle will take a horizontal position. Cement the 
 other end of the fibre to one end of a 
 
 small glass tube passing through the cen- 
 tre of a cork. Fit this cork to the top of 
 a large lamp-chimney or bottle. The 
 length of the fibre should be such as to 
 bring the needle within half a centimetre 
 of the base. This instrument will serve 
 
 FIG. 120. 
 
 as a magnetoscope. A pocket-compass, 
 
 or a magnetic needle, mounted as in Fig. 120, may be used 
 
 instead. 
 
 Magnetize a large darning-needle by stroking the half toward 
 the point with the south-seeking pole of a magnet, and the 
 other half with the north-seeking pole. Ascertain which is 
 the north-seeking pole of the needle as in the last experiment. 
 Now bring its north-seeking pole near that pole of the magneto- 
 scope, and record the effect. Try the other pole. What law 
 seems to govern the action of magnets toward each other ? 
 
 288. Exercise. Hold the north-seeking pole of a strong 
 magnet near the north-seeking pole of a feebly magnetized 
 needle, and ascertain if the effect is in harmony with the 
 law of magnetic action. Now re-examine the polarity of the 
 small needle. Inference. 
 
172 PRACTICAL PHYSICS. 
 
 289. Exercise. Ascertain if a strong permanent magnet 
 will attract iron-filings or tacks through thin plates of mica, 
 wood, paper, glass, copper, zinc, iron, etc. 
 
 290. Exercise. Bend a strip of heavy sheet-iron, 15 cm. 
 by 5 cm., into a ring. Suspend, by a thread, from a wooden 
 support, a small piece of iron, and adjust it to hang at the 
 centre of this hollow cylinder as it rests on the table. Now 
 hold, opposite the ball of iron on the outside of this cylinder, 
 a strong magnet, and compare the effect on the ball with that 
 produced if the ring is removed and the magnet is held at the 
 same distance as before. Try a brass or zinc ring, and see if 
 the effect is the same. 
 
 291. Exercise. Hang as many tacks as possible from the 
 pole of a magnet supported in a horizontal position above 
 the table, using a clamp for the purpose. Hold up to it a 
 sheet of paper carrying carpet-tacks, and notice how many 
 adhere. Now place a second magnet beneath this one, so that 
 its opposite pole is exactly under the one supporting the tacks, 
 and ascertain if the power of the first magnet to support tacks 
 has been affected. Now place the magnet so that like poles 
 are opposite, and repeat the tests. Explain. 
 
 292. Exercise. Hold one end of a rod of soft iron near one 
 pole of a magnet, and, while in that position, dip the other end of 
 the rod into iron-filings. Record the result. Test the soft-iron 
 bar for polarity while in this position, using a pocket-compass 
 for the purpose. Note the effect of removing the magnet. 
 
 Vary the experiment by holding the magnet near to the 
 middle of the rod, and testing the whole rod with iron-filings. 
 Also test for polarity. 
 
MAGNETISM AND ELECTRICITY. 173 
 
 Arrange two such rods end to end along on a table, and not 
 quite in contact. Near one end of the row, hold a strong magnet. 
 Test the last one of the row with iron- filings. If placed with 
 its end projecting over the edge of the table, a dish of filings 
 can be held to it without trouble. Also test each end of these 
 bars with a compass-needle to ascertain their polarity. 
 
 II. NATURE OF MAGNETISM. 
 
 293. Apparatus. Steel Bar, Magnet, Needles, Steel- 
 Pilings, etc. 
 
 294. Exercise. Ascertain if it sensibly affects the weight 
 of a bar of steel to magnetize it. 
 
 295. Exercise. Take a piece of No. 16 iron wire about 30 
 cm. long, anneal it carefully by heating it red-hot, and letting it 
 cool very slowly. Turn at right angles one centimetre at each 
 end for convenience in holding. Now stroke it carefully with 
 a magnet several times, and test its power to lift iron filings. 
 Then give the wire a sudden twist, and again test it. 
 
 Magnetize a knitting-needle ; test its power to pick up small 
 iron tacks ; then, holding one end firmly, make the needle 
 vibrate by plucking the free end, and again test its power to 
 lift small iron tacks. 
 
 296. Exercise. Magnetize a needle, or a piece of steel 
 wire, and dip one end into a dish of small iron tacks, noticing 
 the number adhering as you lift it out. With a pair of crucible 
 tongs, hold the needle in a flame till red-hot, and then plunge 
 it quickly into the tacks, and notice if it picks up as many as 
 before. Test again after the needle has become cold. 
 
174 PRACTICAL PHYSICS. 
 
 Vary the experiment by ascertaining if a magnet will attract 
 a small nail when it is red-hot. Also vary the experiment by 
 letting a heated steel needle cool, having placed it, when 
 red-hot, in a line between the opposite poles of two magnets. 
 
 From the nature of heat, what does this experiment suggest 
 regarding magnetism ? 
 
 297. Exercise. Magnetize a knitting-needle, and roll it 
 in iron-filings, recording the result. Now break the needle 
 into two equal pieces, and test them. Break these pieces, and 
 test them. Why do not filings adhere at the centre? What 
 view of the nature of magnetism is here supported ? 
 
 298. Exercise. Fill a glass tube 1 cm. in diameter and 
 10 cm. long with very short pieces of steel wire, or with steel 
 filings, closing the ends with a cork. Stroke the tube with a 
 powerful magnet, and test it for polarity by holding its ends in 
 succession near one pole of the magnetoscope. Now shake up 
 the contents of the tube thoroughly, and again test its polarity. 
 Inference. 
 
 The coercive force can be imitated by mixing a little oil with 
 the filings. It will be found more difficult to magnetize and 
 demagnetize the tube. 
 
 III. THE MAGNETIC FIELD. 
 
 299. Apparatus. -- Magnets, Short Magnetic Needle 
 mounted, Magnetoscope, etc. 
 
 300. Exercise. Map out the magnetic field of a magnet. 
 Place a short bar-magnet beneath a stiff sheet of writing- 
 paper supported on two wooden bars as thick as the magnet, 
 
MAGNETISM AND ELECTRICITY. 175 
 
 and sift iron-filings evenly over it from a thin muslin bag 
 containing them, tapping the paper gently to facilitate the 
 movements of the filings. Study the figures obtained in this 
 way for a horse-shoe magnet, a disk-magnet, two bar-magnets 
 placed parallel to each other, with like poles adjacent, and 
 separated by about two centimetres ; two magnets with unlike 
 poles adjacent, horse-shoe magnet with its armature on, a 
 bar-magnet with a bar of soft iron near one of its poles, an 
 iron ring when a powerful magnet is near it, a bar-magnet held 
 vertically, etc. 
 
 Permanent copies of these figures may be made as follows : 
 
 Brush a sheet of printing-paper over with a solution of 
 tannin, and place it carefully on the figure after removing the 
 magnet. Place on this a sheet of heavy blotting-paper, and 
 apply a slight pressure. On lifting off the paper, most of the 
 filings will adhere to it, and can be brushed off when dry, 
 leaving dark marks on the paper. 
 
 Place a small magnetic needle successively in different parts 
 of the magnetic field, as marked out by the filings before 
 removing the magnet, and notice its position with reference 
 to the line of force passing through the support. 
 
 A suitable needle may be constructed as follows : Straighten 
 a piece of watch-spring, cut from it a lozenge-shaped piece 
 15 mm. long, and drill a hole 1 mm. in diameter through the 
 centre. Cement, with a little wax, a small cap exactly over 
 this hole to serve as a bearing. To make such a cap, heat the 
 end of a very small glass tube in a Bunsen flame till the glass, 
 by contracting, closes the end. Cut off, with a file, a piece 
 about 3 mm. long, and you will have a cap with a smooth 
 conical hole in it for the reception of the supporting pivot. 
 For a pivot, break off the point of a sewing-needle, and insert 
 it in a piece of wood 1 cm. square and 2 mm. thick for a base. 
 
176 PRACTICAL PHYSICS. 
 
 If the needle is not level after magnetization, adjust it with a 
 little wax. 
 
 301. Exercise. Represent, by a curve, the change in the 
 magnetic strength as you go from the poles of a magnet to 
 the centre. 
 
 Magnetize, as uniformly as possible, a heavy knitting-needle. 
 This is best done by the method known as Divided Touch. It 
 consists in fixing the needle lengthwise between the opposite 
 poles of two permanent magnets, and, while under their induc- 
 tion, stroke the needle, each half, with the pole of another 
 magnet of the same name as the corresponding inducing pole, 
 the stroking-magnets being held in the hands at an angle of 
 about 30 degrees with the needle. The stroking must begin at 
 the centre of the bar, the poles being lifted at the ends, and 
 brought back in an arch to the centre. The stroking should 
 be repeated on the opposite side of the needle. 
 
 A Coulomb's magnetoscope will be required for this experi- 
 ment. To construct one, magnetize to saturation a small 
 cylinder of glass-hard steel about 10 mm. long by 5 mm. in 
 diameter. Suspend this, by a silk fibre, in a glass tube about 
 15 cm. long set into a wooden base. A wire hook sliding 
 through a cork fitted to the tube will serve to support the fibre. 
 The magnet is cemented in a wire stirrup, and should hang 
 about midway between the ends of the tube. To prevent it 
 from swinging, connect it, by a second fibre, to a small lead 
 disk resting on the floor of the tube. 
 
 Place the magnetoscope on the table, and, by means of a 
 magnet, produce a small displacement of the magnetoscope- 
 needle in order to set it in vibration through a small arc. 
 Ascertain the number of oscillations made in thirty seconds, 
 while vibrating under the influence of the earth alone, averaging 
 
MAGNETISM AND ELECTRICITY. 177 
 
 at least three trials. Now support the magnetized knitting- 
 needle in a vertical position, bring its centre near the magneto- 
 scope and in the magnetic meridian. As before, ascertain the 
 number of vibrations made by the magnetoscope-needle in 
 thirty seconds, being careful to set it vibrating through an arc 
 of the same size as before. 
 
 In a similar way, test the ends of the magnet, and four or 
 more places between the centre and the ends. Care must be 
 taken not to vary the distance between the magnet and the 
 maguetoscope, and not to change the position of the magneto- 
 scope on the table. The bringing of like poles together must 
 be avoided so that attraction, and not repulsion, will actuate 
 the instrument. The position of the points on the magnet, 
 which were tested, must be known relatively to the length of 
 the magnet. 
 
 Now square the number of vibrations in .each case, and 
 subtract the square of the number representing the magnetism 
 of the earth. The numbers thus obtained represent the relative 
 magnetic intensities at these points, since the attractive force 
 varies as the square of the number of vibrations. Draw a 
 straight line 10 cm. long to represent the magnet. At points 
 situated like those tested on the magnet, erect perpendiculars. 
 Make the one at the plus pole 2 cm. long to represent the 
 magnetic intensity at that point, and give the others lengths 
 proportional to the numbers just obtained. Through the 
 extremities of these lines, sketch a curve, and you have a 
 graphic representation of the change in magnetic intensity as 
 you go from the middle of a magnet toward either end. 
 
 302. Exercise. Proceeding as in the last experiment, 
 compare the strengths of the north-seeking poles of two bar- 
 magnets. 
 
178 
 
 PRACTICAL PHYSICS. 
 
 303. Exercise. Proceeding as in Art. 301, determine the 
 number of vibrations made by the needle of the magnetoscope, 
 in thirty seconds, when distant from the pole of a magnet 
 2 cm., 3 cm., 4 cm., etc., respectively. Compare the ratios of 
 these numbers representing the strengths of the magnetic field 
 at these distances from the pole with the ratios of the distances. 
 If the experiment is carefully conducted, one set of ratios will 
 be found to be the square of the other set taken in an inverse 
 order. What law is supported by this fact? 
 
 304. Exercise. Determine, from the law of inverse 
 squares, the direction a magnetic needle will have when at rest 
 in the neighborhood of a bar-magnet. 
 
 Magnetize a knitting-needle, and lay it on a straight line 
 drawn on a sheet of paper, marking on this line the position of 
 
 the poles N and 
 S of the magnet 
 at one-tenth of the 
 length of the nee- 
 dle from the end 
 (Fig. 121), as the 
 poles of a magnet 
 are not at its ends. 
 Xake A as a point 
 
 FlO. 121. 
 
 S 
 
 in the magnetic 
 
 field. The north-seeking pole of a magnet at A would be 
 attracted by S along the line AS, and repelled by N along AN. 
 Measure AS and AN, and then lay off AB any convenient 
 number of centimetres, and AD as many times greater than 
 AB as AS squared is greater than AN squared. Complete the 
 parallelogram ABCD, and the diagonal AC will represent, by 
 its length and direction, the magnitude and the direction of the 
 
MAGNETISM AND ELECTRICITY. 179 
 
 resultant magnetic force at A. Verify the conclusion by 
 placing a short magnet at A free to turn, such as was employed 
 in Art. 300. 
 
 Locate a number of these lines of direction, and compare 
 them with the lines of force for the magnet as marked out 
 by the use of iron-filings. 
 
 IV. TERRESTRIAL MAGNETISM. 
 
 305. Apparatus. Dipping-Needle, Iron Bar, Compass, 
 
 etc. 
 
 306. Exercise. Determine the dip of the magnetic 
 meridian. 
 
 Fasten, with a little wax, a thread to the middle of an 
 unmagnetized knitting-needle, finding, 
 by trial, a point of attachment in which 
 the needle takes a horizontal position. 
 Now stroke the needle with a magnet, 
 and suspend it by the thread attached. 
 It now acts as if one end has become 
 heavier than the other. To obtain ac- 
 curately the amount of this dip, a Dip- 
 ping-Needle (Fig. 122) will be needed. 
 
 This, when placed in the magnetic meridian, shows, on a 
 graduated arc, the amount of dip. 
 
 307. Exercise. Procure a thoroughly annealed iron bar 
 75 cm. long, showing little or no polarity when tested with a 
 magnetic needle while the bar is supported horizontally in an 
 east-and-west line. Now support this bar in a position parallel 
 to that taken by the dipping-needle of the last experiment, and 
 
180 PRACTICAL PHYSICS. 
 
 again test it for polarity. Turn the bar end for end, and again 
 test it for polarity. Inference. 
 
 V. FRICTIONAL ELECTRICITY. 
 
 308. Apparatus. Glass Rods, Sealing-wax Rod, Silk, 
 Flannel, Pith-Balls, Electroscope, etc. 
 
 309. Exercise. Balance a common yard-stick, or a strip 
 of lath, on the point of a needle projecting through a cork in a 
 bottle. Hold, near one end of the stick, a rod of sealing-wax 
 immediately after rubbing it briskly with flannel. A rubber 
 comb or ebonite ruler may be substituted for the sealing-wax. 
 
 Try a glass tube after rubbing it briskly with a piece of silk. 
 The tube should be about 50 cm. long and 2 cm. in diameter, 
 with the ends rounded, by softening them in a gas-flame, to 
 prevent cutting the fingers when experimenting with it. The 
 tube and the silk should be warmed before using. Glass free 
 from sodium is best for the purpose. 
 
 Describe the effects these objects have on the balanced strip. 
 
 See if there is any connection discoverable between the 
 mechanical energy expended in rubbing the rod, and the inten- 
 sity of the state developed in it. 
 
 310. Exercise. Excite each of the various rods used in 
 the last experiment, and in the way there described, and 
 immediately bring it near to a pile of pith-balls or small bits 
 of tissue-paper. 
 
 The pith-balls can be obtained from the common elder, or 
 from the corn-stalk. They may have a diameter from 5 mm. 
 to 1 cm. Cut the pith with a veiy sharp knife in order that 
 each ball may have a smooth surface. 
 
MAGNETISM AND ELECTRICITY. 
 
 181 
 
 311. Exercise. Make a hoop out of paper, say, 20 cm. in 
 diameter and 8 cm. wide. Place it upon a table, and hold a glass 
 rod excited by rubbing with silk a little below one extremity of 
 a horizontal diameter of the hoop. Do not let the hoop touch 
 the rod, but keep it at a distance of one or two centimetres 
 from its outer surface. Describe the effect on the hoop. 
 
 312. Exercise. Determine the law of electrical action. 
 Rub a glass rod with silk, and suspend it in a paper stirrup 
 
 (Fig. 123). In like manner, excite a second glass rod with as 
 little delay as possible, 
 and bring it near one 
 end of the suspended 
 one. Note the effect. 
 Now try two rods of 
 sealing-wax or ebonite 
 in the same way, and 
 observe the effect. Fi- 
 nally, try one'of glass, 
 and one of sealing- 
 
 h 
 
 wax, and observe their . FlG - 123 - 
 
 action toward each other. If we represent the electrification 
 of glass by +E, and that of sealing-wax by E, what law 
 expresses the conclusions reached ? 
 
 313. Exercise. Draw a silk ribbon between two layers of 
 warm flannel, and hold it near a wall or some object. Try 
 two strips of ribbon hanging side by side. Explain. 
 
 314. Exercise. Place a sheet of brown paper on a hot 
 dry board. Brush it briskly, for a few moments, with a hair 
 clothes-brush. Cut part of the paper into narrow strips free 
 
182 
 
 PRACTICAL PHYSICS. 
 
 at one end, with a sharp knife, without touching the surface of 
 that part with the hand. Observe the action of these strips 
 toward one another. Explain. 
 
 315. Exercise. Test various articles found in the room, 
 for electrification, after rubbing them with either silk, fur, or 
 flannel. 
 
 Select a Florence flask of about one litre capacity, thoroughly 
 clean and dry it ; fit to it a cork, through which passes a stout 
 brass wire, on the outer end of which is a 
 metal ball about 15 mm. in diameter, or 
 a thick brass disk of the same diameter, 
 having the edges neatly rounded off with a 
 fine file (Fig. 124). File the end of the 
 wire within the flask to a wedge form, 
 the edge having a thickness of not over one 
 millimetre. Cut, out of thin tin or alu- 
 minum foil, two strips, each 5 mm, 
 wide and 6 cm. long, and paste them on 
 the faces of the lower end of the wire so 
 that they will hang side by side. Tin-foil 
 (No. 4), such as is used by dentists, makes 
 excellent strips for this purpose. Such an instrument is called 
 an Electroscope. To use it, bring the article suspected of 
 being electrified near the ball of the instrument ; the divergence 
 of the leaves shows electrification. 
 
 If a little strong sulphuric acid is put in the flask, it will 
 tend to dry the air within it, and increase the duration of the 
 charge. 
 
 316. Exercise. Determine the kind of electrification of a 
 body. 
 
 Fift. 124. 
 
MAGNETISM AND ELECTRICITY. 183 
 
 Charge an electroscope with the unknown kind of electrifica- 
 tion, using a proof-plane for the purpose. A Proof-Plane 
 (Fig. 125) is usually a small metal disk cemented to the end of 
 a glass or ebonite rod. A serviceable instrument can be made 
 by cementing a cent, after filing the edges smooth, to a glass 
 tube about 15 cm. long. To charge the electroscope, slide 
 the metal disk of the proof-plane along the surface to be 
 tested, and then bring it in contact with the electroscope-knob. 
 Repeat the operation till the ends of the leaves 
 are about 1 cm. apart. Now excite strongly, by 
 friction with silk, a dry glass rod. If the silk 
 rubber is coated with amalgam (see Appendix, 
 p. 360), a higher electrification can be secured. 
 Charge the proof-plane by putting it in contact 
 with the rod, and then, without delay, place this 
 charged proof-plane in contact with the electro- 
 scope-knob. If the leaves diverge farther, the 
 object in question was positively charged ; if the 
 leaves collapse, it was probably negative. As ^ 
 increased divergence is a more reliable indication 
 of electrification than a decreased divergence, in case of the 
 latter occurring it is best to repeat the test, using a rod of 
 sealing-wax and flannel in place of the glass rod and the silk. 
 
 It is important that the electroscope be not charged too 
 highly, as, in that case, a decreased divergence might mean 
 that the intensity of the known charge in the proof-plane was 
 less than that of the electroscope, and of the same kind, thus 
 introducing doubt. Always charge the proof -plane as intensely 
 as possible, in order that ambiguity may not arise. 
 
 Test the kind of electrification of the silk ribbon in Art. 313, 
 the paper in Art. 314, common rubber excited by flannel, 
 glass excited by flannel, stick-sulphur excited by flannel, sul- 
 
184 PRACTICAL PHYSICS. 
 
 phur excited by silk, rubber excited by silk, sealing-wax excited 
 by cotton, paper excited by flaimel, etc. 
 
 317. Exercise. Excite a glass rod by rubbing it with 
 silk, keeping the silk rubber from touching the hand by means 
 of a square piece of sheet-rubber such as dentists use. Test 
 the silk for electrification. Similarly test the flannel employed 
 in rubbing sealing-wax, fur in rubbing any resinous substance, 
 etc. Inference. 
 
 318. Exercise. Compare the conducting power of sub- 
 stances for electricity. 
 
 Place one end of a thread of the substance whose conductivity 
 is to be tested, in contact with the electroscope-knob, and the 
 other in contact with a smooth metallic button supported on a 
 rod of sealing-wax. A thread 50 cm. long may be used when 
 possible, and, in case of some substances, it would be well to 
 make it still longer. Now touch the button with a highly 
 charged proof-plane, and decide, from the action of the 
 electroscope, whether the substance is a good conductor, a 
 semi-conductor, or a non-conductor. 
 
 Try silk thread, cotton thread, linen thread, woollen thread, 
 glass thread, rubber, wood, paper, wire, graphite as found in a 
 lead-pencil, any kind of thread wet with water, etc. 
 
 VI. STATICAL INDUCTION. 
 
 319. Apparatus. Insulated Metallic Cylinders and Balls, 
 Electroscope, Metallic Cylindrical Pail, etc. 
 
 320. Exercise. Place end to end, and in contact, two 
 metallic cylinders about 20 cm. long and 4 cm. in diameter, 
 
MAGNETISM AND ELECTRICITY. 185 
 
 having rounded ends, each cylinder being supported on a 
 varnished glass rod inserted in a wooden base (Fig. 126). 
 Wooden cj'linders smoothly covered with tin-foil make a cheap 
 and efficient substitute, the foil being fastened on with flour- 
 paste. Metallic door-knobs mounted on glass rods work well. 
 As you hold near one end, that is, 2 or 
 3 cm. removed, a highly electrified glass 
 rod, by means of a proof-plane and elec- 
 troscope test the outer ends, and the 
 point of contact, of the two cylinders 
 for electrification. If found to be elec- 
 trified, ascertain the kind. Now re- 
 charge the glass rod ; and, as you hold 
 it near the end of one of the cylinders, 
 
 separate the cylinders by several centimetres. Test the ends 
 of the separated cylinders for electrification, comparing results 
 with those obtained when the cylinders were in contact. 
 Explain. 
 
 This experiment will succeed only in a very dry atmos- 
 phere. 
 
 321. Exercise. Connect one end of the insulated metal- 
 lic cylinder of the last experiment with an electroscope by 
 means of a wire, the ends of which are rounded, or bent 
 around into a loop and soldered. Hold an electrified glass 
 rod near the other end of the cylinder, and record the effect 
 on the electroscope. Before removing the excited rod, remove 
 the wire, handling it with some non-conductor. If the wire 
 rests loosely on the cylinder and on- the ball of the electro- 
 scope, it can be lifted off with a glass rod. Ascertain the 
 electrical condition of the electroscope as well as of the 
 cylinder. 
 
186 PRACTICAL PHYSICS. 
 
 322. Exercise. Hold one finger on the ball of an electro- 
 scope, and bring near it an electrified glass rod. Remove the 
 finger before taking away the rod. Determine the electrical 
 condition of the electroscope. Try a rod of sealing-wax 
 excited b}* flannel, in place of the glass rod. 
 
 This is a very desirable way of charging an electroscope with 
 a known kind of electricit} T . The intensity of the charge can 
 be varied by changing the distance the excited bod}* is held 
 from the ball of the instrument. 
 
 323. Exercise. Determine how the amount of electricity 
 induced on neighboring conductors compares with that of 
 the inducing body. 
 
 Procure a metallic cylindrical pail free from points, and 
 support it on a plate of well-dried glass to insulate it. This 
 vessel should have a depth of about 25 cm. and a diameter of 
 about 15 cm. It may be made of tin or copper. Connect the 
 outside, by a wire, to the ball of an electroscope. Suspend 
 by a silk thread a metallic ball, say, 5 cm. in diameter, having 
 a smooth surface and positively charged, within the pail. 
 Notice the indication of the electroscope. With a proof-plane 
 and a second electroscope, determine the electrical condition of 
 the two surfaces of the pail. Ascertain if the position of the 
 electrified ball within the pail in any way affects the attached 
 electroscope. Touch the ball to the bottom of the pail, and 
 observe if the electroscope is affected. Now remove the ball, 
 and test it for electrification. What must have been the 
 amount of the electricity on the inside of the pail compared 
 with that on the ball? What must have been the amount of 
 electricity on the outside of the pail ? 
 
MAGNETISM AND ELECTRICITY. 187 
 
 VII. ELECTRICAL DISTRIBUTION. 
 
 324. Apparatus. Metal Beaker, Pane of Glass, Wide 
 Brass Ring, Electroscope, Brass Chain, Insulated Metallic 
 covered Ball, Cylinder, and Cone ; Proof-Plane, Insulated Metal 
 Disks, etc. 
 
 325. Exercise. Support on a dry pane of glass a metallic 
 vessel of about one litre capacity, free from sharp edges. 
 Charge it with electricity by rubbing an excited glass rod over 
 it. Employing a proof-plane and an electroscope, test the two 
 surfaces for electricity. Inference. 
 
 326. Exercise. Bend into a ring a heavy strip of sheet 
 brass 25 cm. long and 8 cm. wide, soldering the ends together, 
 and filing the edges round. Suspend from the 
 
 inside surface a pair of pith-balls, and a second 
 pair from the outside surface. The inside pair 
 of balls should be at the centre of the ring. 
 Suspend the apparatus by a silk cord from a 
 support. Now electrify, by friction, a glass 
 rod, and rub it across the cylinder, observing 
 the effect on the pith-balls. Inference. 
 
 Fig. 127 shows such a cylinder mounted on 
 an insulated stand. 
 
 327. Exercise. Support the metal vessel 
 of Art. 325 on a dry pane of glass, and connect 
 
 its outer surface with the ball of the electroscope by means 
 of a wire. Suspend within the vessel, from a glass rod, 
 a metre or less of brass chain. Charge the vessel with elec- 
 tricity till the leaves of the electroscope diverge widely ; then 
 
188 PRACTICAL PHYSICS. 
 
 lift up the chain so that less of it lies piled up on the 
 bottom of the dish, observing the effect on the electroscope. 
 Keeping in mind that lifting up the chain practically in- 
 creases the surface of the vessel without decreasing the 
 quantity of electricity, what inference can be drawn regarding 
 the effect on potential produced by changing the amount of 
 surface ? 
 
 328. Exercise. Determine whether the shape of a. con- 
 ductor in any manner affects the distribution of the electrical 
 charge. 
 
 Cover smoothly with tin-foil a wooden ball 8 cm. in diameter, 
 a conical-shaped piece 15 cm. long, with hemispherical ends 
 5 cm. and 1.5 cm. in diameter, respectivel}', and a disk 2.5 
 cm. thick and 8 cm. in diameter, the edges being rounded. 
 Support each of these on a varnished heavy glass rod, as an 
 ignition-tube, set into a suitable base, or suspend each of them 
 by a silk cord. Now charge the first insulated conductor with 
 electricity, and compare the relative magnitude of the charge 
 at different parts by observing how many charges brought 
 by the proof-plane to the electroscope from one place are 
 necessary to produce the same amount of divergence of the 
 leaves of the electroscope as one or more brought from 
 another place. In like manner, test the other conductors. 
 Is there any connection between the electrical density and the 
 degree of curvature of the surface ? Try a conductor pointed 
 at one end, made so by inserting a piece of needle. Can 
 you charge it? Explain. Why avoid points on electrical 
 apparatus ? 
 
 In applying the proof-plane, always place its disk flat against 
 the conductor to avoid changing the shape of the conductor 
 under examination. 
 
MAGNETISM AND ELECTRICITY. 189 
 
 329. Exercise. Determine the effect of neighboring con- 
 ductors on the distribution of the electrification of an insulated 
 conductor. 
 
 Charge with electricity the insulated cylinder of the last 
 experiment, and place near one end of it a similar conductor 
 connected by a wire or chain with the gas, water, or steam 
 pipes of the room. Examine, as in that experiment, the 
 insulated cylinder, comparing the distribution with that found 
 when there was no neighboring conductor. 
 
 330. Exercise. Determine whether the distance of neigh- 
 boring conductors affects the distribution of electricity oa an 
 insulated conductor, and also whether any effects are due to the 
 nature of the medium separating the electrified body from these 
 conductors. 
 
 Construct three lead or brass disks 15 cm. in diameter, the 
 edges being neatly rounded, and suspend them by silk cords 
 so as to hang parallel ; or, better still, mount them on glass 
 supports, securing them to the glass with wax. Connect each 
 outside one with a wire to an electroscope. Charge the middle 
 one with known electricity, and observe the effect on the 
 electroscopes when the disk is midway between the two outer 
 ones. Move the disk nearer to one of the outer ones, and note 
 the effect. Insert a dry unelectrified pane of glass between 
 these two. Try plates of other substances. Inference. 
 
 331. Exercise. Enclose an electroscope in a cage or box 
 made of wire-cloth. Bring any electrified object in contact with 
 this wire covering, and observe the effect on the electroscope. 
 Now connect the cage with the earth by leading a wire from 
 it to the gas-pipe, and again pass electric charges through 
 it, observing the effect on the electroscope. What method 
 
190 PEACTICAL PHYSICS. 
 
 of protecting buildings from lightning is suggested by this 
 experiment ? 
 
 VIII. CONDENSERS. 
 
 332. Apparatus. Tin-Foil, Paper, Leyden Jars, Electro- 
 scopes, etc. 
 
 333. Exercise. Cut three pieces of paper 15 cm. square, 
 and four of tin-foil 10 cm. square. Coat the paper with paraf- 
 fine or shellac varnish. Arrange these pieces in a pile with 
 
 the foil and paper alter- 
 nating. Connect with 
 wire the alternate pieces 
 of foil, making two 
 groups (Fig. 128). Join 
 one of these to the prime 
 
 FIG. 128. conductor of an electri- 
 
 cal machine, and the other to the earth. After working the 
 machine for a minute, touch the wire leading to the earth to 
 the one leading to the machine. Explain. 
 
 The ends of the wires should be rounded. Why? Glass 
 may be substituted for the paper, and gilt-paper for the foil. 
 
 334. Exercise. Place on the table a piece of tin -foil 
 about 25 cm. square, and connect it to the earth by a wire or 
 chain. On this, lay a pane of glass, around which pass two 
 silk ribbons for removing the glass when necessary without 
 touching either the glass or the foil with the fingers. On the 
 glass, lay a small piece of tin-foil, and connect it with the 
 electroscope by means of a wire. Charge with electricity 
 the upper sheet of foil, noticing the effect on the electroscope. 
 Now lift up the glass plate by means of the ribbons, disconnect 
 
MAGNETISM AND ELECTRICITY. 191 
 
 the lower piece of foil from the earth ; then replace the glass 
 plate, all the time watching the indications of the electroscope. 
 Explain. 
 
 335, Exercise. Hold the ball of a Leyden Jar (Fig. 129) 
 in contact with the prime conductor of an active electrical 
 machine, at the same time connecting the outer surface of the 
 jar with the negative conductor of the machine by 
 
 means of a wire or chain. After a few minutes, the 
 jar will have acquired a maximum charge. 
 Using a bent wire, or Jointed Discharger 
 (Fig. 130), connect the two surfaces. If 
 the wire is brought in contact with the outer 
 surface of the jar first, no shock will be 
 experienced by the experimenter. After 
 waiting a few moments, you may be able to 
 FIG. I3o7 obtain from the same jar, without recharging, a second 
 discharge of much less intensity than the first, called 
 the Residual Charge The time necessary for the accumulation 
 of the second charge can be shortened by gently tapping the jar 
 with a glass or wooden rod. What change, suggested by this 
 experiment, is probably effected in a body on electrifying it? 
 
 336. Exercise. Connect the inner surfaces of several 
 Leydeu jars by winding a brass chain about the rods passing 
 through the covers. The outer surfaces may be connected by 
 placing the jars side by side on a sheet of tin-foil. Charge 
 the battery in the same manner as a single jar. Compare the 
 intensity of the charge with that of a single jar by the length 
 of the spark seen on discharging. 
 
 Leyden jars are easily made out of candy-jars by coating the 
 outside with tin-foil to about two-thirds of its height, using 
 
192 PRACTICAL PHYSICS. 
 
 thin flour-paste to cause the foijjo_^jhere- If the opening of 
 the jar is large enough, the inside may be similarly coated ; 
 but, if too small to admit the hand, fill the jar two-thirds full 
 with tinsel or crumpled tin-foil. Fit to the jar a varnished 
 wooden stopper, through which passes a heavy copper or brass 
 wire connecting with the inner surface of the jar by a piece of 
 brass chain. The outer end of the brass rod should terminate 
 in a ball. One cast out of lead will answer as well as any. All 
 glass is not equally good as an electric. The electrical qualities 
 of a jar should be tested before pasting on the foil, by tying on 
 the outside a sheet of foil, filling the inside part full of crumpled 
 foil, in which is inserted the brass rod carrying the ball, and 
 then ascertaining if it will retain a charge for several hours. 
 
 337. Exercise. Support a Leyden jar on a pane of glass, 
 and try to charge it by bringing its ball in contact with the 
 prime conductor of an active electrical machine. Compare the 
 intensity of the charge received, with that received in the same 
 time if its outer surface is connected with the other 
 pole of the machine. Account for the difference. 
 
 338. Exercise. Fasten about a Leyden jar a 
 leather or cloth belt into which small carpet-tacks have 
 been driven, with the points extending outward from 
 the glass (Fig. 131), the heads being in contact with 
 the foil. Use this jar as in the last experiment, com- 
 paring the charge received when insulated, with that received by 
 the same jar similarly insulated, but without the belt. Explain. 
 
 339. Exercise. Charge a Leyden jar so that the inner 
 surface is positive, and a second one so that the inner surface 
 is negative. What will be the electrical condition of the outer 
 
MAGNETISM AND ELECTRICITY. 193 
 
 surface in each case? Now put the outer surfaces in contact, 
 and see if they discharge. Suspend a pith-ball midway between 
 the balls, and account for it& behavior. 
 
 340. Exercise. Charge a Leyden jar having 
 movable metallic coatings (Fig. 132). Separate 
 the jar into its parts, and test the two coatings for 
 electrification. Put the parts together, and then 
 ascertain if there is any charge. What appears to 
 be the office of the coatings? 
 
 In taking the jar apart, the inner coating should not come in 
 contact with the hand. 
 
 IX. ELECTRICAL MACHINES. 
 
 341. Apparatus. Frictional Machine, Holtz Machine, 
 Electrophorus, Proof-Plane, Galvanometer, Electroscope, etc. 
 
 342. Exercise. Make the following tests on a frictional 
 plate-machine : 
 
 1st, Determine the kind of electrification of the prime con- 
 ductor when the conductor that is connected with the rubbers is 
 joined to the earth by a chain. In like manner, test the combs. 
 
 2d, Determine the kind of electrification of the rubbers 
 when the prime conductor is connected with the earth. 
 
 3d, Examine the prime conductor for manner of electrical 
 distribution. 
 
 4th, Test the upper and also the lower half of the plate for 
 electrification. 
 
 5th, Separate the rubbers from the earth, and ascertain if it 
 affects the working of the machine as shown by the striking 
 distance of the spark. 
 
194 PRACTICAL PHYSICS. 
 
 6th, Connect the rubbers with the prime conductor by means 
 of a wire, inserting a short-coil galvanometer in the circuit, 
 and determine, by the indication* of the galvanometer, the 
 direction of the current. See Art. 347. 
 
 343. Exercise. Charge the resinous bed of an Electro- 
 phorus (Fig. 133) by rubbing it with a piece of fur or flannel, 
 
 and determine the kind of 
 electrification . Place the 
 metal disk in contact with 
 the bed, touch the finger to 
 its upper surface ; then re- 
 move the finger, lift the disk 
 by its insulated handle, and 
 determine its electrical condi- 
 tion. Try to charge the disk 
 Fl6 133 without touching it with the 
 
 finger. Account for the dif- 
 ference. Explain the action of the machine. 
 
 To make an electrophorus, fill a pan about 25 cm. in diameter 
 and 2 cm. deep with a mixture of one part, by weight, of 
 beeswax, melted with five parts of shellac. For a cover, cut 
 out of sheet zinc a disk 20 cm. in diameter ; turn over the edge 
 neatly, and solder it, forming a rim free from points or sharp 
 edges. Cement to its centre with sealing-wax a piece of glass 
 rod for a handle. 
 
 344. Exercise. Make the following tests on a Holtz 
 machine (Fig. 134) : 
 
 1st, Determine the kind of electrification of each armature. 
 2d, Determine the kind of electrification of different parts 
 of the stationar} 7 plate. 
 
MAGNETISM AND ELECTRICITY. 195 
 
 3d, Test the combs. 
 
 4th, Test the surfaces of the condensers. 
 
 5th, Connect the poles of the machine with a wire, and 
 insert a short-coil galvanometer to determine the direction of 
 the current. See Art. 347. 
 
 FIG. 134. 
 
 6th, Connect the outer surfaces of the condensers, inserting 
 a galvanometer to determine the direction of the discharge ; 
 i.e., to determine which one is at the higher potential. 
 
 7th, Compare the working of the machine when the con- 
 densers are attached, with that when removed. 
 
 8th, Determine the effect on the spark produced by exchan- 
 ging the balls serving as poles, for others of larger diameter. 
 
196 PRACTICAL PHYSICS. 
 
 9th, Examine in a dark room an active machine, comparing 
 the appearance of positively charged points with those which 
 are negative. 
 
 10th, Set in rapid rotation, by means of a whirling-machine, 
 a Newton's color-disk in front of the active machine in a dark 
 room. Watch the disk during each discharge to ascertain if it 
 is seen to move while illuminated by the spark. What inference 
 can you make regarding the duration of the spark ? 
 
 11 th, Compare the energy expended in driving the machine 
 when excited, with that when not excited. Whence the elec- 
 trical energy ? 
 
 X. VOLTAIC ELECTRICITY. THE BATTERY. 
 
 345. Apparatus. Zinc, Copper, Iron, Lead, etc. , in Sheet 
 Form , Tumbler, Compass, Insulated Wire, etc. 
 
 346. Exercise. Cut from sheet zinc a strip about 10 cm. 
 long and 3 cm. wide, and from sheet copper a second one of 
 the same size. Fasten to one end of each of these a piece 
 of No. 20 copper wire about 20 cm. long, either by soldering, 
 or by passing the end of the wire through a small hole punched 
 in the strip, and twisted on itself so as to make a good contact. 
 Fill a common tumbler about two-thirds full of water, and 
 add to it slowly about one-twentieth as much sulphuric acid 
 (commercial). Now hold the zinc strip vertically in this dilute 
 acid for a few minutes, observe closely the surface of the zinc, 
 and record any changes. Then place the copper strip in the 
 tumbler, holding it near the zinc, parallel to it, but not 
 touching it, and ascertain whether its presence in any way 
 affects the previously noted phenomenon. Now touch the 
 outer ends of the two strips, or the two attached wires, and 
 
MAGNETISM AND ELECTRICITY. 197 
 
 note the effect, if any. Go over these steps several times to 
 make sure that what was seen was no accidental occurrence. 
 
 Wash the zinc strip thoroughly in water, rubbing it with a 
 cloth to remove the black particles of carbon from its surface. 
 It may be found necessary to scour the zinc with sand. Apply 
 with a cloth kept for the purpose a little mercury, performing 
 the operation on a common earthen plate. But little pressure 
 should be used in applying the mercury, to avoid breaking the 
 zinc. Remove all jewellery from the hands before handling 
 mercury. Replace the zinc in the dilute acid, and repeat all 
 the tests which were made with the unamalgamated zinc, com- 
 paring each observation with the corresponding one previously 
 made. 
 
 Ascertain the effect on the phenomena attending the strips, 
 when in the acid, of connecting the two wires with a short strip 
 of cotton, instead of touching their ends. Try successively a 
 piece of silk, wood, paper, gilt-paper, glass, 
 tin-foil, silver, wax, etc. 
 
 If mercury should get on the copper strip, 
 remove it by heating the strip in a flame. In- 
 stead of. joining the ends of the wires together 
 
 FIG. 135. 
 
 by twisting them, it is preferable to employ 
 
 Connectors (Fig. 135). The connection could be made by 
 
 dipping the ends into a small cup of mercury. 
 
 347. Exercise. Prepare strips of zinc and of copper as 
 in the last experiment. Clean the zinc thoroughly in dilute 
 sulphuric acid, and amalgamate it by rubbing it with mercury. 
 Tack these strips on opposite sides of a piece of wood one 
 centimetre wide and about 12 cm. long, being careful that the 
 tacks from opposite sides do not touch. Place these strips in 
 a tumbler two-thirds full of dilute sulphuric acid. Connect the 
 
198 
 
 PRACTICAL PHYSICS. 
 
 free ends of the wires, and then stretch a portion of the wire 
 over a compass-needle, or a magnetic needle mounted as hi 
 
 Fig. 136, holding it parallel 
 to it. Record the effect 
 produced on the needle. 
 Compare the effect with that 
 produced by placing the wire 
 below the needle. Reverse 
 the wire without changing 
 the position of the plates, 
 and compare the effect with 
 that previously obtained. 
 
 FIG. 136. 
 
 FIG. 137. 
 
 Assuming that there is an electric current 
 
 flowing through the wire from the copper to 
 
 the zinc, express as a law the behavior of 
 
 the needle on passing the current parallel to 
 
 it. See if it is possible to hold the right 
 
 hand so that the index finger will point out 
 
 the direction of the current, while, at the 
 
 same time, the thumb will point out the di- 
 rection of the needle deflection. 
 Fig. 137 shows a form of ap- 
 paratus known as Oersted's Par- 
 allelogram, that is well adapted 
 to the work just described. 
 
 Ascertain the effect on the 
 needle of passing the current 
 entirely around it (Fig. 138) by 
 bending the conducting wire into 
 
 a rectangular form, and placing the needle within it. Try two 
 
 turns of wire about the needle. Try several. Inference. 
 A simple method of placing a magnetic needle within a 
 
 FIG. 138. 
 
MAGNETISM AND ELECTRICITY. 199 
 
 looped conductor, as required above, is to set a common 
 pocket-compass in a hole cut in a square piece of board 15 mm. 
 thick, and a little longer on the edge than the diameter of the 
 compass. Around this board, wind insulated copper wire 
 (No. 20), as many layers as needed. The ends of the wire can 
 be fastened by driving short brass wire staples into the block. 
 This will be found a very serviceable galvanometer for many 
 of the experiments that follow. Binding-posts screwed into 
 the block will make it easier to place it in a battery-circuit. 
 Double connectors may be used instead. 
 
 To facilitate reversing the current, as required above, a 
 device called a Commutator may be used. One may be made 
 as follows : 
 
 Bore two holes one centimetre deep, and one centimetre apart, 
 in a block of wood. In these pour mercury, connecting each to 
 a binding- post screwed into the block by a short heavy copper 
 wire. The galvanometer is to be connected tc the binding-posts, 
 the battery to the mercury-cups. To reverse the current, it will 
 be necessary simply to cross the battery-wires. 
 
 Test the rule for determining the direction of a battery-current 
 by means of a galvanometer, by having some one connect it to 
 a batteiy-cell so placed that you do not see the order of connec- 
 tion made ; then, by observing the direction of deflection of the 
 needle, determine which wire is joined to the zinc plate. 
 
 348. Exercise. Make a voltaic element out of strips of 
 zinc and sheet-iron after the plan given in the last experiment. 
 Place the plates in dilute sulphuric acid, connect the poles to 
 the galvanometer, and determine which is the positive one. 
 Try iron and copper ; lead and copper ; zinc and lead ; iron 
 and lead. 
 
200 PRACTICAL PHYSICS. 
 
 XI. EFFECTS OF ELECTRICAL CURRENTS. 
 
 349. Apparatus. Battery, File, Galvanometer, Apparatus 
 for Electrolysis, Fine Wire, etc. 
 
 350. Exercise. Twist the wire leading from one of the 
 poles of a batter}^ about one end of a file, and the other wire 
 about a steel nail. Now draw the nail across the rough file 
 surface. Note the attending phenomenon. Apply the finger 
 to the end of the nail after drawing it several times over the 
 surface of the file, and ascertain if there has been any change 
 in its temperature. Inference. 
 
 351. Exercise. Fasten to each pole of some convenient 
 form of battery a short piece of No. 18 copper wire. Using 
 connectors, join their ends with a piece of No. 30 platinum 
 wire 3 cm. long. Close the circuit, and observe the effect on 
 the platinum wire. Try fine iron wire. Try copper wire. 
 Ascertain if the size or the length of the wire makes any 
 difference. Are wires of different metals affected alike ? 
 Place the galvanometer of Art. 347 in circuit with the battery, 
 and take the reading. Now insert the short piece of fine wire 
 in the same circuit, and again read the galvanometer. What 
 is indicated by the decrease in the deflection of the needle? 
 What have you as an equivalent for the loss of electric current ? 
 
 The battery used must give a strong current. The chromic 
 acid battery is recommended. Any short- coil galvanometer 
 can be used. Be careful to place it so that the wire of the coil 
 is parallel to the needle before closing the circuit. 
 
 352. Exercise. Make a paper tube 5 cm. long and 1 cm. 
 in diameter. Fit corks to the ends. Through one of them. 
 
MAGNETISM AND ELECTRICITY. 
 
 201 
 
 FIG. 139. 
 
 put two pieces of No. 18 copper wire, joining their inner ends 
 with a short piece of No. 30 iron wire. Fill the tube with gun- 
 powder, close the ends with corks, and connect the terminals 
 with long wires to the poles of a battery of two or three 
 chromic acid cells located at some distance from the torpedo. 
 Now close the circuit. Explain. 
 
 Try a torpedo having the ends of 
 the copper wires not joined by a fine 
 wire, but bent together, leaving a 
 break of about 2 mm. Connect the 
 terminals to the surfaces of a heavily 
 charged Leyden jar. Explain. The 
 Electrical Mortar (Fig. 139), or the 
 Gas-Pistol, may be used in place of 
 
 the torpedo to illustrate the heating effects of the electric 
 spark. 
 
 353. Exercise. Bend a glass tube of about 1.5 cm. 
 diameter and 15 cm. long into a V-form. Close the ends with 
 
 corks and thrust through them 
 platinum wires (Fig.. 140), ter- 
 minating within the tube in strips 
 of platinum foil 2 mm. wide and 
 3 cm. long, and reaching within 5 
 cm. of each other. The foil should 
 be soldered to the wires, and var- 
 nished at the junction to prevent 
 chemical action on the solder. The tube may be supported in 
 a burette-holder, or by setting it into a slot cut into the side of 
 an empty chalk-box. Fill this V-tube two-thirds full of a 
 solution of sodium sulphate, colored with litmus or the liquor 
 obtained by boiling purple cabbage in water. Connect the 
 
 140. 
 
202 
 
 PRACTICAL PHYSICS. 
 
 terminals to the poles of a battery of two or three cells joined 
 in series (Art. 369). Remembering that the action of an acid 
 on a vegetable purple is to turn it red, and that of an alkali 
 is to give it a greenish tinge, what effect do you find the 
 electric current has on the solution of sodium sulphate ? Try 
 copper sulphate. Try tin chloride. Use quite dilute solu- 
 tions, and omit the coloring matter in the last two cases. 
 
 354. Exercise. Cut the bottom from a wide-mouthed 
 
 bottle having a diameter of about 8 cm. Insert a good cork in 
 the neck, and through it thrust two platinum 
 wires terminating within the bottle in strips of 
 platinum foil set parallel to 
 each other, and one centi- 
 metre apart. Fill the bottle 
 two-thirds full of slightly acid- 
 ulated water, and support it 
 on the ring of the iron stand. 
 Over these electrodes, invert 
 long test-tubes also filled with 
 the acidulated water. Now 
 place the apparatus (Fig. 141) 
 
 in circuit with a battery of two or three cells 
 
 connected in series (Art. 369). Ascertain the 
 
 relative amount of gases liberated during any 
 
 interval of time by measuring the length of 
 
 the column. Remove each test-tube by hold- 
 ing the finger firmly over its mouth ; invert, 
 
 and apply a lighted match. The one that burns with a slight 
 
 explosion is hydrogen ; the other is oxygen. 
 
 Reverse the current through the apparatus, and ascertain if 
 
 there is any difference in the liberation of the gases. 
 
 FIG. 141. 
 
 FIG. 142. 
 
MAGNETISM AND ELECTRICITY. 
 
 203 
 
 Ascertain the effect of increasing the number of cells in 
 the battery. Compare two different batteries by observing the 
 length of the hydrogen column produced by each during the same 
 interval of time. A convenient form of apparatus for effecting 
 the decomposition of liquids by means of the electric current is 
 shown in Fig. 142. The gas can be drawn off by means of a 
 rubber tube, and tested. This tube must be filled with water to 
 expel the air. Why? The measurement is readily effected by 
 having the tubes graduated. 
 
 355. Exercise. Dampen a sheet of printing- paper with a 
 solution of ferrocyanide of potassium and ammonium nitrate. 
 Lay it on a brass plate connected with the negative pole of the 
 battery. Connect the positive pole of the battery with a piece 
 of iron or steel wire. Use this wire as a pencil, and write on 
 the prepared paper. Compare the effect with that produced 
 when trying to write with the wire not in the 
 
 battery circuit. Explain. 
 
 356. Exercise. Wind neatly on a rod of 
 annealed iron about 10 cm. long and 1 cm. or less 
 in diameter, two or three layers of insulated copper 
 wire No. 18 or 20 (Fig. 143). Put the wire in 
 
 circuit with a bat- 
 tery, and examine 
 the iron core for 
 magnetic proper- 
 ties. Break the 
 
 circuit, and again test the rod. Jar the rod a little, and again 
 
 test it. 
 
 Support the apparatus on a sounding-board (Fig. 144), and 
 
 listen intently near the coil as the battery circuit is opened 
 
 FIG. 144. 
 
 FIG. 143. 
 
204 PRACTICAL PHYSICS. 
 
 and closed. What is the probable origin of the phenomenon? 
 What is suggested by this experiment regarding the nature 
 of magnetism? 
 
 XII. ELECTRICAL MEASUREMENTS. 
 
 a. Resistance of Conductors. 
 
 357. Apparatus. Galvanometers, Daniell's Battery, Set 
 of Resistance Coils, Wheatstone's Bridge, Insulated Wires, etc. 
 
 358. Exercise. Measure the resistance in ohms, of an 
 electrical conductor. 
 
 There will be needed for this work a Constant Battery, a 
 Galvanometer, and a set of Resistance Coils. For most 
 purposes, the Daniell's battery will be found sufficiently 
 constant. Of galvanometers there are a great many forms, 
 each possessing its special points of excellence. In selecting 
 one for any line of work, regard must be had for the condi- 
 tions under which it is to be used. If the current is feeble, 
 owing to the great resistance of the circuit, a long-coil gal- 
 vanometer should be chosen in order that a suitable deflec- 
 tion of the needle may be obtained. A galvanometer having 
 two or more coils is to be preferred for general use, as 
 then the resistance can be adapted to the case. A deflec- 
 tion of the needle of between 25 degrees and 55 degrees is 
 preferable. 
 
 A serviceable tangent galvanometer is easily made as fol- 
 lows : Cut out of well-seasoned wood a ring 30 cm, in diame- 
 ter, and having a cross-section of 2.5 cm. square. Mount this 
 on a circular wooden base provided with levelling-screws 
 (Fig. 145). No iron must enter into the construction. In the 
 
MAGNETISM AND ELECTRICITY. 
 
 205 
 
 outer edge of the ring, cut a rectangular groove 2 cm. wide and 
 2 cm. deep. In this groove wind two turns of heavy copper 
 wire, the ends to be connected to binding-posts on the base. 
 This will give a coil of practically no resistance. Now wind in 
 the same groove, using insulated 
 copper wire No. 26, three other 
 coils of 10, 30, and 90 turns 
 respectively, the ends of each to 
 be connected to its own pair of 
 posts. By making connections, 
 so as to secure the sum or differ- 
 ence of these coils, any of the 
 following series can be secured : 
 10, 20, 30, etc., 130 turns. Fas- 
 ten across the ring a wooden or 
 brass bar supporting a wooden 
 or paper box 10 cm. in diameter 
 and 5 cm. deep, having a glass cover with a hole 1 mm. in 
 diameter drilled through its centre. Place on the bottom of 
 this box a circular piece of mirror-glass to which is cemented a 
 paper ring graduated to degrees. For a 
 needle, magnetize a piece of watch-spring 
 15 mm. long, inserting it edgewise into a 
 disk of elder-pith (Fig. 146). Cement to 
 the pith-disk, at right angles to the needle, 
 a pointer of glass thread made by drawing 
 out a piece of glass tubing when thoroughly 
 softened in a flame. Suspend the needle 
 by a silk fibre from the centre of the glass cover. The needle 
 should hang at the centre of the wooden ring, and within a 
 few millimetres of the scale. When the instrument is levelled, 
 the two ends of the pointer should give the same readings, 
 
 FIG. 145. 
 
 FIG. 146. 
 
206 
 
 PRACTICAL PHYSICS: 
 
 and reversing the current should not alter the amount of the 
 deflection ; if it does, the pointer is either not set at right 
 angles to the needle, or the needle is not properly centred. To 
 eliminate small errors of this kind, average the readings of 
 both ends of the pointer ; reverse the current, and average the 
 readings ; and finally average these two averages for the correct 
 reading. 
 
 In Fig. 147 is shown a more sensitive form of galvanometer, 
 where a form of needle known as Astatic is employed. Such 
 an instrument is desirable for use in con- 
 nection with Wheats tone's bridge or the 
 thermopile. 
 
 For most of the work in this book, a 
 galvanometer constructed as follows will 
 be sufficiently reliable : Procure a circular 
 wooden box 10 cm. in diameter and 10 cm. 
 deep, having a wooden cover with a large' 
 circular hole cut in it, exposing the bottom 
 clearly to view. On the bottom, place a 
 wooden block 2 cm. thick, on which is 
 wound a flat coil of several layers of No. 24 insulated 
 copper wire. Bring the ends through the side of the box, 
 and fasten them to small binding-posts. The scale and the 
 needle are prepared as in the case of the tangent galvanometer 
 described above. To the under side of the ring-cover, cement 
 a clean plate of glass. Attach the fibre supporting the needle 
 to the centre of the cover. This must be done with great care, 
 for, if not centred, the two ends of the pointer will give 
 different readings as the cover is turned around. This instru- 
 ment may be used as a tangent galvanometer, owing to its 
 short needle, without sensible error, for angles not exceeding 
 45 degrees. 
 
 FIG. 14< 
 
MAGNETISM AND ELECTRICITY. 
 
 207 
 
 FIG. 148. 
 
 If the coil is wound in two parts, as shown in Fig. 148, the 
 distance between the parts being a trifle less than the length of 
 the needle, it has been found that the 
 deflection is proportional to the cur- 
 rent up to 50 degrees. When no 
 current is passing through the coils, 
 the needle should hang symmetrically 
 between them. 
 
 Resistance-boxes usually consist of 
 a collection of coils of insulated Ger- 
 man-silver wire of dif- 
 ferent lengths and de- 
 grees of fineness, and 
 consequently of differ- 
 ent resistances, -each 
 coil having some known 
 relation to the standard 
 unit of resistance, the 
 Ohm. By means of 
 
 movable arms or plugs, as the case may be, any required resist- 
 ance can be thrown 
 into the circuit (Fig. 
 149): Fig. 150 shows 
 a cheap form of re- 
 sistance-box suitable 
 for beginners. To 
 close the circuit, each 
 switch must rest on a 
 brass nail-head of the 
 corresponding gradu- 
 ated arc. These contacts must be kept bright to insure 
 good work. In using coils, do not keep the circuit closed 
 
 FIG. 149. 
 
208 PRACTICAL PHYSICS. 
 
 for any great length of time, as they become heated from the 
 current. 
 
 First Method. Form a circuit consisting of a constant 
 battery B, a galvanometer G, a set of resistance coils R, 
 and the conductor X to be measured (Fig. 151). By discon- 
 necting X, and inserting the short thick wire W, the coil 
 may be cut out of the circuit. First, 
 take the reading of G when sufficient 
 resistance has been introduced by means 
 of R to produce a suitable deflection. 
 r_J /^T^ Secondly, insert W, dropping X out of 
 
 -, V./ the circuit, and add sufficient resistance 
 
 through R. to produce the same reading 
 for G. The added resistance is evidently 
 equal to that of X. The deflection of 
 
 the galvanometer had better not exceed 
 Fi ^ 151 45 degrees. The accuracy of this method 
 
 is dependent very largely on the sensi- 
 tiveness of the galvanometer, and the constancy of the battery. 
 It is more accurate for small resistances than it is for large 
 ones. Be as expeditious as possible in making the required 
 observations, that the conditions may change as little as 
 possible. It is recommended to place a telegraph key in the 
 circuit to make and break connections. 
 
 Second Method. Form a circuit consisting of a constant 
 battery B, a tangent galvanometer G, a set of resistance coils 
 R, and the conductor X to be measured, using as little wire as 
 possible in making the connections. Represent the resistance 
 of the battery by r, which, if unknown, can be determined by 
 Art. 367, and that of the galvanometer by g, which, if unknown, 
 can be determined by the first method of measuring resistances 
 of conductors, employing a second galvanometer as a galvano- 
 
MAGNETISM AND ELECTRICITY. 
 
 209 
 
 scope, or as in Art. 365. Adjust G and R so as to secure a de- 
 flection between 25 degrees and 55 degrees. With a resistance 
 R and the unknown X in the circuit, take the reading of G which 
 may be represented by a. Now cut out X, and introduce 
 a resistance R' by means of the resistance-box, to give a 
 different deflection of G, as a'. Substitute the values obtained 
 
 tan a' 
 
 in the formula 
 
 Proof. By Ohm's law, C = -. 
 
 tana 
 E 
 
 , and solve for X. 
 
 , and O' =-?-. 
 R'+r+g 
 
 By the law of the Galvanometer, /^ = 
 
 tan a' 
 
 Therefore 
 
 _^_ r _|_ y _[_ X __ tan a' 
 R ' -f- r + g " tan a * 
 
 As the resistance of a battery varies somewhat with the 
 external resistance, it is advisable to employ one having as low 
 a resistance as possible, and, at the same time, make the 
 external resistance large in comparison, so that the effect on 
 the constancy of the battery of changing the external resist- 
 ance may be small. The best results are obtained by securing 
 a deflection as near as pos- 
 sible to 45 degrees, and hav- 
 ing a and a' nearly equal. 
 When the external resistance 
 is large in comparison with 
 the battery resistance, the 
 latter may be neglected with 
 but slight error. 
 
 Third Method. For this 
 method is needed a Wheat- FlG> 152 ' 
 
 stone's bridge and an astatic galvanometer. The principle 
 applied is, that, if a circuit be set up as shown in Fig. 152, 
 
210 
 
 PRACTICAL PHYSICS. 
 
 and R, R', and R" so adjusted, that, on closing the circuit, 
 no deflection of G is produced, then R'X = RR" , whence 
 
 RR" 
 X = nT' Fig. 153 illustrates a simple form of the Bridge, 
 
 in which two of the resistance-boxes are replaced by a fine 
 German-silver wire. This is constructed as follows : On a 
 varnished board 1.1 metre long and 15 cm. wide, fasten with 
 brass screws strips of copper or brass 1.5 cm. wide, of the form 
 shown in the figure, the pieces ME and HF being 10 cm. 
 long. The spaces between A and the cross-pieces may be one 
 
 centimetre. The 
 ~^ lengths of the 
 
 strips should be 
 such that the in- 
 side distance be- 
 tween E and F 
 is exactly one 
 metre. Solder a 
 stretched Ger- 
 man-silver wire (No. 26) across from E to F. Under this 
 wire fasten a paper scale divided to half -centimetres. Solder 
 binding-posts to these strips so that connections may be made 
 as shown in the figure, the contact at B being made by pressing 
 the wire from the galvanometer against the wire of the bridge. 
 In making connections, use coarse wire, and as little as possi. 
 ble, that the resistance of these wires may be neglected. 
 
 To use the bridge, make the connections as already indicated ; 
 through R, introduce 1, 10, or 100 ohms; then slide B along 
 the wire EF till a point is reached at which the reading of G 
 is zero ; then X equals the reading of R multiplied by the 
 ratio of EB to BF. 
 
 This method is unaffected by any changes in the electrical 
 
 TZI 
 
 FIG. 153. 
 
MAGNETISM AND ELECTRICITY. 211 
 
 current, the degree of accuracy secured depending on the 
 sensitiveness of the galvanometer. 
 
 359. Exercise. Measure the resistance of 40 metres of 
 insulated copper wire, and also of 20 metres of the same kind 
 of wire. Compare the resistance with the lengths. Inference. 
 
 360. Exercise. Measure the resistance of 40 metres of 
 insulated copper wire (No. 23), and also of the same length 
 of No. 30 wire. Compare the resistances with the diameters. 
 Inference. 
 
 361. Exercise. Compare the resistances of equal lengths 
 of wires of different substances having the same diameter. 
 Inference. 
 
 362. Exercise. Compare the resistances of two equal 
 wires of the same material laid side by side, and connected at 
 their ends, witli that of one of them taken separately. 
 
 363. Exercise. Measure the resistance of a coil of fine 
 wire of known diameter, but whose length is unknown, and 
 also measure the resistance of a Jcnoiun length of wire of the 
 same kind. Calculate the length of the unknown coil by 
 
 the formula = -, R and I representing resistance and length 
 respectively. 
 
 364. Exercise. Determine the effect of change of tem- 
 perature on electrical conductivity. 
 
 In Wheatstoiie's bridge, for X put one metre of fine wire 
 (No. 30) made into a coil by winding it carefully on a pencil, 
 not allowing the successive parts of the coil to touch, so that 
 
212 PRACTICAL PHYSICS. 
 
 the current must pass through its entire length. Now set B 
 so as to produce a balance ; then hold a Bunsen flame under 
 the coil ; notice the effect on the balance, and ascertain 
 whether the conductivity is increased or diminished by moving 
 B till the balance is restored. 
 
 Compare iron, copper, and German-silver wires in this way 
 to see if they are equally affected. 
 
 The general effect that the lowering of the temperature of a 
 conductor has upon its conductivity may be roughly shown by 
 connecting the poles of a strong battery with a short piece of 
 iron wire of such a length that the current heats it to a dull red 
 color. Now apply a lump of ice to one portion of the wire, 
 and observe the effect on the other part. Inference. 
 
 365. Exercise. Measure the resistance of a galvanometer 
 by means of its own deflection. 
 
 First Method. Connect, in circuit, the galvanometer, a 
 constant battery of known resistance, and a set of resistance 
 coils, employing short thick wire. Proceed as in Art. 358 
 (second method), except that the X is omitted. By giving, in 
 succession, two values to 72, as K and J?', two values for a 
 are obtained, as a and a'. Now substitute in the formula 
 
 R 4- r 4- a tan a 
 
 - 5 and solve tor q. It will be necessary to 
 
 ^ + r H~ 9 tan a 
 
 determine the battery resistance unless it is known to be small 
 
 in comparison with R and g. 
 
 Second Method. Place the galvanometer in the place of X 
 in Whcatstone's bridge, joining the posts A and B (Fig. 153), 
 previously connected by the galvanometer, by a short, thick 
 wire. A deflection of Q is now obtained. Now place a bar 
 magnet in the magnetic meridian, so that, by its attraction, 
 the deflection of the needle is reduced to zero. Adjust the 
 
MAGNETISM AND ELECTRICITY. 213 
 
 resistance in the arms of the bridge, so that the reading of G- is 
 not changed by connecting or disconnecting A and B. Then 
 
 RR" 
 
 R g KH" whence g = . 
 
 b. Resistance of Batteries. 
 
 366. Apparatus. Darnell's Battery, Galvanometer, Re- 
 sistance Coils, Wheatstone's Bridge, etc. 
 
 367. Exercise. Measure the internal resistance of a 
 battery. 
 
 First Method. Place the cell whose resistance is required 
 in circuit with a tangent galvanometer of known resistance 
 y, and a set of resistance coils. Introduce through the coils 
 a resistance of R and observe the deflection a of G. Then 
 introduce a different resistance R', and observe the deflection 
 
 a' of G. Substitute in the formula R ' g ~^~ r = tan a ', and 
 
 R' -\-g-\-r tana 
 
 solve for r. Do not use too large deflections of the galvanom- 
 eter, as beyond 45 the needle moves out of a uniform field. 
 
 Second Method. When two cells of the same kind are 
 available, then connect them in opposition, that is, with a 
 short thick wire join the two negative poles ; and then, by 
 means of their positive poles, place them in circuit with a con- 
 stant battery, a galvanometer, and a set of resistance coils. 
 Since two equal cells, joined in opposition, neutralize each 
 other, then any deflection of the galvanometer must be due to 
 the constant battery. Hence, two such cells can be treated as 
 a dead conductor, and the resistance measured as in Art. 358. 
 Half of this resistance is that of one of the cells. 
 
 It will be found, however, on connecting two cells in opposi- 
 tion and placing them in circuit with a galvanometer, that a 
 
214 PRACTICAL PHYSICS. 
 
 feeble current is furnished, showing that the cells are not quite 
 equal. Hence this method is not very reliable. 
 
 Third Method. Place the battery in the place of X in 
 Wheatstone's bridge (Fig. 153), connecting C and D by a wire. 
 Now set R as nearly equal to the resistance of the battery as 
 can be estimated, and find a position for B, such that G- main- 
 tains a constant deflection whether the circuit is closed between 
 
 7~> ~f> ll 
 
 C and D or not. Then r = . It is better to employ a 
 
 controlling magnet, and bring the galvanometer reading down 
 to zero, as then the instrument is most sensitive. 
 
 The accurate measurement of the resistance of a battery is 
 not easy, as it varies with the resistance in the circuit at the 
 time, and is constantly changing with the chemical changes 
 going on in the cell. The most that should be expected is to 
 get an approximation to its resistance, under the conditions 
 governing the battery during the time it was under examination. 
 Employing high resistances would tend to retard polarization ; 
 but their use would be open to the objection that errors in such 
 high resistances will introduce errors into the results obtained 
 larger than the battery resistance. Unless you have the most 
 accurately constructed apparatus it is better to employ resist- 
 ances but little, if any, greater than those being measured ; and, 
 in case the galvanometer is over-sensitive and gives too large 
 a deflection, reduce its deflection by a controlling magnet, or 
 employ a shunt, of known value, and compute the resistance 
 of the shunted instrument, as shown in Art. 376. 
 
 368. Exercise. Determine whether the size of the plates 
 and the distance between them affect the resistance. 
 
 Construct a simple cell, as in Art. 346. Measure the in- 
 ternal resistance, when the plates reach 8 cm. into the exciting 
 
MAGNETISM AND ELECTRICITY. 215 
 
 fluid, and compare with that when they reach only 4 cm. into the 
 liquid. Also measure the resistance when the plates are 3 cm. 
 apart, and compare with that when 1.5 cm. apart. Inference. 
 
 Polarization may be prevented during the experiment by 
 keeping up a gentle agitation of the liquid, by means of a 
 small glass rod. 
 
 369. Exercise. Compare the resistance of two cells, of 
 the same size and kind when joined abreast, with that of a 
 single cell. Also measure their resistance when joined in series. 
 Inferences. 
 
 To connect cells abreast, join their like poles together, 
 making of them one pole. To connect them in series, join th.e 
 positive pole of one to the negative pole of the next, thus 
 leaving the negative pole of the first cell and the positive pole 
 of the last one to serve as poles of the battery. 
 
 c. Electro- Motive Force of Batteries. 
 
 370. Apparatus. Same as in the last section. 
 
 371. Exercise. Measure the electro-motive force of a 
 battery. 
 
 For this experiment there will be needed a battery giving 
 a constant current whose E. M. F. is known. For most pur- 
 poses, that is, wherever great accuracy is not required, the 
 Daniell' s cell may be used. If the liquids of this battery are 
 solutions of zinc sulphate and copper sulphate of the same 
 density, then its E. M. F. is about 1.1 volt. 
 
 First Method. Connect in circuit with the cell serving 
 as a standard a set of resistance coils and a galvanometer. 
 Now introduce through the resistance coils a resistance of 
 
216 PRACTICAL PHYSICS. 
 
 R ohms and read the deflection a of the galvanometer. Then 
 substitute the cell whose E. M. F. is to be determined for the 
 standard cell, and adjust the resistance R' so as to obtain the 
 same deflection of the galvanometer as before. Hence, as the 
 
 1 ' 
 
 currents are equal in the two cases, 
 
 - , 
 B'+r'+g' 
 
 and E' = . E in which E and E' represent the 
 
 E. M. F. of the standard cell and the unknown one respectively. 
 By making R and R' large, then r and r' may be neglected 
 
 without sensible error, and E' = .JJ, that is, the E. M. F. 
 
 of the two cells are proportional to the resistances which produce 
 equal deflections of the galvanometer. Multiplying the value 
 
 B'+ g 
 of E by . gives the E. M. F. of the cell under examina- 
 
 tion. 
 
 By employing large resistances and a sensitive galvanometer 
 better results will be obtained as polarization is retarded. 
 
 Second Method. Connect in circuit the standard cell, the 
 tangent galvanometer, and the resistance coils. Introduce 
 sufficient resistance R to give a deflection a, something between 
 20 and 50. Now substitute for the standard cell, the one of 
 unknown E. M. F., and adjust the resistance R 7 so that the total 
 resistance of the circuit is the same as when the standard cell 
 was used, and record the deflection a'. This will require that 
 
 E 
 
 r, r', and g be known. By Ohm's law we have C ^ . -r 
 
 E' C E 
 
 and C'= -nT~\ 7~\ ' whence -77-, = ~wi"> as the denominators 
 
 ~ 
 
 C tan a 
 were made equal. By the law of the galvanometer ~7T? / - 1' 
 
 Hence E ' = E --- By using a sensitive galvanometer of 
 tan a 
 
MAGNETISM AND ELECTRICITY. 217 
 
 several thousand ohms resistance the resistance coils may be 
 omitted and the resistance of the battery neglected. 
 
 Third Method. Connect in circuit with a galvanometer 
 and a set of resistance coils the weaker of the two cells, 
 the standard and the unknown. When a resistance R is used 
 record the deflection a of G. Then add resistance R' to reduce 
 the galvanometer reading any convenient number of degrees, 
 as 10. The galvanometer should be adjusted to give a deflec- 
 tion in the vicinity of 45. Now exchange batteries and 
 introduce such resistance R" as to produce the same deflec- 
 tion a. Then add enough more resistance R'", to reduce 
 the deflection the same number of degrees as before. 
 
 R"' 
 
 From Ohm's law it follows that E' = ^ -E, that is, the E. M. 
 
 F. of two cells are to each other as the resistances which pro- 
 duce equal diminutions of current strength. 
 
 E 
 
 Proof of the above rule : C = -p 7 , when a was 
 
 K r r T" 9 
 
 first observed. On reducing this deflection 10, then 
 
 E 
 
 C ' = p . p-fi - j As the deflection was made the same when 
 -\-r-\-g 
 
 the stronger battery was used then the current strength was the 
 
 E' 
 same and C = ^7, , r/ > On reducing this deflection 10, 
 
 E' 
 
 as before, then C r/ ==-^7T, jgw rrx"* R'" being the extra 
 
 resistance required to bring about the necessary reduction. 
 
 E E 1 E 
 
 Therefore, p . . = p ,, . ..n~* and 
 
 E' 
 
 ft" I 7?^"T ~\~~ ' ^ ^ ne mem ^ ers ^ these equations are 
 
 inverted and the resulting equations subtracted from each 
 
218 PRACTICAL PHYSICS. 
 
 E' R'" 
 
 other, member from member, we have -^r = ^ , whence 
 
 Mi Li 
 
 In measuring the E. M. F. of batteries which polarize rap- 
 idly, as the Leclanche, or whose E. M. F. falls rapidly 
 on closing the circuit, as the chromic acid battery, the ad- 
 justments required by the above methods must be approxi- 
 mated to at first and the battery then allowed to rest for a few 
 moments to recuperate. After that the circuit may be again 
 closed and the former approximations corrected as rapidly, as 
 possible. A few trials will lead to very satisfactory results. 
 It is well to remember, however, that the E. M. F. of a battery 
 changes somewhat with the resistance of the circuit. 
 
 372. Exercise. Determine whether the E. M. F. is af- 
 fected or not by the size of the plates. 
 
 373. Exercise. Measure the E. M. F. of a cell and 
 compare it with that of two cells of the same kind when joined 
 abreast. Also compare it with that of two when joined in 
 series. Inference. 
 
 374. Exercise. Calibrate, any galvanometer so that its 
 readings will be those of a tangent galvanometer. 
 
 ^Connect in, circuit a tangent galvanometer, G, the galvanoiu-. 
 eter to be calibrated, G', a set of resistance coils and a con- 
 stant battery. Now introduce sufficient resistance to reduce 
 the deflection of G' to 1, and read G, then lessen the resist- 
 ance till G' = 2, and read G, and so on till the equivalents of 
 about 50 have been obtained. 
 
 If the resistance is reduced to zero before a deflection of 45 
 is reached, then increase the current by introducing a second 
 
MAGNETISM AND ELECTRICITY. 
 
 219 
 
 cell, repeating the observations for the last galvanometer de- 
 flection observed when the single cell was employed in order 
 that the ratio sustained by the new readings to the old may be 
 obtained and all reduced to the one standard. 
 
 If the two galvanometers are so different in sensitiveness 
 that a current which causes a large deflection of one produces 
 but little effect on the other, then connect the terminals of the 
 more sensitive one by a wire, called a shunt, so that only part 
 of the current passes through the galvanometer. A galvanom- 
 eter calibrated in this way must be used in connection with 
 the shunt employed in calibrating it, whenever its readings are 
 to be used in comparison with this particular tangent galvanom- 
 eter. When used alone the shunt may be dropped and the 
 calibrated readings will be those of a tangent galvanometer. 
 
 375. Exercise. Determine the law for divided electrical 
 circuits, that is, if two conductors join two points of a battery 
 circuit, find how the current in each branch is related to "the 
 resistance of that branch. 
 
 Set up a circuit as shown in Fig. 154, consisting 'of four 
 galvanometers, of known resist- 
 ance, all calibrated by compari- 
 son with the same standard, two 
 resistance coils and a constant bat- 
 tery. Short thick wires should be 
 used so that the resistance may be 
 practically confined to the galva- 
 nometers and the coils. 
 
 1st. Set R and R x so that the 
 total resistance in the branches 
 CD and EF are equal. Compare 
 G and G 15 G 2 and G 3 , G and G-j. 
 Inference. 
 
 FIG. 154. 
 
220 PRACTICAL PHYSICS. 
 
 2d. Set R and R x , so that the total resistance in EF is 
 twice that in CD. Compare as before. Inference. 
 
 3d. Set R and R 1? so that the total resistance in EF is 
 three times that in CD. Compare as before. Inference. 
 
 Frame a law expressing the conclusions reached. 
 
 376. Exercise. Calibrate any galvanometer so that the 
 relative current-strengths are known, and hence the absolute 
 strengths, provided the value in amperes of any one reading is 
 known. 
 
 Connect in circuit a constant battery, two sets of resistance 
 coils and a galvanometer (Fig. 155). 
 If MI = g, then half of the current goes 
 
 through G. If MI = -|, then a third of 
 
 the current goes through G. If R l = ^ 
 then a fourth of the current goes through 
 
 G. If Ri=-^-, then ith of the cur- 
 n-l n 
 
 FIG. 155. 
 
 rent goes through G. 
 
 As the shunt reduces the total resistance of the circuit, to 
 maintain the current constant a suitable compensation must be 
 introduced each time by means of R. To determine the amount 
 of this compensation it is evident that, as the conductivity of 
 
 the galvanometer and the shunt circuit combined is J = 
 
 9 #1 
 
 ^- *, the combined resistance of these circuits is . 
 
 gfii g+ RI 
 
 As .#= 
 
 
 9 then , * = :L> Hence the compensation to 
 
 n-l' g + 
 
 g n\ 
 
 be added is g - == g. . 
 
 H 71 
 
MAGNETISM AND 'ELECTRICITY. 221 
 
 When n = 2, R l = gr, the current in G is one-half, and the 
 compensating resistance is g. 
 
 When n = 3, R = 2 gr, current = , compensating resistance 
 
 =!? 
 
 When n = 4, ^ = 3 #, current = , compensating resistance 
 
 = !</ 
 
 When n = 5, R l = 4 gr, current = |, compensating resistance 
 
 *>. 
 
 Hence, if we put in the circuit the ^-shunt, and through R 
 the compensation -J #, then add resistance through R sufficient 
 to produce a deflection of 1, on removing the shunt and the 
 compensating resistance the current through G will be doubled. 
 
 If this deflection is recorded it will indicate, whenever it is 
 obtained, that the current then flowing is double that which 
 gave the deflection of 1. 
 
 Now, try in succession the jpshiint, J-shunt, etc., with the 
 proper compensating resistances, as determined above, and 
 deflections for three times, four times, etc., the current at 1 
 will be sent through the galvanometer. Tabulate these deflec- 
 tions and the calibrated scale for relative current strengths will 
 be known. 
 
 XIII. ELECTRO-MAGNKTISM AND ELECTRO-DYNAMICS. 
 
 377. Apparatus. Batteries, Iron Filings, Insulated Wire, 
 Bar Magnet, Electro-Magnet, Ampere App., Magnetoscope, Float- 
 ing Battery, Sounder, Telegraph Key, Relay, etc. 
 
 378. Exercise. Connect two or more large cells, in par- 
 allel circuit, with short thick wire. Close the circuit through a 
 heavy wire, and then dip a portion of it into iron filings. Com- 
 pare the result with that obtained when the wire is carrying 
 no current. 
 
222 
 
 PEACTICAL PHYSICS. 
 
 379. Exercise. Thrust the wire of the last experiment 
 
 vertically through a sheet of stiff 
 paper supported in a horizontal 
 position (Fig. 156). After closing 
 the circuit sift a few iron filings 
 on the paper, jarring it slightly 
 with the finger as they fall. Com- 
 pare the figure with that given 
 when the wire carries no current. 
 
 VCJM 
 
 Inference. 
 
 FIG. 156. 
 
 380. Exercise. Coil into flat spirals, 8 cm. in diameter, 
 some No. 20 insulated copper wire, securing the wire in place 
 by means of sealing-wax (Fig. 157). 
 
 Suspend these from two wire hooks, 
 fixed to a piece of board and con- 
 nected to binding-posts, the hooks 
 being placed so that the coils hang par- 
 allel and about 1 cm. apart. The 
 lower ends of the wires clip into a vessel 
 of mercury to a depth of 1 mm. Now 
 pass a current from a chromic acid, or 
 Bunsen cell, through these coils, by join- 
 ing the battery-poles to the posts on the 
 board, and record the effect. Turn one 
 of the spirals over, and again record the 
 effect. Trace the direction of the cur- 
 rent through the spirals, in each case, 
 and devise a law embodying the results. 
 
 Straight wires may be substituted for the spirals ; then, if the 
 battery-poles are connected to the posts, the current will move 
 in opposite directions in the two wires : and if one battery-pole 
 
 FIG. 157. 
 
MAGNETISM AND ELECTRICITY. 223 
 
 is joined to both posts and the other pole is connected to the 
 mercury-cup the currents will have the same direction. A 
 battery of" several cells joined abreast will be necessary when 
 straight wires are employed. 
 
 381. Exercise. Thrust the straight part of the wires of 
 the last experiment through a sheet of paper supported horizon- 
 tally, and study the magnetic field, as in Art. 379 ; first, when 
 the current in the wires have the same direction ; and secondly, 
 when opposite. Test the effect of increasing the current by 
 increasing the number of cells. How would you join them? 
 
 382. Exercise. Determine the laws of electrical cur- 
 rents. 
 
 Construct a rectangular frame, 25 cm. square, out of insu- 
 lated copper wires, No. 20, by winding about four layers around 
 the edge of a square board. Slip the wire off the board, and 
 tie the parts together in a number of places with fine cord. 
 Bend one end of the 
 wire into a hook- 
 form (Fig. 158), 
 the other end to be 
 left straight, ex- 
 tending out from 
 the other side. Bend 
 a narrow strip of 
 bniss into n J-form, 
 giving the hooked 
 part a spoon-shape, 
 so that it will hold 
 a small globule of 
 mercury. Support 
 the strip in a bu- FIG- 158. 
 
224 PRACTICAL PHYSICS. 
 
 rette-holder, and hang the rectangle from it with the straight 
 end dipping into a vessel of mercury. Adjust the shape of 
 the hooked part of the wire so that the upper and lower sides 
 of the rectangle are horizontal, the frame keeping any position 
 given it, and turning on application of the slightest force. 
 The supporting point of the frame should be conical, good 
 contact being secured by a globule of mercury. Connect one 
 pole of the battery to the strip, and the other to the vessel of 
 mercury. 
 
 Wind four or five layers of insulated wire around the edge 
 of a board 20 cm. by 10 cm. Connect this in the same cir- 
 cuit with EF, support it near to EF and in the same plane, 
 with the current moving through it parallel to that in F, 
 and in the same direction, and record the effect on EF. In- 
 ference. 
 
 Remove HK from the circuit, and hold a bar magnet parallel, 
 to EF, or place it beneath it and in the same plane, and record 
 the effect. Reverse either the magnet or the direction of the 
 current, and again record the effect. What law seems to gov- 
 ern the phenomenon ? 
 
 Coil some No. 16 insulated wire into a close spiral (Fig. 159), 
 arranging it for suspension in the same manner as in the case 
 
 of the wire rectangle. Give 
 the spiral, usually called a Sole- 
 noid, a diameter of 4 cm. and a 
 length of 15 cm. Suspend the 
 solenoid in place of the wire 
 frame, adjusting it so that it 
 hangs horizontally and turns 
 FlG> 159> freely on its support. Close the 
 
 circuit, and then hold a strong magnet near one of its ends. 
 Determine the effect of reversing the current. Trace the current 
 
MAGNETISM AND ELECTRICITY. 
 
 225 
 
 FIG. 160. 
 
 through the solenoid. In what direction is it moving in the 
 N-seeking end? 
 
 Apply the law derived from the study of 
 the solenoid to an Electro-Magnet (Fig. 
 160) to determine its polarity when in cir- 
 cuit with a battery. Test the conclusion 
 reached by placing it in a battery circuit 
 and bring its poles in succession near a 
 magnetoscope. 
 
 Double part of the wire of the circuit 
 back on itself as shown in Fig. 161, and 
 hold it parallel to one of the vertical sides 
 
 of the suspended wire rectangle. Account for the 
 lack of motion on the part of the rectangle. 
 Use a strong current. 
 
 Substitute for the simple loop a spiral, with 
 the return wire passing in a straight line through 
 it (Fig. 161). Compare the result with that 
 obtained in the last case. Is the action of the 
 sinuous portion any greater than that of the rec- 
 tilinear ? What must be the effect on the sole- 
 noid to have the wire bent parallel to its axis, as 
 shown in Fig. 159? 
 
 Mount a magnetic needle so as to be free to 
 move in any direction in a horizontal plane. 
 Hold parallel to the needle, and a little above 
 it, a wire carrying an electric current of known direction, and 
 record the effect. Compare this with the solenoid when an 
 electric current passes parallel to its axis, above it, and in the 
 same direction with respect to the line joining its poles, as it 
 did in the case of the magnet. Try the current below in each 
 case. Ascertain the effect of reversing the current. 
 
 FIG. 161. 
 
226 PRACTICAL PHYSICS. 
 
 383. Exercise. Make a small chromic acid battery, using 
 a short wide test- tube, or a light bottle, for a battery- jar. Insert 
 
 it in a cork of sufficient size to float the 
 apparatus in a vessel of water (Fig. 162). 
 Connect the poles of the battery with a 
 small helix of wire. Float the apparatus 
 in a vessel of water, and observe if it 
 assumes any one position in preference to 
 another. Hold a straight wire forming 
 part of a battery-circuit parallel to the 
 
 axis of the helix. Record the effect. Hold a pole of a perma- 
 nent magnet near one end of the helix. Record the effect. 
 Frame a law expressing the action of electric currents on each 
 other, as well as the action of currents on magnets, as proved 
 by this floating battery. 
 
 If the edges of the cork-float are greased, there will be less 
 tendency on the part of the apparatus to keep against the side of 
 the vessel, especially if the latter is filled to the brim with water. 
 
 384. Exercise. Set up a telegraph line, the longer the 
 better. A return wire may be used, or the wires may be con- 
 nected to the gas-pipes, if rooms in the same building are 
 joined. If distant buildings are connected, the earth may be 
 used for the return circuit. In that case earth connections may 
 be secured by connecting the wires to the gas or water pipes, if 
 possible, or to large metal plates buried deep enough to reach 
 moist earth. If the line is set up within a room, a coil of Ger- 
 man-silver wire may be put in circuit to make the line resemble 
 a long one. In any case the insulation of the line must be 
 secured. Measure the resistance of each instrument and also 
 of the complete line. Connect a sounder, a relay, and a set of 
 resistance coils in the line, and compare their working as the 
 
MAGNETISM AND ELECTRICITY. 
 
 227 
 
 resistance of the line is increased by connecting in more wire. 
 Determine the current required to work the relay ; also that 
 required to work the sounder. 
 
 XIV. CURRENT INDUCTION. 
 
 385. Apparatus. Galvanometer, Battery, Helices of 
 Wire, Electric Motor, Bar Magnet, Microphone, Coils of Insu- 
 lated Wire, Sheets of Rubber, Copper, Paper, Zinc, and Iron, 
 Induction Coil, Telegraph Key, etc. 
 
 386. Exercise. Wind smoothly a few layers of insulated 
 copper wire, No. 24, on a hol- 
 low paper or wooden cylinder 
 
 with thin walls (Fig. 163). 
 Connect this helix with a sen- 
 sitive galvanometer. Now in- 
 troduce suddenly into the helix 
 the N-seeking pole of a strong 
 bar magnet. Why is the 
 needle deflected? What di- 
 rection must the current have 
 had? Is there any current 
 when the magnet is stationary 
 within the coil ? Suddenly remove the magnet and compare 
 the effect with that previously obtained. Try the S-seeking 
 pole. Try magnets of different strengths. Try a helix having 
 less wire. Conclusions. 
 
 387. Exercise. Place within the helix used in the last 
 experiment a soft iron core, consisting of a number of No. 18 
 iron wires, the length of the spool. Now move the pole of a 
 strong bar magnet suddenly up to the end of this core, and ob- 
 serve the effect on the galvanometer. Try moving the pole of 
 the magnet rapidly away from the core. Trace out the currents 
 
 FIG. 13. 
 
228 PRACTICAL PHYSICS. 
 
 produced in the helix, and compare their direction with the 
 Amperian currents of the magnet. 
 
 388. Exercise. Connect an Elec- 
 tric Motor (Fig. 164) to a sensitive 
 galvanometer of low resistance. Ro- 
 tate the armature of the machine by 
 rapidly pulling off a string wound on 
 the shaft. Observe the effect on the 
 galvanometer. Reverse the direction of 
 rotation. Explain the action of the 
 machine in the light of the laws of in- 
 duction developed in Art. 386. 
 
 389. Exercise. Wind on a paper bobbin, 2 cm. long, 
 about 30 g. of No. 30 insulated copper wire, and place it around 
 the pole of a bar magnet, supported horizontally (Fig. 165). 
 Connect the terminals of the helix to a sensitive galvanometer. 
 Cut out of thin sheet-iron, such as photographers use in " tin- 
 
 FlG. 165, 
 
 typing," a disk 8 cm. in diameter. Cement to it a wooden 
 handle. Now move the disk suddenly toward the pole of the 
 magnet and observe the effect on the galvanometer. Try 
 moving it suddenly away from the pole. Explain. 
 
 Replace the galvanometer by a second bobbin and magnet 
 (Fig. 166). Opposite the pole of the second magnet and near 
 
MAGNETISM AND ,ELECTEICITY. 
 
 229 
 
 to it suspend, by a thread, an iron disk to the centre of 
 which is cemented a piece of mirror. Place the apparatus 
 where a ray of sunlight may strike the mirror and be reflected 
 on the wall. Now move the first disk in the same manner as 
 
 FIG. 166. 
 
 when the galvanometer was in circuit, and observe the effect 
 on the second disk by means of the spot of light on the wall. 
 
 The apparatus will be more sensitive if the edge of the disk 
 is opposite the pole of the magnet, for then it will turn on a 
 vertical axis. 
 
 Bell telephone receivers may be substituted for the magnets 
 and bobbins employed above. 
 
 390. Exercise. Fasten 
 two square pieces of gas-carbon 
 to an upright strip of thin 
 wood, and join them by a car- 
 bon pencil with tapering ends, 
 resting loosely in conically 
 shaped cavities in the horizon- 
 tal bars (Fig. 167). Place this 
 Microphone* in circuit with a 
 battery and a Bell telephone by 
 
 FIG. 167. 
 
 * The Microphone does not illustrate Current Induction. Its consideration at thia 
 point is found convenient on account of using it in connection with the Telephone. 
 
230 
 
 PEACTICAL PHYSICS. 
 
 twisting wires around the horizontal bars. Listen through the 
 telephone to the ticking of a watch resting on the base of the 
 microphone. Connect two rooms electrically, the microphone 
 and telephone being in the circuit, but in different rooms. 
 Listen at the telephone to the talking of an assistant standing 
 near the microphone. 
 
 391. Exercise. Insert within a helix connected with a 
 galvanometer a second helix in cir- 
 cuit with a battery (Fig. 168). Ob- 
 serve the effect of introducing or 
 removing suddenly this helix. Try 
 opening or closing the circuit without 
 moving the helix. Set up the appa- 
 ratus with a set of resistance coils in 
 the battery circuit. Ascertain the 
 effect of weakening or strengthening 
 the current by varying the resistance. 
 Reverse the direction of the battery 
 current and repeat the tests. Write 
 a law describing the direction of the 
 induced currents as compared with the 
 FIG. 168. battery current. 
 
 392. Exercise. Construct two large flat coils of in- 
 sulated copper wire No. 24. Place one of them in circuit 
 with a battery and some form of current breaker, as a tele- 
 graph key, and the other in circuit with a sensitive galvanom- 
 eter. Lay one of these coils on the other on the table, with 
 a sheet of cardboard between them. Read the galvanometer 
 on closing the circuit and also on opening it. Substitute a 
 
MAGNETISM AND ELECTRICITY. 
 
 231 
 
 sheet of india-rubber for the paper. Try a sheet of copper. 
 Try a sheet of zinc. Try a sheet of iron. Inference. 
 
 393. Exercise. Connect one pole of a battery with a 
 file, and draw across its rough surface the wire attached to the 
 other pole. Observe the intensity and the color of the sparks. 
 Repeat the experiment after introducing into the circuit a helix 
 of wire. Explain. Place an iron core in the helix, and re- 
 peat. Explain. 
 
 394. Exercise. Connect the secondary coil of a small 
 induction coil with a 
 
 galvanometer, and 
 the primary coil with 
 a battery (Fig. 169). 
 Read the galvanom- 
 eter on closing the 
 circuit and also on 
 opening it. Repeat 
 the observations af- 
 ter removing the iron FIG 16Q 
 core. Explain. 
 
 Remove the galvanometer, and test the differences in the 
 induced currents by the physiological effects experienced on 
 holding the wires in your hands. 
 
 The helices of Art. 391 may be used for the above experi- 
 ment. 
 
 395. Exercise. With a battery, a long coil of wire, a 
 sensitive galvanometer, and a telegraph key set up a circuit 
 as shown in Fig. 170. 
 
 On closing the circuit the needle is deflected by a part of the 
 
232 PRACTICAL PHYSICS. 
 
 current passing through the galvanometer. Now bring the 
 
 needle back to zero, and 
 place some impediment in 
 the way so it cannot move 
 in that direction, but is free 
 to swing in the opposite. 
 Break the current, and 
 account for the needle's 
 
 Fl^. 170. , 
 
 moving in the opposite 
 
 direction to that in which the battery current would cause it to 
 move. 
 
 396. Exercise. Connect one pole of the secondary coil 
 of an induction coil, giving a spark at least 2 cm. long, to 
 one surface of a Leyden jar, and the other pole to the other 
 surface. Observe the effect on the spark given by the coil. 
 
 397. Exercise. Around the edge of a wooden barrel- 
 hoop wind several layers of No. 24 insulated wire, fastening 
 the wire in place by tying it in several places with cords. 
 Leave the ends of the wire quite long, and connect them with 
 an astatic galvanometer of low resistance. Now hold the 
 coil in both hands in a plane at right angles to the direction 
 of the dipping-needle, and quickly rotate it through 180 
 around a horizontal axis lying east and west. Observe the 
 effect on the galvanometer. Try the effect of rotating the coil 
 in the opposite direction. Explain. 
 
 Ascertain if there is any induction when the axis of rotation 
 is horizontal and in the magnetic meridian. Try the axis par- 
 allel to the dipping-needle. 
 
 If such a hoop is mounted on an axis provided with a crank 
 for rapid rotation, the wires being connected to a commutator 
 on the axis, quite marked electrical effects are easily obtained. 
 
MAGNETISM AND ELECTRICITY. 
 
 233 
 
 XV. LUMINOUS EFFECTS. 
 
 398. Apparatus. Tin-Foil, Panes of Glass, Plates of Mica, 
 Aurora-Tube, Air-Pump, Glass Goblet, Geissler's Tubes, etc. 
 
 399. Exercise. Cut with a small punch a number of 
 circular pieces of tin-foil, and paste them on a pane of glass, a 
 
 FIG. 171. 
 
 fish-globe, a glass tube, or a Ley den jar without an outer coat- 
 ing, forming any desired pattern (Figs. 171, 172). The edges 
 of these disks should be about 1 mm. apart. Con- 
 nect the poles of an induction coil or of an electrical 
 machine witli the extremities of the design and pass 
 electric sparks through it, conducting the experiment 
 in a dark room. 
 
 400. Exercise. Paste on a plate of mica about 
 15 cm. by 10 cm., a piece of tin-foil 8 cm. by 5 cm. 
 Support it on a plate of glass with the mica surface 
 
 FlG - "2. 
 
234 
 
 PRACTICAL PHYSICS, 
 
 out, and bring the poles of an electrical machine or induction 
 coil within 1 cm. of the surface, the distance between them not 
 exceeding the length of the tin-foil. Set the machine in opera- 
 tion, darken the room, and observe the path of the spark across 
 the mica plate. 
 
 401. Exercise. Substitute for the mica plate of the last 
 experiment a plate of glass, covered with iron-filings, and hav- 
 ing a narrow strip of tin-foil pasted across the two ends beneath 
 the poles of the machine. To make the filings adhere, coat the 
 plate with mucilage, sift on evenly the filings, and set away to 
 dry. 
 
 402. Exercise. Exhaust the air from the Aurora- Tube 
 
 \ 9 
 
 FIG. 173. 
 
 FIG. 174. 
 
 (Figs. 173, 175), and connect the extremities to the poles of an 
 active electrical machine or induction coil. Study its appear- 
 
MAGNETISM AND ELECTRICITY. 235 
 
 ance in a darkened room. Note the effect of reversing the 
 current. 
 
 Substitute for the aurora-tube the apparatus shown in Fig. 
 174, where the mouth of a bell jar is closed with a Florence 
 flask, on which is pasted tin-foil, covering two-thirds of the 
 bulb. A brass chain hangs within the flask, touching the inner 
 surface. One pole of the electrical generator is connected to 
 the brass chain, and the other to the plate of the air-pump. 
 Observe the effect in a dark room, as the air is exhausted from 
 the bell-jar. 
 
 403. Exercise. Coat a glass goblet inside and outside with 
 tin-foil (Fig. 176) a little over half-way up, 
 
 and place it on the table of the air-pump, be- 
 neath a bell-jar provided with a brass sliding- 
 rod passing air-tight through the cork of the 
 jar. Over that part of the rod, within the jar, 
 secure a glass tube, adjusting the apparatus 
 so that the rod touches the bottom of the inner 
 surface of the goblet. Connect the rod and the 
 air-pump table to the poles of an active induc- 
 tion coil or Holtz machine, and then exhaust 
 the air. Conduct the experiment in a dark FlG - 176 - 
 room. 
 
 The best effects are given by a goblet made of uranium glass. 
 
 404. Exercise. Exhaust the air from the aurora- tube 
 (Fig. 175), introduce a gas, as oxygen, hydrogen, coal-gas, 
 etc. ; then exhaust once more, refill and again exhaust, repeat- 
 ing the operation for several times, in order that the tubes may 
 contain nearly pure gas. Now proceed as in Art. 402. 
 
 Dealers in physical apparatus furnish vacuum tubes, or Geiss- 
 ler's tubes, containing rarefied vapors of known substances for 
 
236 PRACTICAL PHYSICS. 
 
 the study of the effects of the electrical discharge on the resid- 
 ual gas. 
 
 XVI. THERMO-ELECTRICITY. 
 
 405. Apparatus. Strips of Zinc, German-Silver, Copper, 
 Bismuth, Antimony, etc., and a Short-Coil Astatic Galvanometer. 
 
 406. Exercise. Prepare two strips, one of zinc and the 
 other of German-silver, each 5 cm. long and 15 mm. wide. 
 Solder them together at one end, and to the free ends solder 
 wires, so as to place them in circuit with a sensitive galvanome- 
 ter. A short-coil galvanometer, having an astatic needle, is to 
 be preferred. Apply the flame of a burning match to the 
 junction of the two strips and observe the effect on the gal- 
 vanometer. Ascertain the effect of a piece of ice on the junc- 
 tion. 
 
 Try strips of copper and zinc ; copper and bismuth ; anti- 
 mony and bismuth. Compare the deflections given. 
 
 XVII. SECONDARY OR STORAGE BATTERIES. 
 
 407. Apparatus. Sheet-Lead, Red-Lead, Galvanometer, 
 etc. 
 
 408. Exercise. Cut out of sheet-lead two rectangular 
 strips, each 10 cm. by 12 cm., and tack them on opposite sides 
 of a strip of dry wood 2 cm. thick. Solder a wire to each strip, 
 then dip the plates into dilute sulphuric acid, and connect 
 them to the poles of a battery of sufficient E. M. F. to decom- 
 pose water. After a few minutes disconnect the plates from 
 the battery and join them to a galvanometer or small electric 
 motor. Inference. Ascertain whether the plates will exhibit 
 any electrical phenomena or not, if some little time is allowed 
 
MAGNETISM AND ELECTRICITY. 287 
 
 to elapse between disconnecting them from the battery and 
 testing them with the galvanometer. 
 
 409. Exercise. Cut out of thin sheet-lead a number of 
 plates, 10 cm. by 15 cm., having on one side an ear 2 cm. by 8 
 cm. (Fig. 177). Cut out of cotton flannel twice as many rec- 
 tangular pieces, 14 cm. by 20 cm. Make 
 a thick paste out of red-lead and sulphuric 
 acid, and apply it with a brush to both 
 sides of each lead plate, and also to the 
 nap-side of the flannel, to a depth of at 
 least 1 mm. Now build up a battery 
 as follows : Lay down a piece of flan- 
 nel, then one of lead, then flannel, then 
 blotting-paper of the size of the flannel, 
 ; then flannel, then a lead plate with the 
 
 ear on the reverse side of the last plate, 
 
 FIG. 177. 
 
 then flannel, and so on. Always place 
 
 the nap-side of the flannel next to the lead, and be careful to 
 have as many plates with the ear on one side as there are plates 
 with the ear on the other, consecutive plates having their ears 
 on opposite sides. When a sufficient number have been put in 
 place, bind them together with a cord, strips of thin board 
 being placed on the outsides. Wire together the ears forming 
 the two poles, and place the plates in a glass vessel containing 
 dilute sulphuric acid. To charge the battery, connect the poles 
 to those of a strong battery for an hour or so. On disconnect- 
 ing the poles and joining them to an electric motor even after 
 the lapse of several hours a rapid motion should be obtained. 
 
238 PRACTICAL PHYSICS. 
 
 CHAPTER VI 
 
 SOUND. 
 I. WAVE MOTION. 
 
 410. Apparatus. Balls, Whirling-Machine, Spiral of 
 Spring Wire, Cotton Rope, Rubber Tubing, Rectangular Trough, 
 Tin Tube, etc. 
 
 411. Exercise. Classify the following motions in two 
 ways, after studying them closely to ascertain their points of 
 resemblance and of difference. 
 
 1st. A ball suspended by a thread, and set in motion as a 
 pendulum . 
 
 2d. A heavy ball suspended by a spiral spring, made by 
 winding closely on an iron rod, 1 cm. in diameter, some spring 
 brass wire No. 18, and set in motion by pulling down the ball 
 and then releasing it. 
 
 3d. A heavy ball, suspended by a wire fastened to it, so as 
 not to turn on it as an axis, and set in motion by twisting the 
 wire. 
 
 4th. A paper disk clamped to the axis of the whirling- 
 machine, and put in motion by turning the drive-wheel. 
 
 5th. A weight with a cord attached, and put in motion by 
 drawing it along on the table. 
 
 6th. A wire stretched tight, with its ends secured by winding 
 them around the heads of two stout nails driven part way into 
 a board, and put in motion by pulling the middle of the wire a 
 little out of line and then releasing it. 
 
SOUND. 239 
 
 412. Exercise. Place a soft cotton rope, 5 m. or 6 m. 
 long, in a straight line on the floor, fastening one end to some 
 heavy object. Holding the other end of the rope in the hand, 
 set up vibrations in it by a quick movement of the hand up and 
 down. Ascertain the path traversed by a point of the rope. 
 Compare the motion of consecutive points. Draw figures in 
 your note-book showing the form of the rope at three succes- 
 sive points of time. Ascertain the effect of changing the time 
 in which the hand makes its up-and-down movement in starting 
 the vibration. Account for the curved form's advancing along 
 the rope. 
 
 413. Exercise. Fasten one end of the rope used in the last 
 experiment, or, what is better, a piece of rubber tubing, having 
 an outside diameter of 1.5 cm., to a hook in the ceiling of the 
 room, and the other end to a hook in the floor directly beneath 
 it. Adjust the rope so that it is under a slight tension. Strike 
 the rope with a short rod at one-fourth from the bottom, and 
 note the action of the pulse formed. Just as this pulse starts 
 to return from the ceiling start a second one, and observe the 
 effect attending its meeting the first one. Try striking the rope 
 one-sixth from the floor. Draw figures showing the form of the 
 rope at the moment the pulse was started ; on its arrival at the 
 ceiling ; on its starting to return ; and at the time the two pulses 
 meet. 
 
 414. Exercise. Fasten up two similar ropes or tubes as 
 in the last experiment, subjecting them to equal tensions. 
 Start pulses in them simultaneously, and of the same length, 
 and compare the rates at which they advance along the ropes. 
 Now increase the tension of one rope, and repeat the compari- 
 son. What force is developed by stretching the rope? Fasten 
 
240 PRACTICAL PHYSICS. 
 
 up a third rope, much heavier than the others ; a rubber tube 
 filled with sand will answer. Compare the movement of 
 pulses in this heavy one with similar pulses in the others. 
 Account for the difference. Increase the tension of the heavy 
 rope, and repeat. Derive from the observations made what 
 determines the speed of propagation of the pulse. 
 
 415. Exercise. Fill about two-thirds full of water a 
 rectangular trough, 1 m. long, 30 cm. deep, and 10 cm. wide, 
 having one side of glass. By suddenly depressing and elevat- 
 ing a large bottle in one end of the trough start a wave, and 
 record the movement of the water as it appears through the 
 glass side. Start other waves, and observe their behavior 
 toward one another. Ascertain if one wave can be started 
 so as to increase the amplitude of the one that preceded it. 
 Try to reduce the amplitude. Record the conditions you had 
 to observe in order to accomplish these results. 
 
 Float some small paraffine balls on the water, and record their 
 motion as the pulse travels along. In the advance of the 
 wave is there an advance of the water? Load some of the 
 paraffine balls with iron-filings, so that they will float at some 
 distance below the surface. Determine from the motions of the 
 balls the character of the motion of the water particles when a 
 wave traverses the trough. 
 
 416. Exercise. Construct a spiral spring, 3 m. long, by 
 winding closely on a rod, 1 cm. in diameter, a quantity of No. 
 18 spring brass wire. Fasten one end of this spiral to a hook 
 in the wall ; and, holding the other end in the hand, stretching 
 the spiral till it swings clear of the floor, send a pulse 
 through it by pressing a few of the coils of the wire close 
 together, and suddenly releasing them. Tie short pieces of 
 
SOUND. 241 
 
 string into several of the coils, and observe their movements as 
 the pulse advances. Describe the motion of the parts of the 
 spiral. Representing the successive coils by a series of short 
 parallel lines, show by a figure the change in relative position 
 of these lines in the neighborhood of a pulse. 
 
 417. Exercise. Place on a table a tin tube, 3 m. long 
 and 10 cm. in diameter, one end of which tapers to a diameter 
 of 2.5 cm. It is preferable to have the tube in parts, to be put 
 together like stove-pipe. Tie over the large end a paper mem- 
 brane, and in front of the small end place the flame of a lighted 
 candle. Observe the effect of slapping two books together in 
 front of the paper membrane. Account for the effect produced 
 on the flame. Why could it not have been due to a wind pro- 
 duced by the books? 
 
 II. SOURCES OF SOUND. 
 
 418. Apparatus. Bell, Tuning-Fork, Long Metal Rod, 
 Pane of Glass, Glass Rod, Tin Flageolet, Tin Whistle, Glass 
 Tube, etc. 
 
 419. Exercise. Strike a large bell or glass bell- jar 
 with a small mallet, made by inserting a stout wire in a large 
 cork. Suspend by a thread a small ball of pith or cork, so as 
 just to touch the edge of the bell. What do you find to be the 
 difference between a sounding bell and a silent one ? 
 
 420. Exercise. Insert two large screw-eyes in a board 
 at points distant one-half of a metre. Stretch between them a 
 piece of steel wire, about No. 20, securing tension by turning 
 the screws. Now draw a violin- bow across the wire, and 
 record any attending phenomenon. Ascertain the condition of 
 the wire by touching it with the edge of a card. Inference. 
 
242 PRACTICAL PHYSICS. 
 
 421. Exercise. Tap a tuning-fork against a block of 
 wood, and, while sounding, touch one prong to the surface of a 
 vessel of water. In what condition are the prongs of the 
 fork? 
 
 422. Exercise. Clamp, in a horizontal position, a metal 
 rod, 1 m. long and 1 cm. diameter, by its middle in a vise. 
 Suspend by a thread a small ball, ivory or glass, about 1 cm. in 
 diameter, so as to rest gently against one of the squared ends 
 of the rod. Rub the other end of the rod longitudinally with 
 soft leather, covered with powdered rosin. What does the 
 effect produced on the ball indicate regarding the condition of 
 the rod? 
 
 423. Exercise. Balance on a small cork a pane of 
 window-glass, about 25 cm. square, and sprinkle evenly over it 
 a little fine sand. Rest on the glass plate, in a vertical posi- 
 tion, over the centre of the cork, a stout glass tube 60 cm. 
 long. Hold this tube by the upper end in one hand, press it 
 firmly against the plate, and rub the lower part longitudinally 
 with a damp woollen cloth held between the thumb and the fore- 
 finger of the other hand. What phenomena attend the friction 
 of the cloth on the tube ? Are they connected? Inference. 
 
 424. Exercise. Connect to a faucet giving water under 
 considerable pressure a tin flageolet, by means of a rubber tube 
 slipped over its mouth, but not covering the embouchure. 
 It will be necessary to wrap the tube with wire to keep it from 
 slipping off. Place the flute in a tall vessel of some kind, and 
 turn on the water. By properly adjusting the water-supply a 
 low musical tone can be obtained on the flute's becoming 
 immersed in water. Touch the vessel with the hand while the 
 
SOUND. 
 
 243 
 
 FIG. 178. 
 
 flageolet is sounding, comparing the sensation with that experi- 
 enced when the flageolet is silent. Inference. 
 
 425. Exercise. Insert a short wooden or tin whistle in 
 one end of a glass tube about 30 cm. long and about 2.5 cm. 
 
 in diameter, closing the other 
 end with a cork (Fig. 178). 
 A suitable whistle may be ob- 
 tained at any toy store. Dis- 
 tribute within the tube a spoonful of fine cork-dust, obtained 
 
 by filing a cork. Hold the tube 
 
 in a horizontal position and 
 
 blow the whistle. Observe the 
 
 effect on the cork-dust. What 
 
 must be the condition of the 
 
 air within the tube when the 
 
 whistle is sounding? 
 
 Remove the whistle, place the 
 
 mouth to the end of the tube, and 
 
 sing a prolonged note of consid- 
 erable intensity. By trial a tone 
 
 can be found which will produce 
 
 the same effect as that given by 
 
 the whistle. 
 
 426. Exercise. -- Draw 
 
 out a glass tube to a jet (see 
 page 356). Connect it by rub- 
 ber tubing to the gas-supply, 
 support it vertically in a clamp, 
 light the gas escaping from the 
 jet, and reduce the flame to the 
 height of about 2 cm. Clamp FIG. 179. 
 
244 PRACTICAL PHYSICS. 
 
 over the jet a glass tube with thin walls, about 40 cm. long and 
 2 cm. in diameter (Fig. 179). Change the position of the jet 
 within the tube till a musical note is emitted by the tube. 
 Compare the flame within the tube when sounding with the 
 flame when the tube is silent. Grasp the lower end of the tube 
 with the hand, and compare the sensations produced by the 
 sounding tube with those produced by the silent one. Oscil- 
 late a small mirror back of the flame, and compare the image 
 of the flame when the tube is silent with that given when the 
 tube is sounding. Explain. 
 
 III. TRANSMISSION OF SOUND. 
 
 427. Apparatus. Air-Pump, Alarm-Clock, Watch, Rub- 
 ber Tubing, Tuning-Fork, Bar of Iron, etc. 
 
 428. Exercise. Place under the receiver of an air-pump 
 a small alarm-clock, separated from the plate by a bed of 
 cotton-wool. Compare the distinctness with which the sound 
 of the alarm-bell is heard before and after exhausting the air. 
 Repeat the experiment, omitting the cotton-wool. Inference. 
 
 429. Exercise. Place a loud-ticking watch on one end 
 of a long strip of lath, and hold the other end to your ear. 
 
 Compare the distinctness 
 with which you hear the 
 sound with that when the 
 ear is away from the lath. 
 Ascertain the effect of 
 wrapping up the watch in 
 a cloth, and then laying it 
 F on the lath. Inference. 
 
 430. Exercise. Connect two rooms by a wire or string 
 
SOUND, 245 
 
 stretched between them (Fig. 180). Support the wire, 
 wherever needed, by passing it through a loop made of cord. 
 The wire must not touch any objects, nor turn any sharp 
 corners. Connect each end to the bottom of a collar-box or tin 
 cylindrical can, by passing it through a small hole, and fasten- 
 ing it into a button. Let an assistant talk near the open end of 
 one box, while you listen at the other. Explain. 
 
 431. Exercise. Fill a piece of rubber tubing, say 2 m. 
 long and 2 cm. in diameter, with water, supporting the two 
 ends so that the tube hangs in a curve. Set a tuning-fork in 
 vibration, and compare the distinctness with which you hear the 
 sound, as an assistant holds the stem in the water of the tube 
 at one end, while your ear is as close as possible to the other 
 end, with that when the tube contains only air. Inference. 
 
 432. Exercise. Suspend a small bar of iron or steel by 
 two strings, each 1.5 m. long. Take one string in each hand, 
 and, stooping over, press the ends into the ears. Now let an 
 assistant strike the swinging bar with a block of wood. Com- 
 pare the distinctness of the sound heard through strings of cot- 
 ton, linen, metal, etc. Inference. 
 
 IV. VELOCITY OF SOUND. 
 
 433. Apparatus. Tuning-Fork, Cylindrical Jar, Glass 
 Tube, Rods of Glass and of Wood, etc. 
 
 434. Exercise. Hold a vibrating tuning-fork, whose rate 
 is known,* over the mouth of a cylindrical jar, about 35 cm. 
 high and 5 cm. in diameter, and pour in water slowly, till 
 a point is reached where the sound is greatly strengthened. 
 
 * A fork whose rate is from 250 to 300 will be found to give the best results. If a 
 fork of higher pitch is used, then select a cylindrical jar of less diameter than 5 cm. 
 
246 PRACTICAL PHYSICS. 
 
 Ascertain, by repeated trials, the air-column giving the loudest 
 resonance, and then determine its length. To the length of the 
 air-column add two-fifths of the diameter of the cylinder, then 
 four times this sum will be the wave-length for this fork. Mul- 
 tiply this by the vibration-number of the fork, and the product 
 will be the velocity of sound in air, at the temperature of that 
 within the cylinder. Why ? 
 
 Ascertain the effect that lowering the temperature has upon 
 the velocity of sound, by packing the jar in melting ice, and 
 determining the air-column required for the best resonance, and 
 hence the velocity of sound in this cooled air. Record the 
 temperature of the air. 
 
 A form for keeping the record is given below. 
 
 Length of resonating jar at 
 
 Temperature of room C., Tern, of jar in ice C. 
 
 First observation . . . .cm. cm. 
 
 Second " .cm. cm. 
 
 Third " cm cm. 
 
 etc. etc. etc. 
 
 Mean cm. cm. 
 
 Wave length cm. cm. 
 
 Velocity of sound . . . cm. cm. 
 
 Change in velocity for 1C cm. 
 
 Vibration-number of tuning-fork used 
 
 435 Exercise. Determine the velocity of sound in 
 carbonic acid gas. 
 
 As in the last experiment, obtain the air-column giving the 
 loudest reinforcement of the tone of a tuning-fork whose vibra- 
 tion number is known. Now fill the jar with carbonic acid, 
 and then add water till the reinforcement is the greatest. 
 Proceed as in the last experiment. 
 
 Compare the ratio of the velocity of sound in carbonic acid 
 
SOUND. 247 
 
 gas and in air with that of the densities of these substances, and 
 determine how the density of the medium affects the velocity of 
 sound. Tabulate results as in the last experiment. The mo- 
 ment when the cylinder is full of gas can be determined by 
 inserting a burning match ; the flame will be extinguished on 
 reaching the gas. 
 
 For method of preparing carbonic acid gas, consult Shepard's 
 Chemistry, Exp. 102. 
 
 436. Exercise. Determine the velocity of sound in 
 hydrogen or coal gas. 
 
 Close gas-tight one end of a glass tube 1 m. long and 4 cm. 
 wide. Fit a cork into the other end, to slide with slight friction, 
 using a long stout wire for a piston-rod. Mount the tube in a 
 vertical position, mouth downward, with the piston pushed up 
 to the closed end. Now fill the tube with hydrogen (see Art. 
 102), by displacement ; and then by moving the piston deter- 
 mine by trial the position where the loudest resonance is 
 obtained for a vibrating tuning-fork of known rate. Then 
 proceed as in Art. 434. What does this experiment show is the 
 effect of density on the velocity of sound ? 
 
 437. Exercise. Determine the ratio of the velocity of 
 sound in a rod of glass, wood, or metal to that in air. 
 
 Close one end of a glass tube 1 m. long and 4 cm. wide with 
 
 a cork, A (Fig. 181). To a rod 1.5 m. long of the material in 
 which the velocity of 
 
 sound is to be deter- /-* c B 
 
 mined, as EB, glue a E =y^-J^. j| 
 
 thin cork piston, B, of f ^/ A b 
 
 such a size as to slide ^ ^ ^ 
 
 r IG* lol* 
 
 freely within the tube 
 
248 PEACTICAL PHY SIC ft. 
 
 AC. By means of an iron clamp fasten the rod at its middle 
 to the table, between two pieces of wood, having the shape 
 shown at F ; the thickness being such that the rod is in the axis 
 of the glass tube AC as it rests on the table ; the hole through 
 these pieces being just large enough to hold the tube without 
 crushing. As AC is free either to move toward D or away 
 from it, the space AB can be lengthened or shortened at pleas- 
 ure. Distribute a little cork or silica powder evenly between 
 A and B. Now excite longitudinal vibrations in BE by gently 
 stroking it toward E with a damp cloth, if the rod is glass, 
 or with soft leather covered with powdered rosin, if it is 
 wood or metal, being careful not to spring the rod out of line 
 for fear of breaking it. These vibrations will be communi- 
 cated by the piston B to the air between A and B, and 
 disturb the powder. By moving AC, a position for B can be 
 readily found at which the agitation of the powder is greatest, 
 being thrown into clearly marked heaps of uniform length sub- 
 divided into parallel ridges. Find the average length of these 
 dust heaps, a&, by dividing the distance between A and B by 
 the number of heaps. Representing this length by s, 2 s will 
 be the length of the air- wave. If the length of the rod is cf, 
 since it is clamped at the centre, then 2 d is the wave-length of 
 the vibration produced in it. Hence d-^-s represents the number 
 of times that sound travels faster in the rod than in air at the 
 temperature of the room. Represent by V the velocity of 
 sound at the temperature of the room, t. Then V = 333 
 
 (1 + .0037 t) *, and the velocity of sound in the rod = V. 
 
SOUND. 
 
 249 
 
 V. PROPAGATION OF SOUND. 
 
 438. Apparatus. Cardboard, "Whirling-Machine, etc. 
 
 439. Exercise. Cut out of stiff cardboard a disk hav- 
 ing a diameter of 30 cm. Concentric with the circumference of 
 the disk draw a cir- 
 cle with a radius of 
 
 2.5 mm. Divide the 
 circumference of this 
 small circle into 
 twelve equal parts 
 (Fig. 182), number- 
 ing them 1, 2, 3, etc. 
 With the point 1 as 
 a centre, and with 
 a radius of 7 cm., 
 draw a circle. With 
 2 as a centre, and 
 with a radius of 7.3 
 cm., draw a second FlG - 182 - 
 
 one. With 3 as a centre, and with a radius of 7.6 cm., draw 
 a third one. Continue in this way, increasing the radius each 
 time by 3 mm., till each point has been used twice as a centre. 
 The lines should be drawn with jet-black ink, and should be 
 J mm. in width. Clamp this disk on the spindle of the whirl- 
 ing-machine, and hold in front of it, and as close as possible, 
 a strip of cardboard in which is cut a slit 3 mm. wide and 10 
 cm. long. In this opening will now be seen parts of these 
 circles appearing as black dots unevenly distributed. Now 
 rotate the disk slowly, and waves of condensation, followed 
 by waves of rarefaction, will appear to move along the slit. 
 
250 PRACTICAL PHYSICS. 
 
 Watch closely one dot, and from its motion account for the 
 effects produced. If these dots represent the air-particles 
 along the radius of a series of sound waves set up in air, then 
 in their motion you have a representation of the movements of 
 the air-particles in the propagation of sound waves. 
 
 VI. REFLECTION OF SOUND. 
 
 440. Apparatus. Cardboard, Whirling-Machine, Watch, 
 Concave Reflector, Tin Tubes, etc. 
 
 441. Exercise. Cut out of cardboard a disk having a 
 diameter of 30 cm. Out of opposite sides of the disk (Fig. 
 
 183) cut two sectors of 
 about ten degrees. Clamp 
 the disk to the spindle of a 
 whirling-machine, and as the 
 disk is made to revolve, blow 
 a whistle or toy trumpet in 
 front of it, and close to it. 
 Compare the sound with that 
 when the disk is at rest. 
 When is the sound loudest? 
 When lowest? Explain. 
 
 FIG. 183. 
 
 442. Exercise. Suspend a loud-ticking watch at the 
 focus of a large concave reflector, such as is used behind wall 
 lamps. About two metres from this place a second reflector, 
 parallel to the first, and with its concave surface toward the 
 watch. At its focus support a small funnel, with its mouth 
 toward the reflector, and a rubber tube leading from its stem to 
 your ear. Compare the distinctness with which you hear the 
 
SOUND. 251 
 
 ticking of the watch with that when the reflectors are removed. 
 Explain. 
 
 The focus of the reflector can be found by letting sunlight 
 fall upon it, and marking the point in front of it at which it will 
 set fire to a match. 
 
 By suspending the watch a few centimetres farther away 
 from the reflector than the focus, a point can be found by trial, 
 still farther removed from the reflector, at which the watch can 
 be heard with much greater distinctness than at any intervening 
 or more distant points. 
 
 443, Exercise. Determine the law of reflection of sound. 
 Lay on a table two tin tubes, each 1.5 m. long and 10 cm. wide, 
 
 FIG. 184. 
 
 forming a V (Fig. 184). Suspend a loud-ticking watch in the 
 outer end of one of the tubes, and listen for the sound at the 
 outer end of the second tube. On a sheet of cardboard draw a 
 semicircular protractor of at least 30 cm. radius, dividing it 
 into 10 sectors. Let these tubes rest on radial lines, on oppo- 
 site sides of the zero, so that the angle each tube makes with 
 the zero radius can be read off on the scale. Across the other 
 ends of the tubes, and perpendicular to the zero radius, hold a 
 piece of cardboard. Move the tube to which the ear is ap- 
 
252 
 
 PRACTICAL PHYSICS. 
 
 plied to a position where the ticking of the watch is most dis- 
 tinct. Compare the angles between the zero radius and the 
 tubes. Make several trials for different positions of the tubes. 
 Tabulate the results. Inference. 
 
 VII. REFRACTION OF SOUND. 
 
 444. Apparatus. Rubber Balloon, Watch, etc. 
 
 445, Exercise. Fill a small rubber toy balloon with car- 
 bonic acid by tying it over the delivery-tube of a carbonic acid 
 generator. Suspend a loud-ticking watch from a suitable sup- 
 
 FIG. 185. 
 
 port, and move as far away as possible and still hear the watch 
 when one ear is turned toward it. Now hold the balloon close 
 to the ear, and ascertain if the loudness of the sound is 
 affected. Explain. 
 
 Fig. 185 illustrates another method of conducting this experi- 
 ment. The ear is placed at/. 
 
 446. Exercise. Fill a balloon with hydrogen gas, and 
 proceed -as in the last experiment. Explain. Try a balloon 
 filled with air. Is the effect the same-? 
 
SOUND. 253 
 
 VIII. LOUDNESS OF SOUND. 
 
 447. Apparatus. Tuning-Fork, Sonometer, Bell, Air- 
 Pump, Tin Tube, Steel Rod, Glass Tubes, Fruit- Jar, etc. 
 
 448. Exercise. Compare the vibratory movement of a 
 feebly sounding tuning-fork with that of a loud sounding one, 
 by means of the effects seen on touching one prong to the sur- 
 face of water. What is here shown to be the cause of the 
 difference in loudness? 
 
 449. Exercise. Compare the vibratory movement of a 
 feebly sounding string on a violin or sonometer with that of the 
 same string when loudly sounding, by suspending in contact with 
 it a small paraffine ball. Account for the difference in loud- 
 ness. 
 
 450. Exercise. Ascertain if the loudness of sound is 
 affected by the density of the medium enveloping the vibrat- 
 ing body. 
 
 1st. Observe the change in the sound emitted by a small bell 
 under a bell- jar of an air-pump, as the rarefaction 
 is increased. Inference. 
 
 The bell should stand on a bed of cotton- wool. 
 Why? The bell-jar should be provided with a 
 sliding-rod for ringing the bell (Fig. 186). 
 
 2d. Fill a large bell-jar with hydrogen, by dis- 
 placement over water. With one hand lift the jar 
 vertically upward, and with the other ring a small 
 bell within it. Compare the sound with that when 
 the jar is full of air. Inference. 
 
 Invert the jar, fill it with carbonic acid gas, and repeat the 
 test. Inference. 
 
254 PRACTICAL PHYSICS. 
 
 451. Exercise. Lay on a table the tin tube of Art. 417. 
 Hang a watch in the opening at the large end, place your ear 
 at the other end, and compare the loudness of the ticking with 
 that when the tube is removed. Explain the action of the tube. 
 
 452. Exercise. Set a timing-fork in vibration, and com- 
 pare the sound, when held in the hand, with that when its stem 
 is held firmly in contact with the bottom of an empty chalk- 
 box. Ascertain what is the condition of the box when the 
 sounding fork is in contact with it, by noticing the effect on a 
 little fine sand sprinkled over it. To what is the increased 
 loudness due? 
 
 Find out whether the fork vibrates as long when its stem 
 rests against the box as when held in the hand. In making 
 this comparison, blows of equal intensity must be given to the 
 fork. A simple method of doing this would be to let a wooden 
 ball swing against the prong, falling in each case from the 
 same height. 
 
 If you have two forks of the same pitch, remove them from 
 the sounding-boxes, placing the boxes on the table in front of 
 you. To give both forks the same impulse, cut out of a board 
 about 6 or 8 mm. in thickness a piece of the shape shown 
 in Fig. 187, the width of each of the prongs, 
 A. A, being somewhat greater than the 
 normal distance between the prongs of the 
 tuning-fork. Slip the latter on obliquely, 
 and straighten up at right angles to the plane 
 of the board, with the surface of the latter 
 even with the surface of the ends of the 
 prongs. Arrange the other fork in the same 
 manner, with respect to the other prong of the 
 board. Now let an assistant hold the handle 
 of the board and strike it a sharp blow with 
 
SOUND. 255 
 
 a hammer, at a point near the forks, while you hold the latter, 
 one in each hand, prongs downward. Both forks will then be 
 put in vibration with nearly the same amplitude. Place one 
 on its sounding-box immediately, holding the other in the hand. 
 As soon as the sound of the one on the box ceases to be heard, 
 place the one held in the hand on its box. Repeat the experi- 
 ment, reversing the positions of the forks, to determine if the 
 difference is due to the forks. Why does the energy of one 
 fork hold out longer than the other ? 
 
 453. Exercise. Compare the loudness of the sound 
 emitted by a vibrating steel rod, clamped by one end in a vise, 
 with that produced by a steel bar of the same length and 
 thickness, but having considerable width. Account for the 
 difference. Compare the duration of the sounds. Why is 
 there a difference ? 
 
 Why is a tuning-fork usually made with two branches? 
 
 454. Exercise. Procure four glass tubes, each about 
 30 cm. long, having different diameters, as 1.5, 2.5, 3.5, and 
 4.5 cm., respectively. Clamp each one successively in a verti- 
 cal position, with one end dipping into a vessel of water. Hold 
 over the open end a sounding tuning-fork, raising or lowering 
 the tube till a position is reached where the sound bursts out 
 with maximum loudness. Measure the air-column in each 
 case, compare it with that given by computation for the fork 
 employed, and deduce the correction to be made for the diame- 
 ter. Tabulate the results. 
 
 455. Exercise. Paste a piece of paper over the mouth of 
 an empty glass fruit- jar. Cut away the paper cover, little by 
 little, the part removed having the form of a segment, till a 
 
256 PRACTICAL PHYSICS. 
 
 loud resonance is obtained on holding a vibrating tuning-fork 
 close to the opening. Ascertain the cause of the resonance by 
 sprinkling a little fine sand over the paper, and watching it as 
 the sounding-fork approaches the opening. 
 
 456. Exercise. Compute the length of the air-column 2 
 cm. in diameter that will reenforce a fork, say C ', at the tempera- 
 ture of the room. Then cut eight glass tubes of this length and 
 diameter (see page 354) , grinding the ends smooth on a piece of 
 sandstone wet with spirits of turpentine. Cut a number of 
 paper disks, of the same diameter as the outside of these tubes, 
 and also a number of rubber connectors. Now it is evident 
 that a tube whose length is any multiple of the first can be pre- 
 pared by joining these together with the rubber connectors, and 
 that by cementing a paper disk over the end of a tube an open 
 one can be changed into one closed at one end. 
 
 Prepare open tubes whose lengths are respectively 2, 3, 4, 
 etc., times the length of the first, and determine by trial which 
 reenforces the sound of the fork used in preparing the tubes. 
 
 Prepare and test closed tubes in the same way. 
 
 If we represent by one the length of the shortest open tube 
 which reenforces the sound, what will be the lengths of the 
 different open tubes found to reenforce it? 
 
 Prepare a similar series for closed tubes. 
 
 IX. INTERFERENCE OF SOUND. 
 
 457. Exercise. Tuning-Fork, Sonometer, T-tubes, Rub- 
 ber Tubing, Glass Tubing, etc. 
 
 458. Exercise. Hold a vibrating tuning-fork near the 
 ear, and as you rotate it slowly about the axis of the stem, 
 
SOUND. 257 
 
 mark the positions where the sound is feeblest, and also those 
 where loudest. Now hold the same fork over a cylindrical jar, 
 serving as a resonator ; find by trial the position in which the 
 sound is feeblest ; then cut off the waves sent out by one prong, 
 by sliding over it a paper cylinder, without touching it, and ob- 
 serve the effect. Explain the varying loudness of the sound as 
 the fork rotates about the axis of the stem. 
 
 459. Exercise. Mount on resonant boxes two large 
 tuning-forks of the same pitch (Fig. 188). Stick a piece of seal- 
 ing-wax, the size of a hickory nut, on the end of 
 one branch of one of the forks. Set the forks 
 in vibration, and compare the sound with that 
 emitted by them before they were loaded. 
 Ascertain the effect of using a lighter or 
 heavier load. Explain. 
 
 A resonant box is a rectangular 
 box of pine, open at one end. Its 
 length is one-fourth of a wave-length 
 of the fork, less about two-fifths of 
 the diagonal of the end of the box. 
 
 460. Exercise. Tune two strings on the sonometer to 
 the same pitch, and then compare the sound emitted by them 
 when plucked simultaneously with that when the tension of 
 one string has been slightly changed. 
 
 461. Exercise. Connect two large T-tubes with rubber 
 tubing, as shown in Fig. 189. Join a funnel to the stem of one 
 of them, and a piece of rubber tubing to the other. Hold a 
 vibrating tuning-fork at A. Now it is evident that the waves 
 divide at B, part traversing each branch, and unite again at K, 
 
258 
 
 PRACTICAL PHYSICS. 
 
 reaching the ear through H. If the tube CDE is half a wave- 
 length longer than F, the waves will meet in opposite phases at 
 K, and no sound at H will be heard. Similar effects will fol- 
 low if the difference is f , f , f , etc., of a wave-length. If CDP] 
 is a wave-length or some multiple of a wave-length longer, no 
 diminution of intensity will be noticed. Any differences in 
 length other than these will result in partial interference. 
 
 FIG. 189. 
 
 Friction of the waves on the walls of the tubing will produce 
 slight deviations from the above results, and the sound may not 
 be completely extinguished owing to the conductivity of the 
 material. 
 
 462. Exercise. Set up two singing flames (see Art. 426) , 
 employing tubes of the same length and diameter. Make a 
 paper cylinder to slide with a little friction over the end of one 
 of the tubes so that its length may be increased if desired. 
 Adjust the lengths of the tubes by moving the paper cylinder 
 till the tones are alike ; then note the effect of changing the 
 position of the paper cylinder. 
 
 X. SYMPATHETIC VIBRATIONS. 
 
 463. Apparatus. Pendulums, Bar Magnets, Tuning- 
 Forks, Glass Tubing, Sonometer, etc. 
 
 464. Exercise. Suspend a heavy weight by a wire or 
 string 1 m. long, and find the time of vibration. Now try to 
 
SOUND. 259 
 
 put this pendulum in vibration by puffs of air directed against 
 the centre of the weight, and timed in unison with the pendu- 
 lum. Try puffs of air irregularly timed. Try puffs of air 
 whose period is some multiple of that of the pendulum. 
 
 Arrange a second pendulum to swing in the same time as the 
 first. Connect the bobs of the two pendulums by a string, 
 which is drawn straight when the pendulums hang vertically. 
 Now set one of the pendulums in vibration, in the plane of the 
 two, and note the effect on the second one. Shorten one of the 
 pendulums by lowering the suspension-point, keeping the bobs 
 in the same horizontal line, and ascertain if the effect is the 
 same as before. Substitute a stiff, very light bar for the string 
 between the bobs, and observe the effect on the time of vibra- 
 tion. 
 
 465. Exercise. Suspend two pendulums, each one metre 
 long, from a horizontal bar ; a third, one-fourth of a metre 
 long ; a fourth, one-half of a metre long ; a fifth, 90 cm. long. 
 Set one of the first two in vibration, and observe the effect on 
 the others. Explain. 
 
 466. Exercise. Construct two pendulums, using bar 
 magnets for bobs. Suspend each magnet by two threads, 
 each 50 cm. long, so that it hangs horizontally. Place the 
 magnets parallel, unlike poles adjacent and several centi- 
 metres apart. Now set one pendulum in vibration in a plane 
 perpendicular to the other magnet, and study the motions for 
 some time. Explain. Shorten one of the pendulums, by low- 
 ering its supporting-point, without changing the position of the 
 magnet, and ascertain if the effects are the same as before. 
 
 467. Exercise. Place near each other on the table the 
 tuning-forks of Art. 459. Set one of them in vibration, and 
 
260 PRACTICAL PHYSICS. 
 
 after waiting a few minutes stop it and listen near the other one 
 to ascertain whether it is motionless or not. Would the effect 
 be the same if one of the forks were surrounded witli a paper 
 cylinder ? What would be the effect of changing the pitch of 
 one fork by sticking a piece of sealing-wax to one of its prongs ? 
 AVhy? 
 
 468. Exercise. Tune in unison two strings on a sonome- 
 ter (Fig. 192), or a violin. Set one string in vibration ; then 
 after a few moments dampen it with the hand, and ascertain if 
 the second one is silent. Shorten one string by moving the 
 bridge under it and repeat the experiment. Explain. 
 
 469. Exercise. Prepare a singing-flame as in Art. 426. 
 Now shift the position of the jet within the tube by lowering it 
 just enough to stop its singing, and then sound near it the same 
 note as was emitted by the tube at first. Can you account for 
 the effect on the flame? Will singing a higher or lower tone 
 work as well ? Try it. 
 
 470. Exercise. Prepare a jet-tube by holding one end of 
 a piece of glass tubing in a gas- flame till the opening has been 
 reduced to about 1 mm. wide. Connect this by a rubber tube 
 to the gr.s- supply, and regulate the flow till a flame some 30 cm. 
 or more in length is obtained, and just on the point of flaring. 
 Now blow a shrill whistle, rattle a bunch of keys, or hiss, and 
 the long flame will be shortened nearly half, and rustle loudly. 
 Turn your back toward the flame and repeat the sounds. 
 Repeat the experiment, standing in a distant part of the room. 
 Explain. 
 
 If the gas- pressure is not sufficient to give a flame of the 
 character described, fill a large rubber bag with gas, connect 
 
SOUND. 
 
 261 
 
 the jet-tube to it, and apply pressure to the bag by means of a 
 heavy weight. 
 
 XI. PITCH OF SOUND. 
 
 471. Apparatus. Siren, Cylindrical Jar, Tuning-Forks, etc. 
 
 472. Exercise. Measure the number of vibrations made 
 in a second by a vibrating body. 
 
 First Method. Cut out of cardboard a disk 25 cm. in di- 
 ameter. Draw on it four concentric circumferences, having the 
 diameters 23, 21.5, 20, and 
 18:5 cm. respectively (Fig. 
 190). Divide these circum- 
 ferences into 48, 36, 30, and 
 24 equal parts respectively. At 
 these points of division, with a 
 sharp, hollow punch, having a 
 diameter of about 1 cm., cut 
 round holes. Mount this disk 
 on the spindle of a whirling- 
 machine, or on the armature- 
 shaft of a small electric motor, 
 and you have a form of Siren. 
 
 If, with a rubber tube, you direct a steady stream of air 
 against one of these rows of holes as the disk rotates rapidly, 
 a musical note is produced by the air-puffs passing through 
 them. Find what the pitch of the tone depends upon. 
 
 Now give the disk such a speed that the tone emitted by 
 blowing steadily against one of the circular rows of holes is in 
 unison with that produced by the body in question. Count 
 the number of revolutions made by the drive-wheel in, say, 20 
 seconds, the speed being kept constant. Find the relative 
 size of the drive-wheel and the spindle -pulley, and from the 
 
 FIG. 190. 
 
262 
 
 PRACTICAL PHYSICS. 
 
 data compute the number of revolutions made by the disk 
 in a second. This multiplied by the number of holes in the 
 
 circle will give the vibration-number 
 sought. 
 
 The speed of the armature of the 
 electric motor may be determined by 
 clamping in contact with it a speed- 
 indicator, such as machinists use in 
 ascertaining the speed of shafting. 
 
 In Fig. 191 is shown a form of 
 siren with a counter. The perforated 
 disk is given a horizontal position, 
 and made to rotate by the stream of 
 air forced through the obliquely cut 
 openings by means of a bellows. 
 
 Second Method. Compute the 
 velocity of sound in metres by the 
 formula v = 333 (1 + .0037 )* in 
 which t is the temperature of the room 
 in centigrade degrees. Now find by 
 trial the length of the shortest air- 
 column giving the loudest resonance when the sounding body 
 is held over it, correcting it for the diameter of the tube. 
 
 Then n = ~ in which I is the wave-length as given by the 
 air-column. 
 
 473. Exercise. Determine the difference of rate of vibra- 
 tion of two sounding bodies, not quite in unison, by counting the 
 number of beats produced during some convenient unit of time, 
 as 30 seconds, and then computing the number per second. 
 
SOUND. 263 
 
 XII. T.AWS OF VIBRATING RODS AND STRINGS. 
 
 474. Apparatus. "Wooden Rod, Sonometer, Siren, Tuning- 
 Forks, etc. 
 
 475. Exercise. Determine the laws governing vibrating 
 rods. 
 
 Take a pine strip 2 m. long, 3 cm. wide, and 6 mm. thick, a 
 second one of the same length and width, but 12mm. thick, and 
 a third one of the same length and thickness, but 6 cm. wide. 
 Clamp these at one end over the edge of a table with small iron 
 clamps, set each in vibration, in succession, and count the number 
 of vibrations made in some convenient period of time. What 
 effect does width and thickness have on the vibration-rate? 
 Now clamp the first one at the middle so that one-half of it is 
 free to vibrate, and determine its rate. What effect does length 
 have on the vibration-rate ? 
 
 Express as laws the results of these experiments. 
 
 476. Exercise. Determine the laws governing vibrating 
 strings. 
 
 A Sonometer (Fig. 192) and a Siren (Fig. 190) will be re- 
 quired for this experiment. The former is a wooden box about 
 150 cm. long, 15 cm. wide, and 10 cm. deep. The material is 
 pine, free from pitch, straight-grained, and about 1 cm. thick, 
 except the top, which may be 5 mm. thick ; the ends should be of 
 hard wood, and have a thickness of about 25 mm. Near the ends 
 glue triangular pieces of hard wood, to serve as bridges across 
 which to stretch the wires. The depth of these bridges should 
 be about 2 cm., and the distance between them 120 cm. ID 
 one of the head pieces insert two stout pins, and in the other 
 two screws, such as are used in pianos, for changing the 
 
264 PRACTICAL PHYSICS. 
 
 tension of the wires. In the same end screw a small iron 
 pulley so that one wire may be drawn over it and the tension 
 measured by weights, or by a spring balance. Suitable weights 
 are easily made out of sheet-lead, riveting a number of thick- 
 nesses together till the required thickness is obtained. A sliding 
 weight, on a lever, having its fulcrum at the end of the box, 
 might be substituted for the pulley and weights. Beneath one 
 of the wires graduate a scale to half -centimetres. 
 
 Now stretch a piano-wire or a catgut string on the sonometer, 
 and produce with the siren, using the inner row of holes, a 
 tone in unison with that given by this string. Without -chang- 
 
 FlG. 192. 
 
 ing the speed of the siren-disk compare the tone produced on 
 using the outer circle of holes with that given by the string 
 when its length is reduced one-half by means of a movable 
 bridge placed beneath the middle of the wire. Also compare the 
 tone given by the next to the outer row of holes with that given 
 by the string when its length is but two-thirds of the whole. 
 Also, compare the tone given by the next to the inner row of 
 holes with that given by the string when its length is imulr 
 four-fifths of the whole. How do these siren-tones compare in 
 vibration-rate? What law must then connect pitch and length 
 of string ? 
 
SOUND, 265 
 
 Stretch two piano-wires or catgut strings of the same diam- 
 eter on the sonometer, one of them in such a way that the ten- 
 sion can be measured. Adjust the tension till the strings 
 sound in unison ; there will then be no audible beats. Now, 
 increase the tension of one of the wires till it is in unison with 
 the other one, reduced in length one-half by means of the 
 movable bridge. How have you affected the vibration- rate in 
 reducing the length one-half ? What effect must tension have 
 on the rate? 
 
 Stretch two wires or strings on the sonometer, the ratio of 
 their weights being 1 : 4. Steel wires No. 27 and 21 B. W. G., 
 or No. 24 and 19, will very nearly fulfil this condition (see 
 Appendix C). Note the tension on the heavy string when its 
 tone is of the same pitch as given by the lighter one. Without 
 changing the tension in either case substitute for the heavy one 
 a wire exactly like the small one. Place a bridge under the 
 first wire at a point where it will cause it to vibrate in unison 
 with the second one. What must have been the difference of 
 pitch of the first two wires ? What effect must weight have on 
 pitch ? 
 
 Stretch with equal tensions a steel and a brass wire of the 
 same gauge-number. Compare the pitch of the sounds. By 
 means of the movable bridge determine the difference in pitch, 
 and hence the ratio of the densities of the two substances. 
 
 What three laws for vibrating strings do you derive from the 
 above experiments ? 
 
 477. Exercise. Set a large tuning-fork firmly in a block 
 of wood, and clamp it to the table. Tie a metre of tine thread 
 to the end of one of its prongs, pass this thread through a 
 small ring held in a clamp, and to the free end attach a small 
 paper tray of known weight. The thread and the prongs of 
 
266 PRACTICAL PHYSICS. 
 
 the fork must lie in the same plane and the thread should 
 have a horizontal position. Now put known weights into 
 the tray till such a tension is secured that, on setting the 
 fork in vibration, the thread will also be thrown into vibration, 
 swinging in one segment. Without changing the length of the 
 thread make the tension one-fourth of what it was at first, 
 and record the number of segments in which the thread vibrates. 
 Try a tension one-ninth of the first. What relation is shown 
 by these results to exist between tension and vibration-rate of 
 strings ? 
 
 Ascertain the effect on the length of string required, of 
 lowering the pitch of the fork, by sticking a heavy coin to the 
 free end of one of its prongs. What law is here suggested in 
 regard to the relation existing between the vibration-rate and 
 the length of the string? 
 
 Substitute for the single thread, one, a third of which is four 
 of these threads twisted together, and the remaining part is 
 single. Change the tension till the string divides into two 
 segments, and observe their relative lengths. What effect does 
 the weight of the string have on the vibration-rate ? 
 
 A heavy wire stretched on the sonometer may be substituted 
 for the fork. The thread is attached to the centre of the wire 
 and stretched at right angles to the wire. The sonometer wire 
 is set in vibration with a violoncello-bow. 
 
 XIII, OVERTONES. 
 
 478. Apparatus. Sonometer, C'-Fork, etc. 
 
 479. Exercise. Tune one of the sonometer strings till it 
 vibrates in unison with a C'-fork. Place the movable bridge at 
 the middle of the scale, that is, at 60, if the scale is 120 cm. 
 
SOUND. 267 
 
 long. The string will now give as its fundamental the first 
 overtone of C'. Place the bridge successively at 40, 30, 24, 
 20, 17^, 15, 13, and 12. The shorter part of the string in 
 each case will give respectively the second, third, etc., over- 
 tones of C'. Ascertain the names of these tones on the Dia- 
 tonic Scale. 
 
 480. Exercise. Pluck the sonometer string at a point 
 other than its centre, and immediately touch the tip of the 
 finger to the middle of the wire. The fundamental tone ceases, 
 but whence the sound still heard ? Compare its pitch with that 
 of the sound emitted by the wire with the bridge at the middle. 
 Ascertain whether the same tone is obtained or not by dampen- 
 ing the wire at the middle, after setting it in vibration by 
 plucking it at the middle. Compare the quality of the tone 
 given by the whole wire when plucked at the middle with that 
 when plucked at some other point. Account for the difference, 
 basing the explanation on the facts revealed by the above 
 experiments. How can any overtone be eliminated from the 
 sound produced by a vibrating string? 
 
 In like manner search for other overtones. 
 
 481. Exercise. Tune two strings in unison on the 
 sonometer. Place a bridge under the middle of one of them, 
 and place on the same wire at various points small V~ sna P e d 
 pieces of paper, called Eiders. Now pluck the whole string at 
 its middle and compare the effect on the riders with that when 
 plucked at some other point. Inference. 
 
 Try the bridge at one-third from the end, one-fourth, etc., 
 and ascertain if the whole string vibrates in thirds and fourths 
 when plucked at a point intermediate between thirds and 
 fourths of the string. 
 
268 PBACTICAL PHYSICS. 
 
 XIV. LAWS OF SOUNDING AIR-COLUMNS. 
 
 482. Apparatus. Glass Tubing, Organ-Pipe, etc. 
 
 483. Exercise. Prepare, as described in Art. 456, eight 
 glass tubes, with paper disks and rubber connectors. 
 
 1st. Join two of the tubes together ; close one end and find 
 by trial a tuning-fork whose tone it enforces. Compare the 
 rate of this fork with that of the fork used in preparing the 
 tubes. Prepare closed tubes that will enforce the tone of such 
 other forks as you have. What do you find that the pitch 
 depends upon? 
 
 2d. Prepare open tubes that will enforce the sound pro- 
 duced by the forks employed in the first case. Compare the 'ir 
 lengths with those of the corresponding closed tubes. Formu- 
 late a law expressing these results. 
 
 3d. Connect two closed tubes which enforce the same fork 
 by their closed ends, and select a fork which they now enforce. 
 Remove the partitions, and see whether the air-column will still 
 enforce the same fork or not. What does this show to be the 
 condition of the air at the middle of an open tube which 
 enforces a certain sound? 
 
 484. Exercise. Fit to a glass tube, 2 cm. wide and 40 
 cm. long, a cork piston. Now set the piston so that the air- 
 column reenforces C'-fork. Blow gently across the open end 
 of the tube, and compare the pitch of the sound with that of the 
 fork. A piece of rubber tubing, flattened at the end by com- 
 pressing it between the thumb and finger, may be used for the 
 purpose ; or, better still, a piece of thin brass tubing flattened at 
 the end, leaving an opening 1 mm. in width. Measure the 
 length of the column. In like manner find the lengths for D', 
 
SOUND. 269 
 
 E', etc., C". Compare the ratios of these lengths with those 
 of the vibration-ratios, and write the law suggested. 
 
 485. Exercise. Ascertain the condition of the air in a 
 sounding air-column. 
 
 A small Organ-pipe, made either of glass, or having one glass 
 side (Fig. 193), and a small wire ring covered with 
 thin paper, will be needed. Sift a little sand over 
 the paper membrane and let it down by a cord into 
 the tube, supported vertically. Blow gently through 
 the mouth-piece, producing the fundamental tone ; 
 at the same time move the ring up and down 
 within the tube. Nodes will be known by the sand 
 remaining almost at rest. 
 
 Close the tube with a cork having a hole through 
 it for the cord supporting the ring, and again search 
 for nodes. 
 
 If the force of the air-current is increased, the 
 pipe will give an overtone. Again search for 
 nodes. 
 
 Make a cork piston and slide it along the tube till 
 it reaches the place where a node was found, and 
 compare the sound with that before the piston was 
 introduced. Inference. B^e. 193. 
 
 486. Exercise. Employing the apparatus of Art. 456, 
 connect several of the tubes together, close one end, and blow 
 gently across the open end to produce the fundamental (lowest) 
 tone. 1 Now increase the force of the blast till an overtone is 
 produced ; that is, a sound of higher pitch. Find by trial what 
 
 iThis will require considerable skill, as it is difficult to obtain the fundamental tone 
 of a tube of small diameter when the length is great in comparison. 
 
270 PRACTICAL PHYSICS. 
 
 length of closed tube has for its fundamental the previously ob- 
 tained overtone. Determine from the number of tubes used 
 which overtone you have. In like manner search out other 
 overtones. Repeat the experiment, employing open tubes. 
 What overtones are found to accompany closed tubes ? Open 
 tubes ? 
 
 XV. HARMONY AND DISCORD. 
 
 487. Apparatus. Tuning-Forks, Sonometer, etc. 
 
 488. Exercise. Compare the pleasantness of the sound 
 produced by two tuning-forks, of the same pitch, with that when 
 to a prong of one of them is cemented a small coin. First, at- 
 tach the coin near the stem ; then at the middle of one branch ; 
 and finally at the end. Explain. 
 
 If you have the forks, compare C' and D', C f and E', C' 
 and F ', C ' and G ', C ' and A ', C ' and B ', C ' and C ", 
 etc. Tabulate those which are found to harmonize. 
 
 Adjustable tuning-forks are now to be had of dealers in mu- 
 sical wares, at very reasonable prices. With two such forks 
 all these comparisons can be made. 
 
 The following substitute may be made for the forks : Set in 
 holes, bored in a board, thirteen test-tubes, each 15 cm. long 
 and about 2 cm. in diameter. Into each pour melted paraffine 
 till an air-column is obtained which responds to some one of 
 the thirteen notes in the octave. Now, proceeding as in Art. 
 484, any one of these may be sounded, and by using a tube 
 with two branches, any two may be sounded together. 
 
 489. Exercise. Tune two strings on a sonometer to the 
 pitch of C'. By means of the movable bridge under one of the 
 
SOUND. 271 
 
 strings produce successively the notes of the musical scale. 
 Determine which harmonize with C ', and which do not. Com- 
 pare other tones by placing a bridge under each wire. 
 
 As placing a bridge under a wire will increase the tension, 
 where both ends of the wire are connected to posts, some 
 allowance will have to be made for this. 
 
 XVI. VIBRATING PLATES AND BELLS. 
 
 490. Apparatus. Chladni-Plates, Large Bell, etc. 
 
 491. Exercise. Cut out of sheet-brass, 1 mm. thick, a 
 plate 25 cm. square, 
 
 a triangular one, 25 
 
 cm. on each side, 
 
 and a circular one 
 
 25 cm. in diameter. 
 
 Mount each one on 
 
 a support, as shown 
 
 in Fig. 194. Round 
 
 the edges with a 
 
 file. Clamp each 
 
 stand firmly to the table, sift some fine sand 
 
 evenly over the plate ; then, touching the 
 
 plates at some point with the finger, draw a 
 
 well-rosined violin-bow across an edge. Try touching the plate 
 
 at different points. Copy in your note-book the figures formed. 
 
 Do you discover any relation between the pitch and the 
 
 figures ? 
 
 492. Exercise. Using the square plate of the last ex- 
 periment, make it vibrate so that the only nodal lines are diag- 
 
272 
 
 PRACTICAL PHYSICS. 
 
 onals of the square. While the plate is vibrating, hold over 
 opposite segments or quarters, and close to the plate, stiff pa- 
 per triangles, having the shape and size of these segments. 
 Observe the effect on the loudness of the sound. Explain. 
 
 493. Exercise. Pro- 
 cure, of a tinsmith, a tube 
 cm. wide and 40 cm. long, 
 having two branches 4 cm. 
 wide, 20 cm. long, and 15 
 cm. apart at the free end 
 (Fig. 195). Hold the ap- 
 paratus above the square 
 plate of Art. 491, with the 
 branches within 1 cm. of its 
 surface. 
 Paste a 
 membrane 
 of thin pa- 
 per across the upper end, and scatter on it a 
 little fine sand. Cause the plate to vibrate in 
 quarters. Compare the effect on the sand when 
 the arms are over a and b (Fig. 196) with that when over a and c. 
 
 FIG. 195. 
 
 FIG. 196. 
 
 494. Exercise. Invert a large bell, and nearly fill it with 
 water. Scatter lycopodium powder or cork-dust on the sur- 
 face. Set the bell in vibration by a blow from a small mallet. 
 Determine from the effect on the powder the position and num- 
 ber of the nodal points. A large glass goblet or bell-jar might 
 be substituted for the bell. 
 
 495. Exercise. Employing the bell of the last experiment, 
 determine the position and the number of the nodal points by 
 
SOUND. 273 
 
 means of a small glass or ivory ball, suspended by a fine 
 thread. The nodes will be recognized as places where the ball 
 is repelled the least by the vibrating surface. 
 
 XVII. ATTRACTION OF VIBRATING BODIES. 
 
 496. Apparatus. -Tuning-Fork, Rubber Balloon, etc. 
 
 497. Exercise. Float an inflated rubber balloon on a 
 vessel of water, shielding it carefully from air-currents. Hold 
 near the balloon a large, vibrating tuning-fork, and observe the 
 action of the ball. Repeat several times to make it certain 
 that the effect observed is not accidental. What must be the 
 atmospheric condition about the fork to produce the effect 
 noticed ? 
 
 498. Exercise. Sprinkle evenly over the square plate of 
 Art. 491 a mixture of fine sand and lycopodium powder. 
 Cause the plate to vibrate, and compare the effects produced 
 on the powder and sand respectively. Explain. 
 
 XVIII. GRAPHIC AND OPTICAL STUDY OF SOUND. 
 
 499. Apparatus. Tuning-Forks, Glass Plates, Vibro- 
 graph, Logograph, Manometric Flame Apparatus, Lissajou Ap- 
 paratus, Sand Pendulum, etc. 
 
 500. Exercise. Cut a wooden block of the form shown 
 in Fig. 197, in which is firmly set the stem of a tuning-fork. 
 Make out of thin brass a narrow rectangular ferrule, with a 
 
274 
 
 PRACTICAL PHYSICS. 
 
 FIG. 197. 
 
 short pointed arm projecting, to slip over the end of one branch 
 
 of the fork to serve as a marker. 
 Beneath the point support a pane of 
 glass sufficiently inclined to cause a 
 small plate of glass placed upon it 
 to slide down by gravity. liaise the 
 supporting surface till the style on 
 the fork just touches the glass plate 
 as it slides under it. Smoke the 
 upper surface of the sliding glass, set the fork in vibration by 
 a blow from a small cork mallet, and observe the tracing pro- 
 duced by the style in the smoke as the glass glides down the 
 plane. Guides made of glass tubes cemented to the plane will 
 keep the moving glass from turning from a straight-line course. 
 Cement a coin to the outer end of the fork, and note the 
 effect on the pitch as shown by the tracing on the glass. 
 
 Compare the tracings given by two forks differing an octave 
 in pitch. 
 
 In Fig. 198 is shown another device for studying the vibra- 
 tions of tuning-forks. It consists of a wooden cylinder, A, 
 
 FIG. 198. 
 
 mounted on an axis, one end of which, B, has a thread upon 
 it working under the small wire staple which keeps it in place 
 
SOUND. 
 
 275 
 
 FIG. 199. 
 
 on the standard. The fork is secured by its stem to the 
 
 block, C, clamped to the base by a screw, D. 
 
 By this means the fork can be set as close to A 
 
 as may be desired. The cylinder is 
 
 smoothly covered with smoked paper, on 
 
 which the fork-style traces its 
 
 record as the cylinder is turned 
 
 by the crank. By measuring 
 
 the rate of rotation of 
 
 A, and counting the 
 
 number of sinuosities 
 
 made by the fork, the 
 
 rate of the fork is 
 
 easily ascertained. By 
 
 using a second block, two forks may be compared. 
 
 501. Exercise. To study sounds produced by wind in- 
 struments, an apparatus constructed as follows will be found 
 quite efficient : Get a good mechanic to turn a wooden mouth- 
 piece like that of a telephone, but somewhat deeper and larger, 
 shown in section in Fig. 200. Glue a parchment-paper dia- 
 phragm, K, across it, fastening to its centre, by wax, a slender 
 needle with its point curved down. Fasten this mouth-piece to 
 a board, B, supported in an inclined position. C is a cross- 
 piece to support the smoked glass, D. M is a guide for the 
 
 glass. C is given such an in- 
 clination that the glass plate 
 moves along by gravity. By 
 changing M, the part of the plate 
 under the marker is changed. A 
 stout pin, F, keeps the needle 
 from being dragged out of posi- 
 tion, and jui elastic, H, drawn down through a hole in B, holds the 
 
 
 FIG. 200. 
 
276 
 
 PRACTICAL PHYSICS. 
 
 needle in contact with the glass plate. Any sounds produced 
 in front of and close to A will move the needle E, and cause 
 a characteristic line to be traced on D. 
 
 502. Exercise. Cut out of a board 2.5 cm. thick, a 
 strip 4 cm. wide and 25 cm. long. Near one end bore a hole 
 
 FIG. 201. 
 
 2.5 cm. in diameter, half-way through it. Cut a second piece 
 of the same width and 5 cm. long, and bore into it a similar 
 
SOUND. 
 
 277 
 
 hole. Glue these two pieces together so that the two holes 
 face each other, separating them, however, by a membrane of 
 thin rubber, thus forming a box divided into two parts by 
 this membrane. Nail the long strip to a piece of board for a 
 support. Bore into the strip A, Fig. 201, a small hole leading 
 into the box, and cement into it a short glass tube, E. In B 
 bore two such holes, and cement in the upper one a jet- tube, 
 and in the lower one a short, straight tube. Connect to E a 
 piece of rubber tubing, with a funnel for a mouth-piece. 
 Connect C to the gas-supply. On turning on the gas, a jet can 
 be obtained at F. Cut a cube out of pine, 10 cm. on each edge, 
 as M. Insert in the centres of two opposite faces stout wires, 
 as K and H. Tie on the lateral faces squares of looking- 
 glass. Rotate this apparatus slowly in front of F, and observe 
 the image. Compare it with that when you sing in the funnel 
 mouth-piece, oo, in pool. Ascertain the effect of changing the 
 pitch. 
 
 Sing the vowel o, giving it the pitch of the note B. Sing the 
 vowel a, giving it the pitch of F. 
 Sing the vowel a, giving it the 
 pitch of C. Try other sounds. 
 Draw a diagram of the name- 
 figure in each case. 
 
 503. Exercise. A com- 
 plete apparatus for the optical 
 exhibition of vibratory motions 
 is shown in Fig. 202. It con- 
 sists of a heavy cubical box on 
 two adjacent sides of which are secured, by means of bolts, 
 the blocks A and F, holding the tuning-forks B and L. 
 Slots cut in the frame make it possible to give the forks any 
 
 FIG. 202. 
 
278 PBACTICAL PHYSICS, 
 
 desired relative position. Small pieces of mirror, equal in size, 
 are cemented to the lateral faces of the prongs at their outei 
 ends. Flexible steel bars might be used in place of forks, 
 fastening them to the blocks by means of screws. The time 
 of vibration of the forks can be changed by fastening small 
 weights to the prongs with wax. 
 
 To use this apparatus, place, a few metres distant from the 
 mirror on the fork at E, a lamp surrounded by a dark chimney, 
 in which is a small hole, giving a small line of light, incident on 
 the mirror. Place the eye so as to see the image in this mirror 
 of the hole in the chimney, and sot the fork in vibration. The 
 
 FIG. 203. 
 
 image becomes an elongated line, and by rotating the fork a 
 sinuous line is produced, varying in amplitude as that of the 
 fork changes. By receiving the reflected ray on a stationary 
 mirror, the image can be projected on a screen, the distance of 
 the screen and the brightness of the effects being governed by 
 the intensity of the light. Clear definition can be secured by the 
 aid of a lens. Fig. 203 exhibits the order of the apparatus. 
 
 Two vibratory motions can be combined by placing the lamp 
 so that the beam of light is incident on the mirror on the fork at 
 D, by which it is reflected to the mirror C, on a second fork, 
 passing thence through a lens to the screen. By moving the 
 
SOUND, 
 
 270 
 
 block A to the position M, the forks can be made to vibrate in 
 the same plane or in parallel planes. If the forks are in unison 
 the luminous line on the screen will lengthen and shorten at regu- 
 lar intervals, but if they vary in pitch the beats resulting from 
 the imperfect harmony will be heard, and at the same time a curi- 
 ous pulsating character will distinguish the image. Using the 
 forks as placed in the figure, the combination of the two rectangu- 
 lar vibratory motions is effected, the image obtained depending 
 on the interval of the forks, becoming more and more complex 
 as the ratio of their vibration-numbers becomes less simple. 
 
 In Fig. 204 is illustrated a cheap substitute for the foregoing 
 apparatus, the forks being replaced by wooden bars. The credit 
 of the device is due to Mr. George M. Hopkins. 
 
 Select a box about 60 cm. square, two flat springs of wood 
 3 cm. wide, 4 mm. thick, and 60 cm. long, or metal springs 
 2.5 cm. wide, 1.5 mm. thick, 
 and of the same lengtii as the 
 wooden ones. Secure these 
 at opposite corners by 
 screws to blocks 2.5 cm. 
 thick. Cement to the free 
 ends of each, and in the 
 plane of vibration, a piece of 
 thin cardboard, having a slit 
 2 mm. wide, parallel with 
 the spring. These cards are 
 placed as near each other 
 as possible. On one of the 
 springs is a sliding-weight 
 of lead, with a set-screw, 
 so that the time of vibration can be changed when necessary. 
 If these springs are now set in vibration, the operator on look- 
 
 FIG. 204. 
 
280 
 
 PRACTICAL PHYSICS. 
 
 ing at the lamp through the two slits will see a band of 
 light, the form depending on the relative rates of the two 
 springs. 
 
 By placing a lamp on one side of the slotted cards, and a 
 lens on the other, an image can be projected on the screen. 
 The figures obtained are known as Lissajou's curves. In the 
 next article the same figures are produced by means of Black- 
 burn's pendulum. 
 
 504. Exercise. Construct a frame like the one shown 
 
 in Fig. 205. The height 
 should be a little over 
 1 m. The pendulum-bob 
 is supported by a double 
 cord passing through the 
 frame, and winding round 
 a violin-key inserted in 
 the centre of the cross- 
 piece, so that, by turning 
 the key, the bob can be 
 raised or lowered. Slid- 
 ing on the cord is a 
 thick leather button, r. 
 The bob may be either 
 a small glass funnel, 
 set into a heavy lead 
 disk, or, what is better, 
 a lead disk having a 
 diameter of 3 cm. and a 
 depth of 4 cm., the inte- 
 rior being funnel-shaped, with a circular opening in the bottom 
 1 mm. in diameter. Fine sand placed in the bob will run out 
 
 FIG. 205. 
 
SOUND, 281 
 
 as the bob swings, and will mark out on a board placed beneath 
 it the path described. 
 
 Set the leather slide 250 mm. above the centre of gravity of 
 the bob, turn the violin-pin till the whole pendulum is 1 m. 
 long, and swings about 5 mm. above the paper ; fill the dish with 
 sand, draw it to one side over a line making an angle of 45 at 
 the centre with that joining the supports. Try in succession the 
 following positions for the slide: 444.4 mm., 562.5 mm., 640 
 mm., 694.4 mm., 734.6 mm., 765.6 mm., 790.1 mm., the length 
 of the pendulum, as a whole, being kept at 1 m. If the above 
 lengths are not accurately secured, the pendulum will fail to 
 retrace the first-formed curve as it continues vibrating. Draw 
 diagrams of the figures obtained. 
 
 An examination of the apparatus will reveal the fact that it 
 consists of two pendulums, one of them 1 m. long, swinging in 
 a plane at right angles to the supporting bar, the other a shorter 
 pendulum, with its point of suspension at the leather slide, 
 swinging in a plane forming any angle at pleasure with the 
 plane of vibration of the longer pendulum. It will also be 
 noticed that the ratios of the lengths of the pendulums in the 
 
 1 4 9 16 25 36 49 64 
 different cases are , , , , , ^, -^, ^ respec- 
 
 tively. What must be the ratios of their times of vibration? 
 The curve obtained in each case is from the composition 
 of two simple harmonic motions. The pendulum returns to 
 the starting-point after a definite number of oscillations, when 
 the periods are commensurable. When the periods are incom- 
 mensurable the pendulum never returns to the starting-point, 
 and consequently the curve is not retraced. 
 
282 PRACTICAL PHYSICS. 
 
 XIX. VOCAL ORGANS. 
 
 505. Apparatus. Glass Tube, Sheet Rubber, etc. 
 
 506. Exercise. Roll around the end of a glass tube a 
 strip of thin india-rubber, leaving about 2 cm. of it projecting 
 beyond the tube. Take two opposite portions of the projecting 
 part in the fingers, and stretch it so that a slit is formed. Now 
 blow through the tube, and a sound will be produced. Ex- 
 plain. Ascertain the effect of varying the tension of the rub- 
 ber. This device is a rough representation of the human 
 larynx. 
 
 507. Exercise. Sing some note of the musical scale, and, 
 without changing the form of the mouth-cavity, hold near it, in 
 a horizontal position, with the prongs over each other, the free 
 ends of a vibrating fork of the same pitch as the note sung. 
 Alter the shape of the mouth-cavity and repeat. Inference. 
 
LIGHT, 
 
 283 
 
 CHAPTER VII. 
 
 LIGHT. 
 
 I. SOURCES OF LIGHT. 
 
 508. Apparatus. Porte Lumiere Magic Lantern, etc. 
 
 509. Exercise. As parallel rays of considerable intensity 
 are required for many of the experiments with light, below are 
 described several ways of obtaining such a light. 
 
 First Method. Sunlight is brighter_than_any artificial light, 
 and a horizontal beam can be re- 
 flected into the work-room through 
 a south window by means of a 
 Porte Lumiere. One can be pur- 
 chased of dealers in physical ap- 
 paratus for about $5, and can be 
 constructed at even a less outlay, 
 as follows : 
 
 Procure a piece of pine board 
 as long as the width of the win- 
 dow, and about 60 cm. wide. In 
 it cut a round hole 12 cm. in diam- 
 eter, the centre of which should be 
 the centre of the line parallel to the 
 edge of the board, and 20 cm. from 
 the bottom. On one face of the board, on opposite sides of 
 
 B 
 
 Fie. 206. 
 
284 
 
 PRACTICAL PHYSICS. 
 
 FIG. 207. 
 
 the centre of the hole T, and having their inner faces 15 
 cm. apart, fasten two wooden arms, DE, 32 cm. long, sup- 
 ported by iron braces, C. Figs. 206, 207. Pivot, by screws, 
 
 between their outer ends, a 
 rectangular board, FH, 2 cm. 
 thick and 15 cm. square, mak- 
 ing the distance, DE, 31 cm. 
 Cut a half-round piece, K, 
 5 mm. thick, with a radius of 
 7 cm., and fasten it by slender 
 screws to the rectangular piece, 
 LM, 25 cm. by 15 cm. QN 
 is a hard- wood cylinder, 2.5 
 cm. in diameter ; it may be cut 
 from an old broom-handle. 
 In one end, as shown at O, 
 cut a slot so that it will clasp 
 
 the piece K, to which it is to be secured by a bolt, around which 
 it is free to turn, with slight friction. S is a triangular block, 
 the shape of which is determined by the method illustrated in 
 Fig. 208. On a large sheet of 
 paper lay off the lines DE 31 cm., 
 and DA 40 cm., forming a right 
 angle at D, a point corresponding 
 to the centre of the hole T. At 
 E, with a protractor, make the 
 angle DEQ equal to the latitude 
 of the place. Where EQ cuts 
 DA is the centre of the hole to 
 be bored for QN. The upper 
 angle of the piece S is evidently 
 equal to the angle DEQ. Cut 
 
 FIG. 208. 
 
LIGHT. 285 
 
 this piece S and fasten it to AD, then bore the hole for QN per- 
 pendicular to the upper face of S. P is a wooden washer, pinned 
 to QN, to serve as a shoulder, and is so placed that QN extends 
 through the board far enough to bring the lower edge of LM a 
 few centimetres above the top of the hole T. R is a pin at 
 right angles to QN, for convenience in turning it. On the front 
 of both LM and FH fasten a good, plane mirror, completing 
 the apparatus. 
 
 Place this porte lumiere in a south window, with the board 
 in a vertical position. Determine by trial the inclination of 
 the mirrors so that sunlight incident on LM is reflected to 
 FH, and from it, in a horizontal line, through T. Now, by 
 turning QN on its axis, the beam of light can be kept in one 
 place, notwithstanding the changing position of the sun. 
 
 QN is parallel to the polar axis when the porte lumiere is in 
 position. The angle between LM and QM changes with the 
 sun's angular distance from the equator, called its declination. 
 If the declination is represented by d, then the angle between 
 
 ML and QN equals . It will be found convenient to 
 
 graduate the piece K to degrees to aid in setting LM. 
 
 Second Method. The best artificial lights are the electric 
 of the arc type and the lime light. For a great many experi- 
 ments, however, a powerful kerosene-lamp will be found suf- 
 ficient. With either of these lights, means will have to be 
 adopted to render the rays parallel. To do this, proceed as 
 follows : Place the light in a large wooden box, provided witli 
 holes in both the bottom and the top for ventilation. The 
 depth of the box must be such that the heat from the lamp 
 will not set it on fire. In one face of the box, exactly opposite 
 the flame, cut a circular opening, about 10 cm. across, depend- 
 ing on the size of the lens. Tack across this, on the inside t 
 
286 
 
 PRACTICAL PHYSICS. 
 
 a glass plate to cut off the heat from the lens, which, mounted 
 in a wooden frame, Fig. 209, is tacked over 
 the opening on the outside. This lens had 
 better be plano-convex, and have a focal dis- 
 tance of 15 cm. The light must be situated 
 at its focus, and be incident on its plane 
 surface. 
 
 Third Method. The common magic lan- 
 tern, by removing the objective and adjusting 
 the condensers, can be made to give a very 
 
 satisfactory beam. This instrument has been so improved of 
 
 FIG. 20.. 
 
 FIG. 210, 
 
 late that in some of its forms it is now capable of giving a 
 light from the use of kerosene varying from 50 to 350 candle- 
 power. Fig. 210 shows one of the simplest in form and best 
 in construction. 
 
LIGHT. 
 
 287 
 
 FIG. 211. 
 
 II. RECTILINEAR PROPAGATION OF LIGHT. 
 
 510. Apparatus. Cardboard, Tapers, Candles, etc. 
 
 511. Exercise.* Support with retort clamps on a table 
 two small sheets of cardboard in vertical parallel planes. In 
 the centre of one of them 
 
 cut a hole 2 mm. in diam- 
 eter (Fig. 211), and place 
 in front of it, at a distance 
 of a few centimetres, a 
 lighted candle or lamp. 
 Compare the images of the 
 source of light formed on 
 the second sheet of card- 
 board as you vary the rela- 
 tive distances between the 
 
 three objects. Ascertain the effect of changing the shape of 
 the aperture, and also the size of it. 
 
 Surround the light with a cylinder of cardboard having a 
 small hole 2 mm. in diameter opposite the flame. By changing 
 the position of this cylinder light may be taken from any part 
 of the flame. Now place in front of this opening a sheet of 
 cardboard with an aperture 5 mm. square. Behind this, and 
 distant from it a few centimetres, set the second sheet. Observe 
 the image formed on it and mark its position. Move the cylin- 
 der surrounding the light so as to take light from a different 
 part of the flame, and again note the character and the position 
 of the image. In this way take light from such points of 
 the flame as when joined will give an outline of the flame, 
 being careful to move neither the cardboard screens nor the 
 
 * All those experiments which require a dark room are marked with an asterisk. 
 
288 
 
 PRACTICAL PHYSICS. 
 
 light. Now join the centres of the images and compare the 
 figure with that of the flame. Remove the cylinder and note the 
 position of the image. Of what do you find the image to be com- 
 posed ? In what way does the size and shape of the aperture af- 
 fect the image ? Write a full explanation of the whole subject. 
 
 512. Exercise.* Ascertain why an image of every object 
 is not seen imprinted on every other object in accordance with 
 the principle governing the formation of images through small 
 apertures, any point in space being considered as such an 
 aperture. 
 
 Set up an apparatus as in the last experiment. Cut a large 
 hole in the cardboard next to the light and cover it with tin 
 foil. Make a pin-hole through the foil and observe the image 
 of the flame formed on the screen. Make other pin-holes and 
 observe the positions of the images. Keep increasing the num- 
 ber till the foil is full of holes and observe the effect. Inference. 
 
 513. Exercise.* Cut out of cardboard two squares 
 
 18 cm. and 3 cm. on an edge respec- 
 tively, and mount them on supports. 
 A simple way would be to secure 
 them with sealing-wax to a heavy 
 strip of cardboard tacked to the edge 
 of a block (Fig. 212). Place these 
 squares successively between a large 
 fan-shaped flame and a screen made 
 of cardboard supported vertically and 
 parallel to the square. Compare the 
 shadows cast by these squares on 
 the screen when the flame is parallel 
 
 to them. Determine the effect of placing the flame edgewise to 
 
 the square. 
 
LIGHT. 289 
 
 Make a pin-hole through the screen in the darkest part of the 
 shadow and look through it toward the flame. Try a hole in 
 the lighter part of the shadow. Try one in the line separating 
 the light from the dark. Try one wholly without the shadow. 
 
 Write out a full explanation of shadows based on the facts 
 developed by these experiments. 
 
 III. PHOTOMETRY. 
 
 514. Apparatus. Cardboard, Lamps, "White Screens, 
 Candles, etc. 
 
 515. Exercise.* Cut from cardboard three squares, 4 
 cm., 8 cm., and 12 cm., respectively, on an edge, mounting 
 them as directed in Art. 513, making the length of support 
 such that their centres are each at the same distance above the 
 table as the light-emitting point to be used in the experiment. 
 Place around the lamp a paper cylinder, and in it cut a square 
 hole opposite the centre of the flame, but smaller than its least 
 dimensions. Now set the largest square facing the aperture 
 and distant from it about a metre. Between it and the light 
 stand the medium-sized one, finding by trial the place where it 
 just cuts off all the light from the largest. In like manner 
 place the smallest one with reference to the intermediate. 
 Measure the distance of each screen from the light. Com- 
 pare the total amount of light incident upon the smallest screen 
 with that incident on the intermediate when the first is removed, 
 and also with that incident on the largest when the other two 
 are removed. Compare the amounts on equal areas. What 
 effect do you find distance to have on intensity of light, that 
 is, the degree of illumination of equal areas ? 
 
 516. Exercise.* Drop a little hot parafflne or beeswax 
 on a sheet of unsized white paper, and warm the paper till the 
 
290 
 
 PRACTICAL PHYSICS. 
 
 wax has thoroughly soaked into it. Give the spot a diameter 
 of about 3 cm. Cut from this paper a circular piece 10 cm. in 
 diameter, with the spot in the middle, and cement it to a wire 
 frame provided with a suitable stem for supporting it in a ver- 
 tical plane. Lay on the table a smooth board 30 cm. wide and 
 3.5 m. long ; draw lengthwise of it a straight line, and graduate 
 it to centimetres. In a rectangular block bore a hole large 
 enough to admit a candle, and in a second block bore four such 
 holes in line and 1 cm. apart. Lengthwise of each of these 
 blocks draw a straight line, bisecting the holes, to be used in 
 determining the position of the candles on the scale on the 
 board. Now support the paper disk on a line between the can- 
 dles, finding by trial a position for it where the wax spot is 
 either invisible or is least conspicuous to one viewing it from 
 a position in line with the board. Read off on the scale the 
 distance of each set of candles from the disk. Take the mean 
 of a large number of trials. As the wax spot is invisible 
 when the two surfaces of the paper disk are equally illuminated, 
 what relation do you find existing between illuminating power 
 and distance? 
 
 517. Exercise.* Measure the candle-power of a light. 
 Support a white paper screen in a vertical plane. About 
 
 FIG. 213. 
 
 10 cm. in front of it fix in a vertical line a wooden rod 1 cm. 
 in diameter, by the aid of wax (Fig. 213). On the sanie side, 
 
LIGHT. 291 
 
 about o() cm. from the screen, place a lighted sperm candle of 
 the size known as " sixes." Now place the light to be meas- 
 ured at such a distance that the two shadows of the rod seen 
 on the screen are of equal darkness. Then the square of the 
 ratio of the distance of this light from the screen to that of 
 the candle is the candle-power of that light. Why ? Make 
 several determinations of the candle-power and find their mean. 
 Tabulate the results. 
 
 518. Exercise.* Another method of determining the 
 candle-power of a light : In Art. 516 substitute for the group 
 of four candles the light whose candle-power is sought. Now 
 move the disk till the waxed spot is dimmest, viewed from 
 either side, and the ratio of the squares of the distances of the 
 lights from the disk will be the candle-power. 
 
 IV. REFLECTION OF LIGHT. 
 
 a. Regular Reflection. 
 
 519. Apparatus. Porte Lumiere, Cardboard, Protractor, 
 Glass Mirror-Plate, Prism, Pane of Glass, Glass Jar, Candle, 
 
 etc. 
 
 520. Exercise. Cut six blocks of wood, each 4 by 6 by 
 8 cm., and two pieces of board 8 by 4 by .3 cm. Tack a piece 
 of cardboard of the size of a postal card to each of two of these 
 blocks, using the thin wooden strips as a backing. With 
 a large darning-needle make a hole in each card 15 mm. 
 from the end, removing with a sharp knife the roughness pro- 
 duced. Place the blocks as shown in Fig. 214. On the centre 
 
292 PRACTICAL PHYSICS. 
 
 block place a small piece of mirror, and on the outside block 
 stand a lamp or candle with its name close to the hole in the 
 card. With one eye at the hole in the other card, mark with a 
 
 long needle, 
 fixing it iii 
 place with soft 
 wax, where 
 the line from 
 the image of 
 the light 
 pierces the 
 FIG ' 214 - mirror. Now 
 
 draw on a sheet of paper a straight line whose length is the 
 distance between the vertical cards. Erect at its extremities 
 perpendiculars equal to the height of the holes above the upper 
 surface of the blocks. Lay off on the line the distance of the 
 marked point on the mirror from one of the cards, and join 
 the point with the extremities of the perpendiculars. Erect a 
 perpendicular at this point, and measure with a protractor 
 the angles between it and the oblique lines. Make several 
 trials of locating the point on the mirror, and hence get several 
 measurements of these angles. Inference. 
 
 521. Exercise. Determine the law for the reflection of 
 light. 
 
 First Method. On one end of a smooth board, 32 cm. wide 
 by 60 cm. long, draw a circle 30 cm. in diameter, and divide it 
 into degrees by means of a protractor. Pivot at the centre two 
 wooden arms (Fig. 215). Glue to the top one, and at right 
 angles to it, a strip of thin board 2 cm. by 3 cm., with one sur- 
 face blackened and exactly in' line with the axis on which the 
 arms turn. Cement to this vertical strip a piece of mirror through 
 
LIGHT. 293 
 
 the amalgam of which is cut a narrow line ; this line when the 
 mirror is in place must be exactly in the axis. To the outer 
 end of the under arm, 
 or pointer, fasten a 
 needle in a normal to 
 the plane of the gradu- 
 ated circle. To the 
 end of the board far- 
 
 Fiu. 215. 
 
 thest from the gradu- 
 ated circle tack a rectangular piece of cardboard, through 
 which, at a point about 1.5 cm. above the board, is a hole 1 mm. 
 in diameter. The free ends of the arms should be bevelled, 
 and a line drawn on this bevelled portion, which, if continued, 
 would pass through the axis. Now place the hole in the card- 
 board, the line of the mirror, and the mark on the outer end of the 
 mirror-arm in such a position that the line on the mirror bisects 
 the image of the hole, and record the reading of the mirror- 
 arm. Then move this arm a few degrees and bring the other 
 arm around so that the image of the vertical needle, as seen 
 through the hole in the cardboard, coincides with the line on 
 the mirror. Compare the angle through which the mirror- 
 arm was moved, with that between the needle-arm and the 
 
 i 
 
 second position of the mirror-arm, as shown by the cir- 
 cular scale. Obtain the mean of a number of trials made 
 at different parts of the scale. What law expresses the 
 results ? 
 
 Second Method. On a smooth board about 1 m. by 30 cm. 
 draw a straight line half-way between the ends. Set a rec- 
 tangular strip of mirror 10 cm. by 20 cm. in the normal plane 
 through this line, fixing it in position by means of a clamp or a 
 little wax. Set in front of this mirror, and distant from it 
 as well as from each other a few centimetres, two darning- 
 
294 
 
 PRACTICAL PHYSICS. 
 
 FIG. 216. 
 
 needles by sticking them in the board and normal to it, 
 as A and B (Fig. 216). Now set C in line with A and the 
 
 image of B, and D in line with 
 /* B and the image of A. Then 
 
 remove the mirror and draw 
 \ 
 
 lines through A and C, and B 
 
 and D., Measure with a pro- 
 tractor the angles these lines 
 make with the line of the mir- 
 ror. Vary the position of A 
 and B and obtain the mean of 
 several values for these angles. 
 If each of these angles is sub- 
 tracted from 90 we have either 
 the angle of incidence or the 
 
 angle of reflection in each case, as it will be observed that C is in 
 line with A and the images of both B and D, and I) is in line 
 with B and the images of both A and C. What relation is here 
 established between these angles? 
 
 To insure greater accuracy the needles which locate lines 
 should not be placed very close together. 
 
 522. Exercise. Measure the angle of a prism. 
 
 First Method.* Cut a slit 1 mm. wide and 3 cm. long in a 
 square of cardboard, and fasten it across the opening of the 
 lantern, or porte lumiere, so that a vertical ribbon of light is 
 obtained. Place the prism with the angle to be measured 
 towards the opening in the cardboard, and approximately 
 bisected by the central plane of the ribbon of light (Fig. 217). 
 Part of the ribbon of light will be incident on one face of the 
 prism and be reflected from it, and the other part will be 
 similarly disposed of by the other face. Now stick perpendic- 
 
LIGHT. 
 
 295 
 
 tilarly in the board supporting the prism two darning-needles, 
 Nj and N 2 , one on each side of the prism and in the reflected 
 beam. Then set N 3 and 
 N 4 , two other darning- 
 needles, in the centres 
 of the shadows cast by 
 N! and N 2 , respectively, 
 
 and distant 
 centimetres. 
 
 several 
 Remove 
 
 the prism, draw lines 
 
 through the points 
 
 marked by the needles, FlG 217 
 
 and measure with the 
 
 protractor the angle they form at D. Half of this angle is 
 
 the angle of the prism, since EDF = EAF + AED + AFD = 
 
 EAF -f AEH -+- AFK = 2EAF. 
 
 FIG. 218. 
 
 Second Method. Place the prism on the stand of the Spec- 
 trometer (Fig. 218), with the angle to be measured turned 
 toward the slit, the plane of light approximately bisecting the 
 
296 PRACTICAL PHYSICS. 
 
 angle. Now move the telescope till the intersection of the 
 cross- wires is exactly on the image of the slit reflected ; first 
 from one face, and, secondly, from the other face of the prism. 
 The difference between the readings for these two positions, 
 given by the vernier attached to the telescope-arm on the 
 horizontal scale around the edge of the table of the instrument, 
 will be double the angle of the prism. 
 
 It will be readily seen that this method differs from the first 
 one, simply in the use of a telescope and verniered scale to 
 secure more accurate determinations of the angles involved. 
 
 b. Diffused Reflection. 
 
 523. Exercise.* Find the effect of an irregular, surf ace 
 on light. 
 
 Let a beam of light be incident successively on a good 
 plane mirror, a tarnished surface, a pane of window-glass, 
 a pane of ground-glass, and a sheet of white writing-paper. 
 Compare the brightness of the spots of light formed on the 
 wall by reflection from these surfaces. Inference. 
 
 524. Exercise.* Fill a large glass jar with smoke by 
 burning touch-paper within it. Cover up the top of the jar 
 with a piece of cardboard, through which is a hole 1 cm. in 
 diameter. Set a plane mirror at an angle so that it will reflect 
 a beam of light into the jar through the opening in the cover. 
 Compare the effect with that when an empty jar is used. Ex- 
 plain. 
 
 c. Amount of Light Reflected. 
 
 525. Exercise.* Ascertain if the amount of light re- 
 flected from a surface is affected by the size of the incident 
 angle. 
 
LIGHT. 297 
 
 Support a small plane mirror in a retort-holder, giving it 
 such an inclination that a strong beam of light incident upon 
 it is reflected to the surface of a shallow basin filled with water, 
 striking it obliquely. By varying the distance of the water 
 from the mirror, as well as the inclination of the mirror, any 
 incident angle at the surface of the water may be obtained at 
 pleasure. Compare the brightness of the reflection from the 
 water on the wall as given under different angles. Inference. 
 
 526. Exercise.* Place a sheet of writing-paper on a 
 table, and near it a lighted candle. Find a position for the eye 
 where an image of the candle can be seen in the paper, and 
 observe the size of the angles of incidence and of reflection. 
 Inference. 
 
 V. MIRRORS. 
 
 527. Apparatus. Plane Mirrors, Darning-Needles, Small 
 Iron Rings, Pane of Glass, Bottle, Candles, Cardboard, Protrac- 
 tor, Glass Tube, Concave and Convex Mirrors, Porte Lumiere, 
 Lenses, Small White Screens, Spherometer, Scale, etc. 
 
 a. Plane Mirrors. 
 
 528. Exercise. Find where the image of an object in a 
 plane mirror is situated. 
 
 First Method. Select a smooth board, about 1 m. long and 30 
 cm. wide, draw a line across the middle of it and support a plane 
 mirror in the normal plane containing this line, either by means 
 of a clamp or sealing-wax. Set a darning-needle perpendicular 
 to the board, about 15 cm. in front of the mirror, and also 
 a second one in an exact line with the first one and its image 
 
298 PRACTICAL PHYSICS. 
 
 in the mirror (Fig. 219), at, say, 30 cm. from it. As far 
 as possible to one side of these set two more needles, so that 
 the line of sight through them passes exactly through the 
 
 image of the first needle 
 set. Now remove the mir- 
 
 M ^^^ ror and draw lines through 
 
 the points marked by the 
 needles, producing them till 
 they intersect. Measure 
 the distance of this inter- 
 section from the reflecting 
 surface of the mirror, that 
 is, from the line drawn 
 across the board, and also 
 
 measure the distance of the first needle set from the same 
 point. Make a number of trials and obtain the mean. In- 
 ference. 
 
 Second Method. Procure at a hardware store two iron 
 rings, about 3 cm. across. Cement across them fine wires, 
 forming diameters at right angles. Draw across the middle of a 
 smooth board, 2 in. long, a straight line, and a second one length- 
 wise of the board, and perpendicular to the first. Graduate this 
 last line to half -centimetres each way from the intersection. 
 
 Secure with seal- 
 ing-wax in a verti- 
 cal plane and on the 
 zero-line a piece 
 of mirror, 10 cm. 
 square, with the 
 FlG 220 amalgam removed 
 
 from the upper 
 half (Fig. 220) . Cement each ring to the end of a wire, fixed 
 
LIGHT. 299 
 
 vertically in a small block of wood, the length of wire to 
 be such that the centre of each ring is 5 cm. above the board 
 supporting the mirror. Draw on the block in the plane of the 
 ring a line to aid in obtaining the position of the ring on the 
 linear scale. Set one of the rings behind the mirror, distant 
 from it several centimetres, and the other one in front. Now, 
 the upper half of the first ring can be seen through the un- 
 silvered part of the mirror when the eye is placed level with 
 the line dividing the silvered from the unsilvered part, and 
 the lower half of the other one will give an image behind the 
 mirror. Carefully adjust the position of the ring in front of 
 the mirror till the image of its lower half forms an exact con- 
 tinuation of the upper half of the one back of the mirror, 
 making the ring and cross seem complete on moving the eye 
 either to the right or the left. This position is easily deter- 
 mined by observing that when the front ring is too near the 
 mirror, on moving the eye to the right the image and object 
 will appear to separate, the image going to the left ; and if too 
 far from the mirror, the reverse is the case. Now read off on 
 the scale the distance of each ring from the mirror. Repeat 
 the experiment several times, and obtain the mean of the 
 measurements. Inference. 
 
 529. Exercise.* Procure a large pane of window-glass, 
 say, 1*2 by 20. Support it in a vertical plane back of a rectan- 
 gular opening, smaller than the glass, cut in a large sheet of 
 cardboard. The planes of the cardboard and glass make a 
 small angle with each other (Fig. 221). Place a lighted candle, 
 L, between the screen and the glass, leaving the image alone 
 visible through the opening. Behind the glass set a large bottle 
 of water, finding, by trial, a position where to one standing in 
 front of the opening in the cardboard the candle appears to be 
 
300 
 
 PRACTICAL PHYSICS. 
 
 burning within the bottle. Compare the distances of the candle 
 and the bottle from the glass plate. Inference. 
 
 o 
 
 FIG. 2-21. 
 
 The above experiment, in addition to locating the apparent 
 position of the image of an object in a plane mirror, also illus- 
 trates one method of producing spectral phenomena on the stage. 
 
 530. Exercise. Determine the law for the number of 
 images in cases of multiple reflection. 
 
 Cut out of mirror-plate two pieces, each 15 cm. square. 
 Hinge them together at one edge by pasting a strip of cotton 
 across the backs of both. Stand them vertically on a sheet of 
 
 paper on which is drawn a protractor 
 scale, placing the axis of the mirrors 
 in line with the centre of the circle 
 (Fig. 222) . Now stand a lighted taper 
 between the mirrors, and count the 
 number of images for any specified an- 
 gle of the mirrors. Try 90 , 60 , 45 , 
 and 40 . Note the relation sustained 
 by the angle of the mirrors to the en- 
 tire circle, and compare in each case 
 with the number of images. Account 
 for so many images being visible. 
 Place two such mirrors parallel, and note the number of 
 
 \ 
 
 FIG. 222. 
 
LIGHT. 301 
 
 images. Explain. Show that the result agrees with the law 
 governing the number of images. 
 
 Note the image of a candle in a very thick mirror. Explain. 
 Verify your explanation by blackening one surface of a thick 
 piece of glass, with the amalgam removed, and observing the 
 image of the candle in it. To blacken the glass hold it in the 
 smoke emitted by burning turpentine or camphor. 
 
 531. Exercise. Coat with asphaltum varnish a glass tube 
 30 cm. long and 2.5 cm. in diameter. Make a pin-hole in a 
 small piece of cardboard ; hold it across one end of the tube, 
 with the pin-hole in the axis of the tube. Now, with the open 
 end to the eye, look at the bright sky. Describe the appear- 
 ance, and account for it. 
 
 6. Curved Mirrors* 
 
 . 532. Exercise.* Determine how a concave mirror dis- 
 poses of incident light. 
 
 First. Let a small beam of light be incident, perpendicu- 
 larly on the mirror. The floating dust will mark out the path of 
 the rays, showing that the rays are reflected through a point 
 called the principal focus. Measure the distance from this point 
 to the vertex of the mirror. Twice this distance gives the radius 
 of curvature, and hence enables you to locate the centre. Mark 
 both of these points in front of the mirror with pointers held 
 by clamps, or by wires set in large corks for supports. 
 
 Sunlight can be used for finding the principal focus, by as- 
 certaining the point of greatest intensity of light in front of the 
 mirror ; that is, where the light, reflected on a piece of card- 
 board, produces the smallest bright spot. 
 
 Secondly. Let a pencil of light diverging from a point 
 beyond the' centre of curvature be incident on the mirror, and 
 
302 PRACTICAL PHYSICS. 
 
 find where it focuses with reference to the centre and the prin- 
 cipal focus, as shown by the illuminated dust-particles. In like 
 manner locate in succession the focus for a pencil of light 
 diverging from the centre, from a point between the centre and 
 the principal focus, from the principal focus, and from a point 
 between the principal focus and the mirror. 
 
 Tliirdly. Let a converging pencil be incident on the mirror, 
 and determine its course after reflection. 
 
 A simple way to obtain a diverging pencil for the above ex- 
 periments is to let a beam of light be incident on a lens having 
 a focal distance of about 50 cm. The lens will refract the 
 light through a point, producing a pencil diverging from its 
 focus. For a converging pencil, the part between the lens and 
 the focus may be used. 
 
 533. Exercise.* Ascertain the properties of a convex 
 spherical mirror. 
 
 Proceed as in the last experiment, making such modifications 
 as the problem demands. 
 
 534. Exercise.* Determine the character of the images 
 of an object given by spherical mirrors 
 
 Support the concave mirror in a vertical position on a long 
 table, and place in front of it a lighted candle at a distance 
 greater than the radius of curvature of the mirror. On the 
 same side of the mirror support a small paper screen, finding 
 by trial a position for it where a sharply defined image of the 
 candle is formed on it. Compare the distances of the object 
 and image respectively from the mirror; also, size, position, 
 etc. Now gradually move the candle nearer to the mirror and 
 determine the character of the image for each new position, 
 particularly when the light is at the centre of curvature, between 
 the centre and the principal focus, at the principal focus, and 
 between the focus and the mirror. 
 
LIGHT. 303 
 
 In the case of the convex mirror, what is the character of the 
 image? Ascertain the effect that the position of the object has 
 upon the character of the image. 
 
 535. Exercise. Measure the radius of curvature, and 
 hence the focal distance of a concave spherical mirror. 
 
 First Method.* Support the mirror vertically on a long 
 table ; place in front of it a sheet of cardboard in which is cut 
 a hole 1 cm. square. Illuminate the opening by placing a lamp 
 back of it, and place a screen to receive the image of it formed 
 by the mirror. Move the screen till the outline of the image is 
 brightest and has the sharpest outline. Measure the distance 
 of the object from the mirror, and also that of the image. If 
 these are represented by a and b respectively, and the radius by 
 R, then 
 
 I - * = 1 = I whence R = 2a ^ and f = 
 
 nth TJ ^ .17, ' 
 
 ab 
 
 b " R~ f a + b ' a-\-b 
 
 Second Method. Insert a small piece of stiff white paper in 
 the eye of a darning-needle to serve as an index, and at the 
 same time to make it more conspicuous. Set it vertically in 
 front of the mirror, finding by trial a place where the point of the 
 paper coincides with the image of it seen in mid-air. Measure the 
 distance from the pointer to the vertex of the mirror. Obtain 
 tii,' average of several trials ; the result will be the radius of 
 curvature. Why? How would you get the focal distance? 
 
 Third Method. Place the spherometer on the curved sur- 
 face, and, proceeding as in Art. 11, obtain the altitude of the 
 segment that would be cut off by the plane of the three legs of 
 the instrument. Let h = this altitude, and s = the side of the 
 
 equilateral triangle formed by the feet. Then R = -- -I , 
 
 6h 2 
 
 a relation deduced geometrically from the properties of a sphere. 
 
304 
 
 PRACTICAL PHYSICS. 
 
 This method cannot be applied to the ordinary glass mirrors, 
 as they are usually plano-convex lenses silvered on the convex 
 surface. 
 
 536. Exercise. Measure the radius of curvature of a con- 
 vex spherical mirror. 
 
 First Method. Locate the position of the image as directed 
 in Art. 528. Measure the distance of the object, and also the 
 image, from the vertex of the mirror. Then 
 
 112 n 2ab 
 
 - = . , whence H = . 
 
 b a R a b 
 
 Second Method.* Cut a round hole 5 cm. in diameter in a 
 sheet of cardboard, and support it several centimetres in front 
 
 of the mirror and per- 
 pendicular to its axis 
 (Fig. 223). Let a strong 
 beam of light be inci- 
 dent on the cardboard, 
 part passing through the 
 opening, making a round 
 image on the mirror, and 
 
 li a second one on the 
 
 PIG. 223. , , 
 
 cardboard, by reflection. 
 
 Measure the diameter, DE, of the spot on the screen ; FH, or 
 AB of the opening or spot on the mirror ; and LK, the distance 
 from the screen to the mirror. Then if AB = a, DE = 6, LK 
 = c, and KC =/= JR, we have, by geometry, 
 
 M 
 
 B 
 
 , R _ 
 
 " ~ 
 
 2ac 
 
 Third Method. Employ the spherometer as in Art. 535. 
 
 537. Exercise.* Compare as to brightness and sharpness 
 of outline the image given by a concave mirror when the light is 
 
LIGHT, 
 
 305 
 
 cut off from all but the central portion, with that when the 
 whole surface of the mirror is used. Bend a piece of bright 
 tin into a semicircular form, place it on a sheet of white paper 
 with its concave surface toward the light, and. notice how it 
 reflects the rays. Explain. 
 
 VI. SINGLE REFRACTION OF LIGHT. 
 
 538. Apparatus. Porte Lumiere, Rectangular Battery-Jar, 
 Protractor, Cardboard, Prisms, Darning-Needles, Spectrometer, 
 Plane Mirrors, Globular Receiver, etc. 
 
 539. Exercise.* Measure the index of refraction of a liquid. 
 Cover one face of a large glass rectangular battery-jar with 
 
 paper, out of the centre of the covering having cut as large a cir- 
 cle as possible. Across this circular opening draw a horizontal 
 and a vertical diameter (Fig. 224) . Graduate the margin of the 
 circle to degrees, the ex- 
 tremities of the vertical 
 diameter to be marked 
 zero, and those of the 
 horizontal one 90 . Pro- 
 vide a strip of card- 
 board considerably wid- 
 er and longer than the 
 top of the jar, and cut 
 in it, cross-wise, a slit 
 
 FIG. 224. 
 
 2 mm. wide and 5 cm. 
 
 long. Fill the jar with water exactly to the horizontal diame- 
 ter of the circle. Place the cardboard containing the slit on 
 top of the jar. With a plane mirror supported in a retort- 
 holder reflect a strong beam of light through the slit at such 
 
 \\ 
 
306 
 
 PRACTICAL PHYSICS. 
 
 an angle as to be incident on the liquid exactly back of the 
 centre of the circle. Read off on the scale the angle that the 
 incident ray makes with the vertical, and also that made by 
 the refracted ray seen in the liquid. Change the position of the 
 slit and the mirror so as to get a number of these angular 
 measurements for different beams. Divide the sine of each 
 angle of incidence (see Table XX.) by the sine of the corre- 
 sponding angle of refraction, and the average of these quo- 
 tients will be the index of refraction. 
 
 A large square bottle, or a tin tank with one glass face, may 
 be substituted for the battery- jar. In using the battery- jar it 
 will render the rays more distinct to cement black paper on the 
 faces. 
 
 Any of the following liquids may be used for this experi- 
 ment: Water, alcohol, naphtha, turpentine, kerosene, etc. 
 
 540. Exercise. Determine the index of refraction of 
 
 glass. 
 
 First Method.* Tack across the opening of the porte 
 
 lumiere, or lantern, a piece of cardboard in which is cut a 
 
 vertical slit 1 mm. 
 wide and 3 cm. long. 
 In the path of the 
 ribbon of light which 
 passes through the slit 
 place a glass prism 
 of known angle (see 
 Art. 522), supported 
 Flo 225 on a smooth , hori- 
 
 zontal board, with 
 
 its edges parallel to the plane of the ribbon of light, and 
 
 intercepting it at such an angle that it suffers the least deviu- 
 
LIGHT. 307 
 
 tion from its course ; a result recognized by slowly turning the 
 prism about its axis till the bright-colored image on the wall 
 departs least trom the line of light before it suffers refrac- 
 tion. Now set perpendicularly in the board a darning-needle, N 1? 
 to mark the place where the light is incident on the prism (Fig. 
 225). Set a second one, N 2 , in the shadow cast by N x . Remove 
 the prism and set a third one, N 3 , in the shadow now cast by 
 N\. Draw lines through the points marked by the needles, and 
 measure with a protractor the angles between them. Make 
 a number of trials, and determine their average. This will 
 be the angle of deviation for the prism. If a = the angle of 
 the prism and d the deviation, then the index of refraction, 
 
 sin A (a-f- d) 
 of i = ^rr t -. 
 
 Kin a 
 
 Second Method. Place the prism on the stand of the spec- 
 trometer of Art. 522, a form in which the telescope is attached 
 to a movable arm carrying an index moving over a graduated 
 circle. Place the prism in the position of least deviation. 
 This is found by observing the slit through the telescope, at the 
 same time slowly turning the prism till the dark vertical line 
 seen in the green part of the image moves out of the field 
 in the same direction on turning the prism either way. Now 
 read the index of the telescope-arm when the cross-hairs are 
 exactly on the dark line in the green. If not visible, use the 
 dark line in the yellow. Then remove the prism, and obtain 
 the reading when the slit is in the field of the telescope. Ob- 
 tain the average of several determinations of these readings, 
 and their difference will be the angle of deviation for the prism. 
 To obtain the index of refraction, apply the formula of the first 
 method. 
 
 Obtain the index, using dark lines seen in other colors of the 
 spectrum. 
 
308 
 
 PRACTICAL PHYSICS, 
 
 541. Exercise.* Using the apparatus of Art. 539, place 
 the cardboard against the end, so that the slit is near the 
 bottom of the jar. Now place a plane mirror, so as to throw 
 a beam of light on to a second mirror lying on the table close 
 to the slit, and incident at such an angle that it passes through 
 the slit into the liquid, reaching the surface opposite the centre 
 of the circle. Observe the course of the light after incidence, 
 taking the readings on the graduated scale. Explain. 
 
 Raise the slit, changing, accordingly, the position of the 
 mirror till the ray, after incidence, passes out along the surface. 
 Measure the angle of incidence, thus obtaining the critical angle 
 for the liquid. Try different liquids. 
 
 542. Exercise.* Procure a globular receiver, about 10 
 cm. in diameter, with two tubulures (Fig. 226). Close each 
 neck with good corks, through which pass as large glass tubes 
 
 as possible. Coat the outside of the 
 globe with black varnish, except the 
 area included within the small circle, 
 indicated by the dotted line, op- 
 posite the neck to be used as the 
 horizontal one. Fill the globe with 
 water, having first closed the horizon- 
 tal tube with a cork ; connect the 
 upper one with a rubber tube to a 
 tank supplying water, and adjust the 
 apparatus in the opening of the porte 
 
 lumiere so that the light is incident on the unvarnished part, 
 and all light is cut off from entering the room. Now remove the 
 stopper from the* exit- tube, and notice how the light follows the 
 stream of water. Explain. A strip of red glass placed between 
 the globe and the source of light produces a very striking effect. 
 
 FIG. 226. 
 
LIGHT. 
 
 309 
 
 543. Exercise.* Let a small beam of light be incident 
 perpendicularly on one of the faces about the right angle of 
 what is known as the right-angled prism. Observe the course 
 of the light. Explain. 
 
 VII. LENSES. 
 
 544. Apparatus. Porte Lumiere, Convex and Concave 
 Lenses, Cardboard, Scales, Telescope, Spherometer, Candles, 
 
 etc. 
 
 545. Exercise. Measure the principal focal distance of 
 a convex lens. 
 
 First Method. Tack a piece of cardboard, about 15 cm. 
 square, across one end of a common lath (Fig. 227). Be- 
 ginning at the cardboard, lay off a half -centimetre scale on 
 the wooden strip. Now 
 hold the lens on the 
 strip parallel to the 
 screen, direct the ap- 
 paratus toward the sun , 
 and slide the lens along 
 till a position is found 
 where the light forms 
 the smallest and bright- 
 est image of the sun on the screen. Read off on the scale the 
 distance of the lens from the screen for the focal distance 
 required. Obtain the mean of several independent determi- 
 nations. 
 
 Second Method.* Support the lens in a vertical plane, plac- 
 ing on one side of it a cardboard screen, and on the other a 
 sheet of cardboard with a circular aperture, 1 cm. in diameter, 
 having two threads, mutually perpendicular, stretched across 
 
 FIG. 227. 
 
310 PRACTICAL PHYSICS. 
 
 its centre, and illuminated on the opposite side from the 
 lens by a lamp or candle placed near the opening. Adjust 
 the apparatus so that the centre of the opening lies in the 
 principal axis of the lens. Now find by trial a position for 
 the lens between these sheets of cardboard where a sharply 
 defined image of the threads is formed on the other screen. 
 Measure the distances between the lens and the image and ob- 
 ject respectively, representing them by a and &, then the focal 
 
 distance = '=- Obtain the mean of several determinations. 
 a-r-6 
 
 This method neglects the thickness of the lens. As this is 
 usually small, the value of / would not be materially altered. 
 
 Third Method.* Using the apparatus of the last method, 
 adjust the distances so that the image and object are equal in 
 size. Then one-fourth of the distance between them is the 
 focal distance of the lens. Obtain the mean of several deter- 
 minations. 
 
 Fourth Method. Focus a small telescope, as a common spy- 
 glass, on some object so far distant that the rays from it may 
 be considered as parallel without sensible error. Now place the 
 lens, whose focal distance is to be measured, in front of the 
 telescope, and look through the two at some figure on a piece 
 of cardboard held in a clamp. Move the cardboard to such a 
 distance from the lens as to be clearly visible. The distance of 
 the cardboard from the lens is the focal distance sought. Ob- 
 tain the mean of several trials. 
 
 Fifth Method. If the lens has sufficient surface, the radius 
 of curvature of each surface can be determined by the sphero- 
 meter, as in the case of mirrors (Art. 535). Representing by 
 r and r' the radii of curvature of the two faces, and by i, the 
 
 index of refraction, then f= T~/ , ;V The average in- 
 
 L 1 \r -f- r ) 
 
LIGHT. 
 
 311 
 
 dex of crown glass may be taken as 1.5 without sensible error. 
 
 2 rr* 
 Hence, /= q; r ^ koth surfaces have the same curvature, 
 
 then r = r' and/=r, that is, the focal distance equals the ra- 
 dius of curvature. If the lens is plano-convex, then r' = oo 
 and/=2?\ For the meniscus lens the radius of curvature for 
 the concave surface must be taken as negative. 
 
 546. Exercise. Measure the principal focal distance of a 
 concave lens. 
 
 First Method.* Cover the face of the lens, that is turned 
 away from the light, with paper, in which is cut a smooth, round 
 hole 2 cm. in diameter, exactly over the optical centre. Sup- 
 port the lens so that a beam of light parallel to the principal 
 axis is incident upon it. Hack of the lens, and parallel to it, 
 place a card- 
 board screen. 
 The light, after 
 passing through 
 the lens, will 
 diverge as if it 
 came from the 
 principal focus, 
 and will form 
 a round image 
 on the screen. 
 
 Hence, if we measure the distance AB (Fig. 228), the diameter 
 of the image ; the distance CD, the diameter of the aperture ; 
 and the distance EH from the lens to the screen ; we can com- 
 pute the focal distance EF, neglecting the thickness of the lens, 
 as it is usually small. Representing these distances by a, 6, 
 
 Flo. 228. 
 
312 PRACTICAL PHYSICS. 
 
 and c, respectively, we derive from the triangles in the figure 
 , be 
 /== ^6- 
 
 By moving the screen till AB = 2CD, the distance of the 
 screen from the lens is the focal distance. 
 
 Try both ways, obtaining the mean of several determinations. 
 
 Second Method. Place in contact with the concave lens a 
 convex one, making the combination equivalent to a convex 
 lens. Measure the focal distance of the combination, as in 
 
 Ff' 
 
 Art. 545, and also of the convex lens alone. Then f= = -, 
 
 f ./ 
 
 in which F is the focal distance of the combination, and /' of 
 the convex lens. 
 
 Third Method. Employ the spherometer as in Art. 545, 
 making the r's in the formula negative when the surface is con- 
 cave. 
 
 547. Exercise.* Ascertain how a lens disposes of a 
 pencil of light. 
 
 First. After determining the focal distance, support the 
 lens in a clamp, and let a diverging pencil of light be incident 
 upon it, as in Art. 532. Ascertain where the rays focus when 
 the light diverges from a point beyond twice the focal distance, 
 at twice the focal distance, at less than twice but beyond the 
 focus, at the focus, and, finally, between the focus and the lens. 
 Test both convex and concave lenses. 
 
 Secondly. Try a converging pencil. In the case of a con- 
 cave lens vary the degree of convergence by using lenses of 
 different focal distances to produce the pencil of light. 
 
 548. Exercise.* Determine the character of the images 
 formed by lenses. 
 
LIGHT. 313 
 
 First. Place on a long table a cardboard screen, a mounted 
 convex lens of known focal distance, and a lighted lamp or 
 candle, arranging them in the order named, and with their 
 centres in the same horizontal line. Place the light succes- 
 sively at more than twice the focal distance, at twice the focal 
 distance, at less than twice but beyond the focus, and, finally, 
 between the focus and the lens, determining in each case, if 
 possible, the position of the screen where the well-defined image 
 of the flame is formed upon it. Compare the image in each 
 case with the object as regards size and position. 
 
 Secondly. Compare the image formed when a lens of 
 small diameter is used with that when one considerably 
 larger is employed and adjusted to give an image of the 
 same size. 
 
 Thirdly. Cover a lens with a paper disk in which is cut 
 a ring of holes near the circumference, and also a ring near 
 the centre. Mount the lens so that a beam of light is inci- 
 dent upon it and focuses on a screen. Ascertain if the outer 
 ring of holes focuses at the same distance from the lens as 
 the inner row. 
 
 Fourthly. Compare the definition of the image formed 
 when light is admitted through the whole lens with that given 
 when the light incident on the outer edge of the lens is cut 
 off by a paper ring placed over it. 
 
 Fifthly. Study the images given by a concave lens. 
 
 549. Exercise. Measure the magnifying power of a 
 lens. 
 
 First Method. Measure the focal distance of the lens, then 
 
 25cm. 
 the magnifying power = j h 1, in which 25 cm. is taken 
 
 as the distance of distinct vision. 
 
314 
 
 PRACTICAL PHYSICS. 
 
 Second Method. Focus the lens on a finely divided scale 
 securing clear definition. Place a second scale at the dis- 
 tance of distinct vision, 25 cm. Now look with one eye 
 through the lens at the one scale, and with the other eye at 
 the second one. On the eye's becoming accustomed to the 
 conditions of the experiment, the magnified image of one 
 scale will be seen superposed on the other. Count how many 
 divisions of the magnified scale exactly cover a certain num- 
 ber on the other. Divide the latter by the former, the 
 quotient will be the magnifying power. 
 
 VIII. DISPERSION. 
 
 550. Apparatus. Porte Lumiere, Cardboard, Lenses, 
 Prisms, Glass Bulb, etc. 
 
 551. Exer- 
 cise.* Tack 
 
 across the open- 
 ing of the porte 
 lumiere, or lan- 
 tern, a piece 
 of cardboard in 
 which is cut a 
 very narrow slit 
 with straight 
 smooth edges. 
 Project with a 
 convex lens of 
 about 30 cm. 
 focus an image 
 of this slit on 
 a distant white 
 screen. Close to the lens, between it and the screen, place 
 
 FIG. 229. 
 
LIGHT. 315 
 
 a prism of crown glass (Fig. 229), of 60 angle, and change 
 the position of the screen, keeping it at the same distance 
 from the lens, to a position where the light falls perpendicularly 
 upon it. Turn the prism around till the least deviation is 
 secured. Describe the image. 
 
 Compare the spectrum given by a prism of crown glass with 
 that given by one of flint glass, or one of carbon disulphide 
 
 Try two prisms, setting the second one behind the first, 
 with its base turned in the same direction. 
 
 To make a carbon disulphide prism proceed as follows : 
 
 Cut off the ends of a stout glass tube, 4 cm. in diameter, 
 by planes inclined to each other at an angle of 60, and 
 their line of intersection perpendicular to the axis of the tube 
 (see page 354). Grind the ends smooth on a flat sand- 
 stone. Drill a hole through the side of the tube. This 
 hole had better be made before cutting off the ends, to 
 avoid lost labor from a possible breaking of the tube in 
 drilling it. Cement with good glue two pieces of the best of 
 thin plate-glass on these faces ; mirror-plate with the amal- 
 gam scratched off is the best, as it is more likely to be true. 
 When dry, fill the angles on the outside between the glass 
 plate and the tube with a cement made of glue dissolved in 
 common molasses by the aid of heat. Now fill the cell through 
 the hole In the side, cork, and cover the cork with cement. 
 
 The cell must not be filled in the vicinity of a flame, as 
 carbon disulphide is very inflammable. 
 
 552. Exercise.* Project, as in the last experiment, a 
 spectrum of some strong light on a screen. Cut a hole 
 through this screen so that one color passes through and is 
 incident on a second prism. Ascertain if any new colors are 
 obtained by the second dispersion. Inference. 
 
 \V\ 
 
 ith ^SJy\ 
 
 ide. 
 
316 PEACTICAL PHYSICS. 
 
 White printing-paper or cotton cloth, pasted over a light 
 wooden frame, will make a suitable screen. 
 
 553. Exercise.* Project, as directed in Art. 551, a 
 spectrum on a screen, using a short slit. Behind the prism 
 place a second prism with its edges perpendicular to the 
 edges of the first, and in a position to receive 1 the light on 
 issuing from the first. By this arrangement there will be in- 
 cident on the second prism rays of each color, each one by 
 itself, making it possible to determine whether a prism re- 
 fracts each color alike or not ; for if it does, the new spec- 
 trum will occupy a position parallel to the old one. Inference. 
 
 554. Exercise.* Project a spectrum on a screen as di- 
 rected in Art. 551. Now place a second prism like the first 
 behind the first, but reversed in position. Observe the char- 
 acter of the image. Slide a piece of cardboard along gradu- 
 ally between the prisms and observe the changes in the image. 
 
 Try two prisms reversed in position, one of them crown 
 glass, and the other flint. 
 
 555. Exercise.* Project a spectrum on the screen as 
 directed in Art. 551. Between the prism and screen hold a 
 large convex lens to receive the spectrum. Move the lens 
 along the line of light, and it will be possible to find a posi- 
 tion where a white image of the slit is produced on the 
 screen. 
 
 If the spectrum is received on a concave mirror a similar 
 result can be obtained. 
 
 What does this experiment prove the colored image to 
 be? 
 
LIGHT, 317 
 
 556. Exercise.* Fill an air-thermometer bulb, 4 cm. 
 in diameter, with clear water. In front of the porte ramie re, 
 or lantern, place a large white-paper screen in which is a 
 circular opening about 3.75 cm. in diameter. Support the bulb 
 in a clamp so that the cylindrical beam of light is incident 
 on it. There will be formed on the screen a circular spectrum 
 resembling a rainbow. The distinctness of the bow will de- 
 pend on the distance of the bulb from the screen, and the 
 nearness of the bulb to a true sphere. With sunlight in a 
 very dark room the secondary bow can be seen. 
 
 IX. COLOR. 
 
 557. Apparatus. Forte Lumiere, Colored Paper, Prisms, 
 Lenses, Cardboard, Color-Top, Colored Glass, etc. 
 
 558. Exercise. Paste a strip of white paper 3 cm. long 
 and '2 mm. wide on a piece of black cardboard several times 
 larger. View this whole strip, placed in a strong light, 
 through a glass prism, holding its edges parallel to the 
 length of the strip. Examine in a similar manner strips of 
 red, blue, yellow, etc., paper. What color or colors do you 
 find in the light reflected by each paper? 
 
 559. Exercise.* Project the solar spectrum as directed 
 in Art. 551. Examine the color of pieces of colored paper 
 when held successively in the different colors of the spec- 
 trum. Explain. 
 
 560. Exercise.* Place common salt in the wick of an 
 alcohol lamp and analyze the light emitted by it as in Art. 
 558. Examine a highly colored picture by its light and ac- 
 count for the appearance. 
 
318 
 
 PRACTICAL PHYSICS. 
 
 PURPL 
 
 561. Exercise. Procure at a toy store a Newton's color- 
 top, or any top having a heavy metallic disk. Cut out of 
 colored paper a disk about 10 cm. in diameter, 
 with a small opening at the centre of the 
 size of the top-handle. Slit them along a 
 radius (Fig. 230), from circumference to FIG. 230. 
 
 centre, so that two or more of them can be placed together, 
 
 exposing any propor- 
 tional part of each 
 one as desired. Select 
 seven disks whose 
 colors most nearly 
 represent those of the 
 solar spectrum, put 
 them together so that 
 equal portions of the 
 colors are exposed, 
 and then place this 
 compound disk over 
 the handle of the top 
 when rapidly rotat- 
 ing. Examine the 
 
 FIG. 231. 
 
 colors in a strong light. 
 
 Try violet, red, and green disks, exposing 
 equal portions. Inference. In like manner 
 try red, green, and blue. Inference. 
 
 Try two disks whose colors are opposite in 
 Fig. 231. Inference. Try any two alter- 
 nate colors. Inference. Ascertain the effect 
 of using unequal portions. Try a black disk 
 and a white one. 
 
 A small whirling machine, Fig. 232, or 
 an electric motor, may be substituted for the top. 
 
LIGHT. 
 
 319 
 
 562. Exercise.* Project on the screen the spectrum of 
 the sun or the electric light. By means of a large lens converge 
 the rays to a focus, producing a white image of the slit on the 
 screen. Prepare two strips of black cardboard, in each of 
 which is cut a slit 2 mm. wide and 2.5 cm. long, and insert 
 them in a strip of blackened wood with a groove cut in it so 
 that the slits can be adjusted at any desired distance apart 
 (Fig. 233). Place this screen between the lens and the 
 prism and set the slits so that one color passes through 
 each opening. Observe the color of the image formed by the 
 lens. 
 
 Ascertain if any two col- 
 ors will produce a white 
 image. 
 
 Intercept one of the 
 spectrum colors by a nar- 
 row strip of cardboard 
 held by a clamp between 
 the prism and the lens, and 
 note the color of the image. 
 
 ^-j/ 
 
 FIG. 233. 
 
 563. Exercise.* Pro- 
 ject a bright continuous spectrum on the screen, look steadily 
 at it for a minute, at the end of which time, without removing 
 the gaze from the screen, shut off the light giving the spectrum, 
 and turn up the gaslight or lamp. Observe the change in the 
 image as you continue to look at the screen. Explain. 
 
 564. Exercise. Lay a circular piece of blue paper, 15 
 mm. in diameter, with a thread attached, on a small sheet of 
 white or gray paper. Look steadily at the blue paper in a strong 
 
320 PRACTICAL p/irxivs. 
 
 light for 15 seconds, then, without moving the eye, suddenly 
 pull away the blue disk, and observe the color of the after- 
 image. Try other colors. 
 
 565. Exercise.* Project on a screen with a lantern, or 
 porte lumiere, and lens an image of a round hole in a piece of 
 cardboard. Look steadily at the image for 25 seconds, then, 
 without removing the eye, withdraw the cardboard, and observe 
 the color of the after-image. 
 
 Repeat the experiment 
 with the aperture covered 
 with red glass. Try glass of 
 other colors. Try the chemi- 
 cal tank (Fig. 234) filled 
 with a solution of picric acid. 
 Try other colored solutions. 
 
 FIG 2Mi 566. Exercise.* Paste 
 
 an image of an object cut 
 
 out of opaque paper on a piece of colored glass of the size of 
 a lantern slide. Project an image of this object on the screen, 
 gaze steadily at it for a few moments, then suddenly cut off the 
 projecting light, and turn up the gas or lamp. Observe the 
 after-image. Explain. 
 
 X. SPECTRUM ANALYSIS. 
 
 567. Apparatus. Porte Lumiere, Prisms, Spectroscope, 
 Platinum Wire, Colored Glass, Test-Tubes, etc. 
 
 568. Exercise.* Proceeding as in Art. 551, project the 
 solar spectrum on* the screen, using a very narrow slit and a 
 
LIGHT. 321 
 
 carbon disulphide prism. If the focusing is carefully done, and 
 the room is quite dark, a number of dark lines will be seen 
 crossing the spectrum vertically, showing that the solar spec- 
 trum is not continuous. Diagram their position. 
 
 These lines are easily seen by placing the eye in the 'pencil of 
 light diverging from the prism. 
 
 569. Exercise. Turn the slit of the spectroscope (Fig. 
 218) toward a distant white building. Focus the telescope, and 
 place the prism at the angle of least deviation for that part of 
 the spectrum in the field. It will be found easier to study the 
 spectrum if the telescope tube is thrust through a sheet of card- 
 board to cut off from the eye the light not passing through the 
 apparatus. 
 
 Make a map of a few of the more prominent lines, by taking 
 the reading of the angular scale found on the platform of the 
 instrument when the intersection of the cross-hairs is on the 
 dark line, and laying it off on one side of a rectangle, say 10 
 cm. long, representing the spectrum. As the ends of the rect- 
 angle correspond to the readings given by the angular scale of 
 the spectroscope for the limits of the spectrum, the number of 
 degrees corresponding to each centimetre of the rectangle is 
 easily ascertained, 
 and each dark line 
 located by comput- 
 ing how many centi- 
 metres correspond 
 to the angular dis- 
 tance the line is from 
 the end of the spec- FIG 235 
 
 trum. 
 
 As spectroscopes are expensive, the student may construct 
 one by observing the following directions : 
 
322 PRACTICAL PHYSICS. 
 
 Make out of heavy pasteboard a box 30 cm. long (Fig. 235), 
 whose cross-section is a rectangle. One of the lateral faces 
 should be shorter than the opposite one, as shown in Fig. 236. 
 
 FIG. 236. 
 
 In the oblique end cut a small aperture 3 mm. in diameter and 
 considerably nearer the shorter face. In the opposite end cut 
 a rectangular opening 3 cm. square, and cement over it a slit 
 prepared by pasting tin foil smoothly over a piece of clear 
 glass, and cutting a line through the foil 1.5 cm. long by 
 drawing a knife-edge across it. The depth and width of the 
 box will be determined by the size of the prism P. Paint the 
 inside of the box a dead black, using thin shellac varnish and 
 lamp-black. Set the prism in the position shown in Fig. 230, 
 fastening it in place by gluing blocks in the angles. The box 
 must be provided with a tight-fitting cover. The prism described 
 in Art. 551 will show many of the Fraunhofer lines on direct- 
 ing the slit S toward the bright sky and holding the eye close 
 to the opening E, looking in a line perpendicular to that face. 
 
 570. Exercise.* Take a piece of platinum wire of about 
 the diameter of a fine sewing-needle ; bend the end into a small 
 loop about 2 mm. in diameter ; fuse a small bead of the salt to 
 be experimented with into the loop, and fasten the wire in a 
 clamp so that the bead is brought into the front edge of a gas 
 or alcohol flame at a point a little below the slit of the spectro- 
 
LIGHT. 323 
 
 scope. On looking through the telescope a bright-line spectrum 
 will be seen. Examine in this way the spectra of the following 
 substances, mapping the more prominent lines as directed in 
 Art. 569 : A salt of lithium, potassium, sodium, strontium, 
 barium, etc. Search for Fraunhofer lines occupying the same 
 positions as these bright ones. 
 
 571. Exercise.* Direct the slit of the spectroscope 
 toward the electric light. Place close to the slit a Bunsen 
 flame, and hold in it a pellet of sodium. Mark the position 
 of the dark line crossing the spectrum. Now shut off the 
 electric light, and a bright line will be seen occupying the 
 place of the dark one. Explain. 
 
 572. Exercise.* Observe the spectrum of sunlight when 
 blue glass is placed over the slit of the spectroscope. Try glass 
 of some other color. Ascertain the effect of superposing two 
 or more pieces. Try a test-tube filled with an ammoniacal 
 solution of copper sulphate. Try, successively, solutions* of 
 picric acid, quinine, etc. Compare the spectrum with the 
 color of the substance. 
 
 573. Exercise. Place before the slit of the spectro- 
 scope a test-tube containing a few clippings of copper. Pour 
 on the copper a few drops of nitric acid, and study the 
 spectrum of sunlight after passing through the reddish- 
 brown gas ' which will now fill the tube. 
 
 574. Exercise.* Support before the slit of the spectro- 
 scope a Geissler's tube charged with some known gas, and 
 observe the spectrum on illuminating the tube with an induc- 
 tion coil. 
 
 1 After chemical action has stopped, cork the tube to prevent the fumes from escap 
 intf and corroding the metallic parts of the spectroscope. 
 
324 PRACTICAL PHYSICS. 
 
 XI. INTERFERENCE OF LIGHT. 
 
 575. Apparatus. Porte Lumiere, Thick Glass, Iron 
 Clamp, Window-Glass, India-Ink, Lenses, Nobert Grating, 
 Perforated Cardboard, Mother-of- Pearl, etc. 
 
 576. Exercise.* Procure two square pieces of heavy 
 plate glass, about 8 cm. on an edge. Clean- them thoroughly, 
 then press them gently together by means of common spring 
 clothes-pins on three of the corners, and the supporting clamp 
 at the fourth corner. Let a beam of sunlight be incident 
 on the surface at an angle of 45. In the reflected beam 
 place a lens, and project an image of the porte-lumiere open- 
 ing on the screen. .Notice the colors on the image as the 
 pressure at the clamp is changed. Explain. 
 
 Beautiful colors are seen if two such pieces of glass are 
 firmly pressed together at their centres by means of a small 
 iron clamp. 
 
 577. Exercise.* Make out of coarse iron wire a ring 
 8 cm. in diameter, soldering it to a wire for a handle. Dip 
 the ring into a soap solution prepared as directed in Art. 80, 
 and support it in the beam of light in the place of the glass 
 plates in the last experiment. Observe the play of colors 
 across the image on the screen. 
 
 Observe the phenomenon when one-colored light is employed. 
 
 578. Exercise. Paint one side of a strip of window- 
 glass with India-ink, rendering it opaque. When dry, rule, 
 with a fine needle, a number of parallel lines, as close to- 
 gether as possible, by cutting through the ink to the glass. 
 
LIGHT. 325 
 
 Now stand about 5 m. away from a lighted lamp and view it 
 through this grating. P^xplain. 
 
 View through this grating a slit placed across the porte 
 lumiere. 
 
 579. Exercise.* Project with a lens an image of a slit 
 placed across the porte lumiere, having the room as dark as 
 possible. Over the slit place a Nobert grating with its lines 
 parallel to the slit. Observe the series of spectra. Compare 
 the relative spaces occupied by the colors with the relative 
 spaces when the spectrum is obtained by a prism. 
 
 Photographs of these gratings are nearly as efficient as the 
 originals, and cost only about one-fourth as much. 
 
 580. Exercise.* Reduce the opening in the porte lumiere 
 to a circular hole 2.5 cm. in diameter. Cover this aperture 
 with a piece of perforated cardboard, and project with a 
 lens an image of it on the screen. Try two pieces, slowly 
 sliding one over the other. Explain. 
 
 581. Exercise.* Substitute for the glass plates in Art. 
 576 a piece of mother-of-pearl, and place a slit in the open- 
 ing of the porte lumiere. A peculiarly colored image should 
 be obtained. Now substitute for the pearl an impression of 
 it taken in black sealing-wax. Explain. 
 
 XII. OPTICAL, INSTRUMENTS. 
 
 582. Apparatus. Florence Flask, Lenses, Cardboard 
 Telescope, etc. 
 
 583. Exercise.* Fill a -litre globular flask with dis- 
 tilled water to represent the eyeball. Cover one-half of the 
 
326 
 
 PRACTICAL PHYSICS. 
 
 globe with black paper, with a round hole cut in it. This will 
 represent the iris and pupil. Place a convex lens of long focal 
 distance in front of this hole to represent the cornea and the 
 crystalline lens combined. Support a lighted candle in front 
 of this hole, and at such a distance as to form a clear image on 
 a paper screen placed behind the globe. Now move the candle 
 toward the globe till the image is quite indistinct, and then en- 
 deavor to restore the distinctness of the image by interposing a 
 second convex lens. Also move the candle away from the 
 globe, and restore the distinctness of the image by interposing 
 a concave lens. What defects of the eye are illustrated in 
 these experiments? 
 
 584. Exercise.* The principle of the microscope may 
 be illustrated as follows : Select two convex lenses of the focal 
 distances 3 and 5 cm. respectively. Mount them carefully 
 in cork or wooden rings, as shown in Fig. 237, cutting a 
 
 small portion from one 
 edge to produce a flat 
 surface. Glue these 
 |p mounted lenses on a 
 small board 15 cm. 
 long by 3 cm. wide, 
 placing the one of 
 longer focus at the 
 end A, to serve as the 
 eye-glass, and the other distant from it 11 cm., as at C, to 
 serve as object-glass. Cut two cork disks, B and D ; insert 
 into one of them a rectangular piece of stiff writing-paper, and 
 into the other a similar piece of thin sheet-brass. Slightly oil 
 the paper to render it translucent, and drill in the brass plate 
 a number of small holes, arranged in the form of a cross, at 
 
 FIG. 237 
 
LIGHT. 
 
 327 
 
 the height of the centre of the lens above the base. Before 
 placing the brass plate D in position, place the paper screen 
 B about 4 cm. from the lens A, and move it to and fro till a 
 position of distinct vision is found for it when viewed through 
 A. Now place a flame at the other end of the board, exactly 
 in line with the centre of the lenses, and between it and C place 
 the brass plate D, distant from C about 17.5 mm. Move 1) 
 till a distinct image of the cross is formed on B ; then a magni- 
 fied image of the cross will be seen through A, but more clearly 
 defined if B is removed. What is the office of each lens? 
 
 To determine the magnifying-power ascertain, as in Art. 
 549, the magnifying-power of the eye-piece and object-glass 
 separately, and obtain their product. 
 
 585. Exercise. The principle of the telescope may be 
 illustrated as follows : Mount two convex lenses as directed in 
 the last article, having the focal distances 30 cm. and 5 cm. 
 respectively. Cement the larger one, A, to one end of a board 
 50 cm. long by 10 cm. wide (Fig. 238), and the other, B, to a 
 second board 5 
 cm. square, but of 
 such a thickness 
 as to bring the 
 centres of the 
 lenses in a line 
 parallel to the 
 large board when 
 the small board 
 
 rests upon it. Prepare a translucent screen as in the last 
 article. Place the apparatus on one end of a long table, with 
 the lens A directed toward a candle-flame at the other end. Set 
 the screen to receive the image of the candle formed by A ; 
 
 FIG. 238. 
 
328 
 
 PRACTICAL PHYSICS. 
 
 then by moving the eye-piece B, a place will be found, giving 
 an enlarged image of this image on the translucent screen, and 
 a brighter image of the candle on removing the screen. What 
 is the office of each lens ? 
 
 If the eye-piece is made of two lenses, b and c (Fig. 239), 
 
 b having a focal distance of f> 
 cm. and c of 3 cm., the distance 
 between them being 9 cm. ; on 
 placing the screen between b and 
 c, an erect image of the candle will 
 be obtained instead of an inverted 
 one as before, and on looking 
 through b an erect and magnified 
 image of the candle will be seen. 
 What is the office of the lens c? 
 
 FIG. 239. 
 
 586. Exercise.* The principle of the Galilean tele- 
 scope may be illustrated as follows : Substitute for the lens B 
 in the last experiment a concave lens of 5 cm., focal length. 
 Distinct vision will be secured on placing B between the screen 
 and the lens A. 
 
 587. Exercise. Determine the magnif ying-power of a 
 telescope. 
 
 Direct it toward the open sky, and there will be seen near the 
 eye-piece, and a little beyond it, a small illuminated circle. 
 This is an image of the objective opening of the telescope. 
 Measure the diameter of this image, employing a finely divided 
 scale. The magnifying-power is equal to the quotient of the 
 diameter of the object-glass by that of this illuminated circle. 
 
LIGHT. 329 
 
 XIII. DOUBLE REFRACTION AND POLARIZATION OF 
 
 LIGHT. 
 
 588. Apparatus. Iceland Spar Crystal, Tourmaline 
 Tongs, Polariscope, Lenses, etc. 
 
 589. Exercise. Place a crystal of Iceland spar over a 
 small dot on a white sheet of paper, and observe the dot 
 through it. Rotate the crystal about an axis perpendicular 
 to the paper, and notice the behavior of the images of the dot. 
 Mark the relative brightness of these images while the crystal 
 rotates as you view them through a tourmaline plate or Nicol 
 prism. 
 
 590. Exercise. Procure a pair of tourmaline tongs, an 
 instrument consisting of two thin plates cut from the tourma- 
 line crystal and mounted as shown in 
 
 Fig. 240. Look through the plates 
 at the bright sky and observe the 
 changes in brightness as one plate is FIG 94u 
 
 turned on an axis within the support- 
 ing ring. 
 
 Set the plates so that the view is darkest, then place between 
 them a quartz spectacle-lens, known as a pebble-lens, compar- 
 ing the effect with that produced by a glass lens. 
 
 Opticians prepare thin plates of crystalline substances, such 
 as Iceland spar, quartz, arragonite, etc. Place any of these 
 you may be able to procure between the plates of the tongs 
 and observe the peculiar figures and the play of colors as one 
 of the plates is rotated. 
 
 591. Exercise. Examine with a polariscope pieces of un- 
 annealed glass, as glass stoppers, paper weights, Rupert's 
 
330 PRACTICAL 1>UYHI(!H. . 
 
 drops, etc. ; also thin plates of mica, selenite, quartz, Iceland 
 spar, etc. 
 
 An efficient polariscope may be constructed as follows : Cut 
 a rectangular piece of board 36 cm. long, 10 cm. wide, and 2.5 
 cm. thick, and also a right triangular one, having the sides 
 about the right angle 24.5 cm. and 17.4 cm. respectively. 
 
 Fasten these pieces to- 
 gether as shown in Fig. 
 241, the shorter side 
 about the right angle 
 being the vertical one. 
 At A, 5 mm. from the 
 end of the board, cut 
 
 " t- 
 
 FlG 241 a groove to support a 
 
 plate of ground glass, 
 
 H, 10 cm. square. Between H and B place three or four 
 pieces of thin plate glass, each 10 cm. square, on a piece 
 of dead-black paper to serve as a polarizer. At E, 4 cm. 
 from B, support in a transverse groove perpendicular to the 
 plane of BD, a glass plate, to serve as a shelf for supporting the 
 objects under examination. At D glue a wooden block 5 cm. 
 high, and 2.5 cm. thick, having an aperture through its centre 
 2.5 cm. in diameter, parallel to the surface of the plane, to 
 support the analyzer. This analyzer may be constructed in 
 either of two ways : first, by procuring from an optician a small 
 Nicol prism, and mounting it in a centrally apertured cork 
 inserted in a paper or brass tube, 2.5 cm. in diameter (Fig. 242, 
 A) ; or, secondly, by procuring a paper or metal tube as before, 
 fitting to it an inner tube of pasteboard divided obliquely (Fig. 
 242, C), at an angle of 35 25' with the axis of the tube, 
 and placing between these two parts 12 or 15 elliptical micro- 
 scope cover-glasses, shown in section in Fig. 242, B. In either 
 
LIGHT. 
 
 331 
 
 ' 
 
 B 
 
 Fiu. 24-2. 
 
 case one end of the tube is capped, and in the cap is a central 
 opening 2 mm. in diameter. A shoulder is provided for the 
 tube by gluing on the outside a paper ring. 
 
 In using the instrument let light from the bright sky pass 
 through H, and be incident on K, by which it is reflected through 
 the object on E, 
 to the analyzer F. 
 On rotating F on 
 its axis , a fine play 
 of colors will be 
 seen on the ob- 
 ject, due to inter- 
 ference. 
 
 A very convenient instrument for investigations in polari- 
 zation is Norrernberg's doubler, a simple form of which may be 
 constructed as follows : Knock out the opposite sides, EL and 
 PM, of a large cigar-box, and on the other two lateral faces fix 
 
 guides for the polarizing plate B 
 (Fig. 243), so that the plate makes 
 an angle of 35 25' with the edge EF. 
 On the end FM lay a piece of good 
 looking-glass the size of the end ; and 
 in the other end cut a hole, in which 
 the analyzer A, either a Nicol prism 
 or a bunch of glass plates, can be ro- 
 tated. The objects under exami- 
 nation are placed on the looking- 
 glass. The light incident on B is 
 reflected to D and partially polarized ; 
 D in turn reflects it through A to the eye. If desired, a hori- 
 zontal shelf between B and A could be put in, having a circular 
 opening for the passage of light. Objects could then be ex- 
 amined resting on this shelf over the opening. 
 
 FIG. 243. 
 
332 
 
 PEA CTICAL I'll ) r SI( '8. 
 
 592. Exercise. Procure several strips of glass, such as 
 are used in preparing microscope slides. Form on the centre of 
 each a paraffine ring 2 cm. in diameter. Support the glass in 
 a horizontal position, and put within the circle a few drops of 
 a solution of some chemical salt, and let it remain undisturbed 
 until crystals are formed. Examine these under a microscope 
 with a polarizing attachment. The following list of salts is rec- 
 ommended : Alum, potassium bichromate, mercury bichloride, 
 boracic acid, potassium carbonate, citric acid, potassium chlo- 
 rate, potassium iodide, ammonium nitrate, copper sulphate, iron 
 sulphate, potassium sulphate, potassium ferrocyanide, etc. 
 
 An instrument suitable for examining such crystals can be 
 constructed as follows : Construct an analyzer as directed in 
 the last article, and fit it in the draw-tube 
 of a compound microscope (Fig. 244), be- 
 tween the eye-piece and the object-glass. 
 A similarly constructed tube must be made 
 for a polarizer, and fitted to a second tube 
 somewhat shorter, turning freely within it 
 without falling out. Cement this outer tube 
 to the under side of the microscope stage 
 with the axis of the tube exactly in that of 
 the draw-tube above, but leaving the inner 
 tube free to turn on its axis. Very satisfac- 
 tory results can be obtained from the com- 
 mon draw-tube microscopes, and even the 
 simple botanizing glass can be easily adapted 
 to exhibit the phenomena of polarized light 
 (see "The Scientific American" for July 31, 1886). Paper 
 tubes to fit the tubes of the microscope are easily made by 
 gumming, writing-paper, and winding it around a cylinder of 
 the proper size. 
 
 FIG. 244. 
 
LIGHT. 333 
 
 593. Exercise. Dissolve salicine in one part alcohol to 
 four parts water, made rather hot, obtaining a saturated solu- 
 tion. Pour a layer on a microscope slide, and evaporate 
 quickly with rather a strong heat. Examine the crystals 
 obtained under the microscope with the polariscope attach- 
 ment. 
 
APPENDICES. 
 
APPENDICES. 
 
 APPENDIX A. 
 THE PHYSICAL LABORATORY. 
 
 594. The Room. Where a separate room can be pro- 
 vided for experimental work in Physics, it should be large, well 
 ventilated, and have a southern exposure. Opening off from it 
 should be a room for the storage of apparatus. Provision 
 should be made for darkening the windows, either by inside 
 blinds or opaque curtains mounted on spring rollers. If cur- 
 tains are used, the lateral edges must slide in deep grooves, 
 made by nailing strips on the casing, to prevent the light from 
 entering the room around the edges. 
 
 A few heavy flat-top tables, about 32 in. high, 3 ft. wide, 
 and of such length as the room permits, should be obtained. 
 These tables should have no iron in their structure, and to make 
 it possible to clamp apparatus on them the top should pro- 
 ject at least four inches beyond the frame. In a part of the 
 room where there is a good light, place a carpenter's work- 
 bench, with a vise and anvil upon it. Above it, on the wall, 
 fasten a cupboard, to contain such tools as saws, planes, 
 brace and bits, drills, hammer, chisels, try-square, flies, wire- 
 cutter, soldering-iron, oil-stone, nails, screws, both iron and 
 brass, tacks, etc. This part of the equipment should not be 
 overlooked. School authorities will seldom refuse to appro- 
 priate money to be spent in this way. 
 
 A side-table for the few chemicals needed will be found con- 
 venient. A sink for waste water must by no means be omitted. 
 
338 PRACTICAL PHYSICS. 
 
 Connect the room with the water system if there is one ; if not, 
 place a galvanized iron tank at one end of the sink, having a 
 capacity of two or three barrels, to be filled with water from 
 the well or cistern by means of a force-pump. 
 
 As soon as possible put a well- filled bookcase in the room, 
 with a table and chairs near by, where students may look up 
 points regarding their work. Such books as the following are 
 recommended : 
 
 Ganot's Physics, by Atkinson ; Practical Physics, by Guthrie ; 
 Cooke's Chemical Physics ; Elementary Practical Physics, by 
 Stewart and Gee ; Practical Physics, by Glazebrook and Shaw ; 
 Physical Manipulations, by Pickering ; Experimental Physics, 
 by Weinhold ; Physical Constants, by Everett ; The Art of 
 Projecting, by Dolbear ; Light, by Wright ; Light, by Mayer 
 and Barnard ; Sound, by Mayer ; Sound, by Tyndall ; Magnet- 
 ism and Electricity, by Guthrie ; Electrical Rules and Tables, 
 by Munro and Jamieson ; Fleming's Short Lectures to Elec- 
 trical Artisans ; Practical Mechanics, by Perry ; Physical Meas- 
 urements, by Kohlrausch ; Practical Electricity, by Ayrton ; 
 Handbook of Electrical Testing, by Kempe. 
 
 The walls of the room would look more attractive if they 
 were decorated with the pictures of prominent scientific men. 
 Bare walls are not very inspiring ; good work is not wholly in- 
 dependent of the student's surroundings. Charts of spectra 
 neatly framed would be both useful and ornamental. 
 
 If illuminating gas is procurable, by all means introduce it 
 into the laboratory, supplying each table with jets suspended 
 from the ceiling, making connections with them by rubber 
 tubing. The advantage of this method is that the tables can 
 be moved about if necessary ; there is no iron beneath them to 
 interfere with the action of magnetic needles, and when the gas 
 is not in use the fixtures are out of the way. 
 
THE PHYSICAL LABORATORY. 339 
 
 It is not to be expected that every luxury, or even every con- 
 venience, can be provided at the outset. Let the essentials be 
 secured, and then add from time to time such fixtures as will 
 enable the work to be done with greater accuracy and at less 
 inconvenience. 
 
 If the recitation-room is large, and the class small, the back 
 part of the room might be fitted up for experimental work. 
 This would be much better than the entire omission of this im- 
 portant kind of training. The days of teaching science at long 
 range, as it were, are passed. That the pupil must come in 
 actual contact with the phenomena to be studied is recognized 
 by every wide-awake instructor. The apparatus should be put 
 in his hands, with clear directions regarding its use ; in this 
 way there are trained all of the powers of the mind, the obser- 
 vational not the least important. 1 Faraday used to affirm that 
 he always wished to perform experiments himself ; that he 
 always learned something in doing the work that the descrip- 
 tion in words could not convey to him. An experiment which 
 fails is often more instructive than one which succeeds. In 
 finding the cause of failure more will often be learned than 
 when the work goes through, as if by routine. 
 
 595. Apparatus. It is a mistake to suppose that elabo- 
 rate and highly finished apparatus is necessary for successfully 
 prosecuting experimental work in Physics. Neither should it 
 be expected that all the required appliances for the complete 
 investigation of every department of the subject can be pro- 
 
 1 A few experiments performed by himself will give the student a more intelligent 
 interest in the subject, and will givo him a more lively faith in the exactness and unifor- 
 mity of nature, and in the inaccuracy and uncertainty of our observations, than any 
 reading of books, or even witnessing elaborate experiments performed by professed 
 men of science. J. CLERK MAXWELL. 
 
840 PRACTICAL PHYSICS. 
 
 vided at the outset. Let some of the more important pieces be 
 secured, selecting them with the view of adding the others as 
 soon as practicable. In this way an outfit will be obtained 
 in time, where each piece has its place and all fit harmoniously 
 together. Much can be done with a few wisely chosen pieces. 
 Although the author does not believe that giving instruction in 
 physical technics is the proper work of the laboratory, yet he 
 would permit a limited amount of apparatus construction, if too 
 much time is not consumed in it. Each class will usually have 
 its handy boy, whose mechanical gifts can be turned to good 
 account by having him construct, now and then, a desirable 
 piece of apparatus. The school janitor is generally a man of 
 some mechanical skill, and will willingly construct frames, 
 supports, and the like. A small fee levied each term, to cover 
 incidentals, will always be cheerfully paid by the patrons of the 
 school, and in the course of the year will amount to a handsome 
 sum, to be devoted to improving the equipment. 
 
 Among the first things to be purchased are appliances for 
 measuring Metre sticks can be procured of the Metric Bureau 
 for 25 cents each ; several of these should be obtained. For 
 measuring small linear quantities, where a selection from the 
 instruments described in the first chapter has to be made, it is 
 recommended that the Dividers, Diagonal Scale, and Micrometer 
 Caliper be chosen,^ and that several of each of the first two be 
 purchased. The Circular Protractor will be needed for angular 
 measurements. Cheap and efficient ones are now made of 
 horn. 
 
 Good reliable Balances are indispensable to every laboratory, 
 but unfortunately they are expensive. The Jolly Balance can 
 be constructed by any one at all skilful with tools, and makes a 
 very good substitute for the beam balance, provided accurate 
 weights are used. If a support is fitted to the Jeweller's Hand 
 
, THE PHYSICAL LABORATORY. 341 
 
 Balance, a good deal of work can be accomplished with it, if 
 one is very careful. Balances sensitive to a centigramme can be 
 imported, duty free for schools, from Germany for about $6.50. 
 With one set of Accurate Weights for comparison, cheap ones can 
 be adjusted, and, in fact, it is not a difficult matter to make 
 weights out of sheet-brass, brass wire, and aluminum wire. 
 
 Of Glass Tubing there should be a liberal supply of both large 
 and small sizes. Select tubes having thick walls, as they are 
 stronger, and bend without collapsing. Rubber Tubing for con- 
 nections, and for many other purposes described in the preced- 
 ing pages, is one of the necessities. 
 
 A few shillings appropriated for wire, brass, copper, and iron, 
 of various diameters, will well repay. For electrical work 
 covered copper wire will be required ; the desirable numbers are 
 indicated in the chapter on electricity. 
 
 In constructing supports and many simple devices, there will 
 be frequent use for ivell-seasoned pine lumber of different thick- 
 nesses. Material of this kind should be always on hand. 
 
 If gas is available, the best lamp for heating purposes is the 
 Bunsen Burner (Fig. 245), as it gives a very hot and smokeless 
 flame. In using the burner care should be taken to regulate 
 properly the supply of air through the holes near 
 the base, for if too much air is admitted, the flame 
 is likely to strike down the tube and burn at the 
 lower part, giving a smoky flame, the heat of 
 which is expended, in a measure, on the tube. 
 When gas is not available, resort must be had to 
 the alcohol lamp, or to some form of gasoline 
 burner. An alcohol lamp can be extemporized 
 out of a bottle, to which is fitted a perforated 
 cork, through which passes some candle-wick. 
 The top of the cork can be protected from the flame by a layer 
 
342 
 
 PRACTICAL PHY8ICS. 
 
 FIG. 246. 
 
 FIG. 247. 
 
 of plaster-of -Paris. In Fig. 246 is shown the Mouth Blow- 
 pipe, an instrument easily made from two pieces of glass tubing 
 and a sound cork. When great heat is required, as 
 jn manipulating heavy glass tubing, resort must 
 be had to the Blast Lamp (Fig. 
 247) . Fig. 248 shows a very con- 
 venient form of Blower for supply- 
 ing air to the blast lamp. 
 
 Fig. 249 represents the Florence 
 Flask. The laboratory should be 
 supplied with several of these, 
 varying in size from a half -litre 
 to a litre and a half. When heat 
 is to be applied to one, place it 
 in a sheet-iron shallow saucer, containing fine sand, or a square 
 
 of asbestos paper, supported 
 on a ring of the iron stand (Fig. 
 262), to secure a uniform dis- 
 tribution of heat. 
 The Glass Re- 
 tort (Fig. 250) 
 may often take 
 the place of the 
 flask, especially 
 when any dis- 
 tillation is to be 
 done. Fig. 251 
 
 exhibits a very useful form of Condenser. A large bottle or 
 flask may usually be used as a substitute. Funnels (Fig. 252) 
 are almost indispensable. They may be of either glass or tin. 
 One form is provided with a stop-cock. The Graduate (Fig. 253) 
 is employed for the volume measurement of liquids. These 
 
 FIG. 248. 
 
 FIG. 249. 
 
THE PHYSICAL LABOEATOEY. 
 
 343 
 
 FIG. 250. 
 
 FIG. 251. 
 
 instruments should be graduated in both the English ard the 
 metric system. At least two sizes will be desirable, one having 
 a capacity of 25 ccm. and graduated to 
 centimetres, and a second one holding 
 at least 500 ccm. The Cylindrical Grad- 
 uate (Fig. 254) can- 
 not well be dispensed 
 with, being almost 
 a necessity in deter- 
 mining the volume of irregular solids by the 
 displacement of water. These should be 
 graduated to cubic centimetres. Two or three of these should 
 
 find a place in the laboratory, and 
 
 may be used in place of the conical 
 
 form. Fig. 255 shows the Pipette- 
 
 Tube, and 
 
 the manner 
 
 of using 
 
 it. A glass 
 
 tube, drawn 
 
 out a little 
 
 at one end to narrow the opening, 
 makes an excellent substitute. Beakers 
 (Fig. 256) are to be had of various 
 sizes and shapes. A few holding a 
 litre, and several of less volume 
 should be provided. Copper beakers 
 are very desirable, as there is no 
 danger of breaking them by sudden 
 changes of temperature. The first outlay is somewhat greater, 
 but it pays in the end to procure them. A dozen, at least, of 
 large Test- Tubes will be needed, and two or three times as many 
 
 FIG. 252. 
 
344 
 
 PRACTICAL PHYSICS. 
 
 FIG. 25 1. 
 
 of smaller size (Fig. 257). To clean them, a specially con- 
 structed brush (Fig. 258) is recommended. 
 
 It is frequently desirable to reduce 
 a substance to a fine powder. In that 
 case a Mortar and Pestle (Fig. 259) 
 is necessary. If 
 the substance to 
 be powdered is> 
 not very hard, a 
 stout bowl might 
 be used with a 
 pestle made out 
 of hardwood. 
 Very hard sub- 
 sStances must be 
 
 broken with a hammer or in an iron 
 mortar. For condensing solutions or dry- 
 ing substances 
 use an Evapo- 
 rating Dish (Fig. 
 
 260). They are made of either glass 
 or porcelain. Common white stone- 
 ware saucers are an excellent substi- 
 tute, and are quite inexpensive. In 
 heating them, the temperature must be 
 increased gradually, and they should 
 never be exposed to the naked flame, 
 but should be set in a dish of sand and 
 kept at a moderate heat. Where 
 
 there is danger of overheating during evaporation, or where 
 it is necessary to keep a substance at a constant moderate 
 temperature, the Water-Bath (Fig. 201) is recommended. This 
 
 Fie. 255. 
 
 FIG. 256. 
 
THE PHYSICAL LABORATORY. 
 
 345 
 
 is only a copper basin provided with several rings of different 
 sizes, that the top may be adjusted to the dish to be placed 
 upon it. 
 
 Figs. 262 and 263 illustrate the Iron Stand 
 and the Universal Holder , respectively., Each 
 student, or set of students, working together, 
 ought to be supplied with one of each, and 
 
 FIG. 258. 
 
 occasionally more than one of the latter will 
 be found convenient. The price of the iron 
 stand varies with the number of rings supplied 
 with it. For most work the single ring will be 
 sufficient. The universal holder can be made 
 by any good mechanic, and in this way secured 
 at a price within reach. The Burette holder differs from 
 
 FIG. 257. 
 
 FIG. 259. 
 
 FIG. 260. 
 
 FIG. 261. 
 
 the universal in being adjustable only to height. It is much 
 less expensive, and answers equally well in supporting lenses, 
 cardboard screens, jet-tubes, etc. Fig. 264 exhibits a good form 
 of Test-Tube Back, and Fig. 265 a Test -Tube Holder, the latter 
 
346 
 
 PRACTICAL PHYSICS. 
 
 to be used when heating a solution in a flame. 
 small heated vessels, or 
 heated substances, the Cru- 
 cible Tongs (Fig. 266) will 
 be found convenient. The 
 adjustable Table Support, 
 (Fig. 267) will be found 
 useful in supporting beak- 
 ers, prisms, etc., but is not 
 indispensable. Fig. 268 rep- 
 resents the Tinner's Ni2-)- 
 useful instrument 
 
 In handling 
 
 K) 
 
 FIG. 262. 
 
 pers, a 
 
 FIG. 
 
 form. 
 
 FlG. 264. 
 
 FIG. 265. 
 
 for cutting metals in sheet 
 
 Fig. 269 is a Clamp for closing -rubber tubes. Fig. 270 
 shows a Cork Borer and the manner of 
 using it. A small round file makes a good 
 substitute. In 
 reducing the size 
 of a cork, use 
 a flat coarse-cut 
 file. To prevent 
 
 small corks splitting when drilling holes through them, wrap 
 them firmly with several turns of stout twine. 
 In perforating rubber corks, keep the borer wet 
 with a solution of caustic potash. 
 
 In electrical work a few good battery cells 
 are needed. These should be selected in view 
 of the kind of service required of them. For 
 
 intensity, where 
 constancy is imma- 
 K3) terial, there is noth- 
 266. ing better than the FlG . 2 67. 
 
THE PHYSICAL LABOEATOEY. 
 
 347 
 
 Ghrenet Battery (Fig. 271), charged with the chromic acid 
 
 solution. For con- 
 stancy, where 
 strength of current 
 is not so much of an 
 object, the Darnell's FIG. 259. 
 
 Batter y (Fig. 272) is superior to most others. The forms of 
 
 FIG. 270. 
 
 batteries are legion, but for cheapness and efficiency there is 
 none superior to 
 the two men- 
 tioned. It is too 
 expensive to rely 
 upon batteries 
 for such currents 
 as are required 
 for electric light- 
 ing. Here resort 
 must be had to 
 the Dynamo. 
 Small ones are 
 now to be had 
 giving one small 
 arc light, suit- 
 FIG. 27i. able for optical FlG . 273 . 
 
348 PRACTICAL PHYSICS. 
 
 work, for about $100. Mr. Geo. M. Hopkins, in the Supplement 
 to the " Scientific American," No. 600, gives full directions 
 for constructing such a dynamo. Where water or steam power 
 is available, there is no more important instrument for the 
 physical laboratory than the dynamo, on account of the strong 
 light that can be obtained from it. Sunlight is so uncertain, 
 that if optical work is made dependent on such a source of 
 light many a disappointment will be met with, and considerable 
 disorganization of the work will result therefrom. 
 
 596. Conducting the Work. Probably the greatest 
 drawback to carrying on experimental work in physics is the 
 apparent impossibility of accommodating such large numbers of 
 students as are always found desirous of studying the subject. 
 When the class is very large it is recommended that it be 
 divided into five divisions, one division to meet for work each 
 day for, say, two hours, working in sections of two pupils each. 
 The problems should be assigned a few days in advance, that 
 they may be carefully studied in all their parts by the pupils 
 before entering the work-room, so that no time will be lost in as- 
 certaining what is to be done, and in what manner. It is also 
 recommended that they be reviewed by the instructor, before the 
 class, before the pupils are set to work upon them. Each pupil 
 should have his appointed place in the room, where his work 
 should all be done, except where the nature of it requires a 
 change. The apparatus needed for his work should be placed on 
 his table in advance, say, the Saturday before, remaining there 
 during the week for the use of the different sections. When 
 duplicate pieces of apparatus are not on hand, and several pupils 
 require the same piece at some stage of their work, a special table 
 had better be provided for such appliances where they may be 
 found when needed. This is more especially true of the air- 
 
THE PHYSICAL LABORATORY. 349 
 
 pump, whirling-machine, Atwood's machine, electrical machine, 
 etc. On completing an experiment the pupil should be required 
 to make carefully worded notes on all that he has observed. This 
 record should be submitted for approval immediately after 
 completing the experiment, and if found correct, as well as 
 complete, in all its parts, then the next experiment can be 
 entered upon ; but if unsatisfactory, the pupil should return to 
 the same experiment, and repeat it till all errors are corrected 
 and omissions supplied as far as possible. 
 
 When the classes are small, or assistance is furnished the 
 instructor, the number of hours devoted to experimental work 
 should be increased. Four or six hours per week spent in the 
 laboratory, and perhaps three in the recitation-room, drilling on 
 principles and reviewing the facts developed by experiment, 
 when carried on for a school year, will demonstrate that there is 
 no study in the curriculum that surpasses physics in the breadth 
 of mental discipline imparted. 
 
 It is not expected that each pupil will attempt all the work 
 described in this book, but a judicious selection should be made, 
 giving each pupil some work under each topic, the amount to 
 be determined by the time available, the aptness of the pupil, 
 and the laboratory facilities. Many topics might be omitted 
 entirely, and if found desirable the order of the others might be 
 changed, if by so doing there is secured a closer conformity to 
 the order found in the text-book used in the class-room. 
 
 The following list of articles selected from the preceding 
 pages is suggested, as offering a fairly complete and eas} r 
 course, supplementing to good purpose the experiments of the 
 recitation-room : 
 
 2, 4, 5, 9, 12, 13, 18, 20, 24, 25, 31, C2, 64, 67 to 70, 
 73, 78, 79, 83, 84, 108 to 123, 137 to 148, 151 to 163, 182 to 
 197, 216,219,222, 234, 239, 241, 246, 247, 253,254, 269 to 274, 
 
350 PRACTICAL PHYSICS. 
 
 285 to 300, 306 to 312, 315 to 322, 325, 326, 331, 346 to 353, 
 358 to 361, 378 to 382, 386, 387, 391, 412 to 416, 428, 429, 
 431, 434, 441 to 443, 452, 454, 456, 472, 476, 483, 485, 
 491, 492, 504, 511, 512, 516, 517, 521, 522, 528, 530, 532, 534, 
 539, 541, 545, 547, 548, 558, 561, 564. 
 
 In response to numerous inquiries from teachers, concerning 
 physical apparatus, and where it can be bought at fair prices, 
 the author would take this occasion to say that anything 
 described in the preceding pages can be furnished by either 
 Eberbach and Son, Ann Arbor, Mich. ; E. S. Ritchie and Sons, 
 Brookline, Mass. ; A. P. Gage, Boston, Mass. ; or Jas. W. 
 Queen & Co., Philadelphia, Pa. By writing to either of these 
 houses, and referring to the articles and figures of this book, 
 you can promptly learn at what prices the various appliances 
 can be obtained. The author will gladly give any information 
 in his power regarding apparatus, answer any questions as to 
 its use, and aid teachers in any way he can in overcoming diffi- 
 culties encountered in endeavoring to teach physics on the plan 
 outlined in these pages. 
 
 597. The Note-Book. Every pupil must supply him- 
 self with a note-book in which to record the transactions of the 
 laboratory. This book should be a model of neatness ; work 
 slovenly done should be rejected, and the pupil should be re- 
 quired to rewrite it. The use of loose sheets of paper for note- 
 taking should not be permitted. Calculations and sketches 
 should be shown on the left-hand page, and observations, descrip- 
 tions, formulae, and theory on the right-hand page. During the 
 evening following the day devoted to experimentation, the pupil 
 should prepare a full report of his day's work, describing the 
 character of each experiment, the nature of the apparatus em- 
 ployed, the results obtained, and the inferences which he thinks 
 
THE PHYSICAL LABORATORY. 351 
 
 can be deduced from them. After these reports have been 
 examined by the instructor, and the errors which were pointed 
 out corrected by the pupil, they should be neatly copied into 
 a second book provided for the purpose. One recitation-hour 
 per week may be very profitably devoted to the consideration 
 of these reports in the presence of the whole class, the in- 
 structor passing upon their accuracy, completeness, and literary 
 execution. 
 
 598. The Graphic Method. This method is frequently 
 employed to find out the probable form of the law connecting 
 two quantities which are so related that a change in one is 
 attended by a change in the other ; as, for instance, in Art. 74, 
 where an increase in the weight placed in the pan produces 
 a change in the length of the wire, and in Art. 88, where a 
 change in the temperature of the solvent is attended by a 
 change in the solubility of the substance. It consists in repre- 
 senting by a line the data obtained by the observer in the course 
 of his investigations, the shape of the line indicating the form 
 of the law connecting the dependent facts. To construct 
 the line, procure a piece of cross-section paper of suitable size. 
 This is merely a good quality of writing-paper divided into 
 equal small squares, by a great number of horizontal and verti- 
 cal lines, the most desirable sizes for these squares being 1 mm. 
 or .1 inch on a side. Such paper can be purchased of any 
 dealer in mathematical instruments. Now select some suitable 
 scale to be used in representing the things to be compared, the 
 chief condition being that the units be such as to bring all the 
 work on one sheet. For instance, in Art. 74, the number of 
 units of weight used each time may be represented by as many 
 divisions laid off on one of the horizontal lines, the side of a 
 square serving as the linear unit. If this is found to require 
 
352 PRACTICAL PlIYSIVti. 
 
 too long a line, the side of a square may represent two or more 
 units of weight ; and, on the other hand, if the line is too short, 
 a larger unit may be chosen. In like manner any convenient 
 unit may be selected to represent the elongation of the wire. 
 After suitable units have been decided on, not necessarily the 
 same for both quantities, then measure toward the right on 
 the horizontal line, passing through the corner of some one of 
 the squares (usually taken near the lower left-hand corner of the 
 sheet, and called the origin} a sufficient number of spaces and 
 parts of a space to represent the numerical value of the first of 
 the dependent quantities, and then, in the perpendicular through 
 the point just located, measure off a distance to represent the 
 numerical value of the second quantity, marking with a cross 
 the point thus located. In like manner, locate points, using 
 the remaining data, making all measurements from the same 
 origin, and employing the same units. Negative data should 
 be measured off in directions exactly opposite to those used for 
 positive quantities. Through the points located, sketch as 
 smooth and symmetrical a curve as possible. The greater the 
 number of points, and the closer they are together, the better it 
 will be for sketching the curve. The simpler the line passing 
 through these points, the less complex the law connecting the 
 quantities ; as, for instance, a straight line would imply that one 
 quantity is proportional to the other. On account of the errors 
 which unavoidably enter into all observations, the points will 
 not all lie exactly on a smooth curve, but may be a little to one 
 side of it. Thus, the Graphic Method often portrays to the eye 
 just where mistakes have been made by the observer, and also 
 enables him to get approximate values for intermediate points 
 in the problem. See Stewart and Gee's Practical Physics, 
 Vol. I., page 275. 
 
THE PHYSICAL LABORATORY. 353 
 
 599. Summary of Laboratory Rules. Pupils are 
 advised to observe carefully the following : 
 
 1. Be orderly and neat in manipulation. Keep all apparatus 
 clean, never setting away any apparatus without wiping it with 
 a chamois, if metal, and if glass, washing it and thoroughly 
 drying it. 
 
 2. Economize time by remembering that frequently two or 
 more operations can be carried on simultaneously ; never, how- 
 ever, if either one needs close and constant attention during 
 any considerable period of time. 
 
 3. Prepare thoroughly for every experiment, so that every 
 condition will be observed, and no failures result from a neglect 
 of some requisite. Do not substitute for what is the best pos- 
 sible, that which will barely do. 
 
 4. Ascertain the reason for every step taken in working 
 through an experiment, noting which are essential conditions 
 permitting no variations, and which are non-essential only in 
 so far as they conduce to greater accuracy, and hence may be 
 modified as lack of apparatus may compel. 
 
 5. Be exact and methodical. Let nothing pass unnoticed, 
 although you may not see its significance at the moment. 
 
 6. Keep your note-book by you, and record in it carefully, 
 neatly, and at the time the results of the observations, and also 
 make sketches of the apparatus used. 
 
 7. Do not crowd the notes; leave plenty of room after each 
 experiment to write out a full explanation of the facts, together 
 with the principles revealed by them. If several similar quan- 
 tities are recorded, arrange them in tabular form with parallel 
 columns. 
 
354 PRACTICAL PHYSICS. 
 
 APPENDIX B. 
 LABORATORY OPERATIONS. 
 
 600. Cutting Glass. To cut small glass tubes, make a 
 deep scratch with a three-cornered file across the tube as it rests 
 on the table ; then holding the tube, as shown in Fig. 273, with 
 
 the scratch turned from 
 you, press suddenly out- 
 ward with the thumbs, 
 and it will break off as 
 desired. To cut off large 
 tubes, flasks, bottles, 
 etc., make a deep scratch 
 
 .b IG. 27o* 
 
 with a file, then apply to 
 
 it either a pointed piece of glowing charcoal, a heated metal 
 rocjj or a fine gas-jet. The sudden expansion by heat will 
 generally produce a crack ; if not, then touch the heated spot 
 with a wet stick. A crack thus started may be led in any 
 desired direction by keeping the source of heat moving slowty 
 a few millimetres in front of it as it advances. To get a 
 small-pointed gas-flame for the above purpose, connect a glass 
 jet-tube to the gas-supply by a piece of rubber tubing. 
 Another way to cut a glass cylinder is to wind a turn of fine 
 platinum wire around it, just where the scratch has been made, 
 bringing the ends as close together as possible without touch- 
 ing. Now pass through the wire an electric current of suffi- 
 
LABORATORY OPERATIONS. 
 
 355 
 
 cient intensity to bring the wire to a white heat. Glass plates 
 are readily cut with the common " glass-cutter," an instrument 
 provided with a highly-hardened steel wheel in place of a point. 
 
 601. Smoothing the End of a Glass Tube. Warm 
 the end by passing it to and fro through the Bunsen, or spirit 
 flame ; then hold it obliquely in the flame, with the end just in- 
 serted, slowly turning the tube around. Remove from the 
 flame soon after the flame becomes a bright yellow. In the 
 case of large tubes it will be necessary to smooth them by 
 grinding on a smooth flag-stone wet with water. 
 
 602. Bending Tubes. Warm the tube for several inches 
 each side of the place 
 
 where the bend is to be 
 
 by slowly passing it 
 
 through the flame ; then 
 
 bring the tube into the 
 
 gas-flame, slowly rotating 
 
 it on its axis, heating it 
 
 evenly for about three 
 
 centimetres. When the 
 
 flame becomes a bright 
 yellow the 
 tube will be 
 soft. Then 
 
 gently bend the ends from you until the required 
 angle is obtained. Fig. 274 shows how to hold 
 the tube. In bending moderately large tubes a 
 flat flame is preferable. Fig. 275 exhibits an 
 attachment for the Bunsen burner to produce 
 FIG. 275. such a flame. The fish-tail gas-burner or the 
 
 FIG. 274. 
 
356 PRACTICAL P//rN/Y'S'. 
 
 kerosene lamp gives a very suitable flame for use in bending 
 small tubes. 
 
 603. Closing the End of a Tube. Soften the tube 
 at the end by holding it in the flame, and then pull the end 
 out with another piece of glass. Keep removing the small tail 
 that is left till it becomes quite small ; then heat the end for ji 
 few minutes, turning the tube in the fingers. If the tube is 
 held in an inclined position in the flame, the opening will keep 
 contracting till finally it closes up. 
 
 604. Drawing out Tubes. Thoroughly soften the tube 
 uniformly for three centimetres of its length, then remove 
 from the flame and pull the parts asunder till the diameter 
 is about 1 mm., holding the tube steadily till it cools, to avoid 
 crooking it. Now scratch it w T ith a file at the smallest part and 
 break it in two, smoothing the ends in the flame. 
 
 605. Drilling Holes in G-lass. Small holes are quite 
 readily drilled through glass by using a hard drill, wet with a 
 solution of camphor in oil of turpentine. A three-cornered 
 file, with the end broken oft % , makes a good drill for glass. 
 Large holes may be drilled with a brass tube and emery powder 
 moistened with water. A piece of wood, with a hole in it of 
 the required size, cemented to the glass plate, makes an excel- 
 lent guide for the drill. The tube can be rotated by the fingers, 
 or if a wooden pulley is attached to it, the common drill-stock 
 bow may be used. If the drill is moistened with a paste of 
 fluor-spar and sulphuric acid, the labor of drilling glass is much 
 lessened. 
 
 606. Drawing on G-lass. Drawings in India-ink for 
 lantern projections are easily executed on glass by first flowing 
 
LABORATORY OPERATIONS. 357 
 
 the plate with a solution of plain collodion, and allowing it to 
 dry. As the transparency is not in the least affected, the plate 
 may be placed directly over the picture to be reproduced, and 
 traced in India-ink with a fine steel pen, even by one having 
 little or no artistic skill. 
 
 607. Useful Cements. Frequent use will be found for 
 reliable cements. The following are confidently recom- 
 mended : 
 
 For cementing wood, leather, metal, or glass to glass, melt 
 at 100 C. one part of gutta-percha and one part of pine-pitch, 
 stirring till homogeneous. Soften the cement by heat when 
 needed for use. 
 
 For an acid-proof cement, make a concentrated solution of 
 sodium silicate, and form a paste, with powdered glass. 
 
 For work in electricity an excellent insulating cement is made 
 by melting together rosin, 3J Ibs., beeswax, 2J Ibs., Venetian- 
 red, 2 Ibs., and Venice turpentine, 12 oz. Less Venice tur- 
 pentine will make it harder. 
 
 608. Silvering Glass. Dissolve 154 grains of silver 
 nitrate in 17 fluid ounces of distilled water. Add ammonia 
 water until the precipitate formed is nearly redissolved. Filter 
 and add distilled water, so as to make the whole 34 fluid ounces. 
 This gives solution A. Thirty-one grains of silver nitrate are 
 dissolved in 34 fluid ounces of boiling distilled water ; dissolve 
 23 grains of Rochelle salt in a small quantity of water, add it 
 to the boiling nitrate, boil till the precipitate becomes gray. 
 Filter and allow to cool. This gives solution B. Clean the 
 glass object perfectly by rubbing it with strong nitric acid, 
 using a stick for the purpose. Wash off the acid, then wash 
 the article with caustic potash, then with alcohol, and finally 
 
358 PRACTICAL PJrrSTC8. 
 
 with distilled water. Place the object, with the side uppermost 
 which has to be silvered, in a clean dish, and while still wet 
 pour over it, and mix equal quantities of the solutions A and B, 
 covering it half an inch. In about two hours, according to the 
 temperature, the silvering is complete ; the hotter the quicker ; 
 the slower the better. The object is now taken out, cleaned of 
 its superfluous silver, dried, and varnished. If the coating 
 is thick, the silver surface may be polished with rouge powder 
 on cotton-wool. 
 
 609. Cleaning Mercury. Mercury is an absolute neces- 
 sity in many lines of investigation. During its use it is liable 
 to become alloyed with zinc or tin, or both, rendering it unfit for 
 the service required of it in experimenting. To remove these 
 metals proceed as follows : To every 100 parts of mercury add 
 10 parts of a strong solution of ferric chloride and 100 parts of 
 water. Shake in a strong bottle till thoroughly mixed, the mer- 
 cury becoming broken up into small globules. Set aside for two 
 or three days in a cool place, then decant off the liquid from 
 the mercury, and afterwards wash thoroughly by shaking it up 
 again with dilute hydrochloric acid, and finally with hot water. 
 Remove with porous paper as much of the water as possible ; 
 .then pour into a filter having a small pin-hole in the bottom, 
 and finally dry over a water-bath. 
 
 610. Soldering. Prepare a soldering fluid by adding 
 scraps of zinc to hydrochloric acid till it refuses to dissolve any 
 more. Wet the surfaces to be joined with this fluid, place 
 between them a few pieces of soft solder, an alloy of lead and 
 tin ; then apply heat either by holding the article in a flame, by 
 touching it with a heated soldering-iron till the solder melts, or 
 by directing upon it a blow-pipe flame ; on cooling, the surfaces 
 will be firmly joined together. 
 
LABOEATOEY OPERATIONS. 359 
 
 611. Amalgamating Battery-Zincs. Dissolve 15 com. 
 of mercury iii a mixture of 170 ccm. of nitric acid and 625 
 ccm. of hydrochloric acid. Keep the liquid in a glass-stop- 
 pered bottle. To use, immerse the zinc in the fluid for a few 
 aiinutes, then remove, and rinse thoroughly in water. 
 
 612. Battery Fluids for the Carbon and Zinc 
 Battery. 
 
 No. 1. Water, 8 kilo. ; pulverized potassium bichromate, 1.2 
 kilo. ; sulphuric acid, 3.6 kilo. Put the powdered potassium 
 bichromate in the water, and when dissolved add the acid in a 
 fine stream, with constant agitation. 
 
 No. 2. Dissolve 4 oz. of chromic acid in one quart of 
 dilute sulphuric acid, 1 vol. sulphuric acid to 12 of water, and 
 allow the solution to cool and settle. 
 
 The last of these solutions is greatly to be preferred to the 
 former, as the absence of potassium prevents the formation of 
 chrome alum crystals, the defect of the first solution. Chromic 
 acid can now be obtained at greatly reduced prices, and pro- 
 duces a solution lasting much longer than that prepared from 
 the bichromate. 
 
 As the chromic acid solution is frequently used as a de- 
 polarizer in the Bunseu battery, the following preparation from 
 chromic acid will be found very efficient : Dissolve one pound of 
 chromic acid in one part of water, and add seven fluid ounces 
 of sulphuric acid, with stirring. It is claimed that the con- 
 stancy is improved by adding one- third volume of nitric acid. 
 
 613. Care of Batteries. All the connections in a bat- 
 tery must be kept clean and bright, and the zincs well amalga- 
 mated. The porous cups must be thoroughly soaked in water 
 before using, and kept in water while the battery is idle. In 
 
360 PRACTICAL PHYSICS. 
 
 the Daniell's battery they become clogged in time with copper, 
 and hence useless. They can be renovated by soaking in nitric 
 acid, but it is probably just as cheap to throw them away and 
 substitute new ones. In the carbon battery, where the potas- 
 sium bichromate solution is used, the carbons become clogged 
 with chrome alum crystals and chromium oxide, greatly increas- 
 ing the resistance. If the carbons are soaked for an hour in 
 nitric acid the difficulty will be removed. Chromium oxide is 
 formed in the case of the chromic acid solution, and in time 
 affects the action of the battery. 
 
 It often happens that the carbons become detached from the 
 brass clamp in the case of the Grenet battery, and need to be 
 resoldered, a thing easily done if the end of the carbon is first 
 plated with copper. To do this, connect to the negative pole 
 of a Daniell's battery the carbon plate, and to the other a 
 strip of copper. Let these dip close together, but not in 
 contact, in a vessel containing a solution of copper sulphate, 
 removing them when the plating covers completely the surface 
 to be soldered. Cover with beeswax the surface not to be 
 plated. 
 
 614. Electrical Amalgam. Take two parts by weight 
 of tin, one part of zinc, and eight parts of mercury. Melt the 
 tin in an iron ladle, add the zinc, and raise it to the melting- 
 point. Now add the mercury, and stir the mixture till it is 
 cool. Apply to the rubber by mixing with the amalgam a little 
 lard. 
 
 615. Cleaning Electrical Machines. To remove dust 
 from electrical machines, use a cloth wet with kerosene oil. 
 The efficiency of both the Frictional and the Holtz Machine is 
 frequently largely increased when this is done. Even the old 
 form of Holtz machine seldom fails to work when treated in 
 this way. 
 
TABLES FOE REFERENCE. 
 
 361 
 
 APPENDIX C. 
 
 TABLES FOR REFERENCE. 
 
 Table I. 
 CAPILLARITY. 
 
 Height to which the liquid will rise in a tube 1 mm. in 
 diameter : 
 Alcohol . .11.4 mm. ' Mercury 9.2 mm. 
 
 Bromine 9.0 
 
 Ether . 9.5 
 
 Turpentine 12.7 
 
 Water . 29.3 
 
 Table II. 
 
 DENSITIES OF VARIOUS SUBSTANCES. 
 
 Benzine 0.72 to 0.740 
 
 Benzole 0.899 
 
 Birch 0.690 
 
 Bismuth, cast 9.822 
 
 Blood 1.0(50 
 
 Boxwood 1.280 
 
 Brass, cast 8.400 
 
 Brass, sheet 8.440 
 
 Brick ...... 1.6 to 2.000 
 
 Bromine 3.187 
 
 Butter , . . 0.942 
 
 Calcium chloride .... 2.230 
 
 Camphor 0.988 
 
 Carbon disulphide . . . . 1.293 
 Carbon dioxide, liquid . . 0.947 
 Cedar, American .... 0.554 
 Chalk . 1.8 to 2.800 
 
 Acetic acid . . . 
 
 . . . 1.060 
 
 Agate 
 
 . . . 2.615 
 
 Alcohol, absolute . 
 
 . . . 0.806 
 
 Alcohol, common . 
 
 . . . 0.833 
 
 Alum 
 
 . . . 1.724 
 
 Aluminium . 
 
 . . . 2.670 
 
 Amber .... 
 
 . . . 1.078 
 
 Antimony, cast. 
 
 . . . 6.720 
 
 Apple-tree wood . 
 
 . . . 0.790 
 
 Arsenic .... 
 
 . . . 8.310 ' 
 
 Ash, dry .... 
 
 . . . 0.690 
 
 Ash, green . . . 
 
 . . . 0.760 
 
 Asphalt ...... 
 
 . . . 2.500 
 
 Basalt . . . 
 
 . . . 2.950 ! 
 
 Beech, dry . . . 
 
 0.690 to 0.800 | 
 
 Beeswax . . . 
 
 . . . 0.964 
 
 Bell-metal . . , 
 
 . . . 8.050 
 
362 
 
 PRACTICAL PHYSICS. 
 
 Cherry-tree . . . . . 0.710 
 
 Chestnut 0.606 
 
 Chloroform 1.525 
 
 Clay 1.920 
 
 Coal, anthracite . . 1.26 to 1.800 
 
 Coal, bituminous . 1.270 to 1.423 
 
 Cobalt 8.800 
 
 Concrete, ordinary . . . 1.900 
 
 Concrete, in cement . . . 2.200 
 
 Cork 0.240 
 
 Copper, cast 8.830 
 
 Copper, sheet 8.878 
 
 Deal, Norway 0.689 
 
 Diamond 3.530 
 
 Earth 1.520 to 2.000 
 
 Ebony 1.187 
 
 Elder 0.690 
 
 Elm ........ 0.579 
 
 Elm, Canadian . . . . 0.725 
 
 Emery 3.900 
 
 Ether 0.736 
 
 Emerald 2.770 
 
 Feldspar 2.600 
 
 Fir, spruce 0.512 
 
 Fluor-spar 3.200 
 
 Galena e 7.580 
 
 German-silver 8.432 
 
 Glass, flint . . . 3.000 to 3.600 
 
 Glass, crown 2.520 
 
 Glass, plate 2.760 
 
 Glycerine 1.260 
 
 Gold 19.360 
 
 Gypsum, crys. . , . . . 2.310 
 
 Granite 2.650 
 
 Graphite 2.500 
 
 Gun-metal 8.561 
 
 Gutta-percha 0.966 
 
 Heavy spar 4.430 
 
 Honey 1.450 
 
 Human body 0.890 
 
 Hydrochloric acid, aq. sol. . 1.222 
 
 Ice 0.917 
 
 Iceland spar 2.723 
 
 Iron, bar ....... 7.788 
 
 Iron, cast 7.230 
 
 Iron, wrought 7.780 
 
 India-rubber .... 0.930 
 
 Iodine ..... = . 4.950 
 
 Iron pyrites . . . . . 5.000 
 
 Ivory , . . 1.820 
 
 Lard ....,.,. 0.947 
 
 Lead, cast ...... 11.360 
 
 Lead, sheet ...... 11.400 
 
 Lignum vitae . . . . , 1.333 
 
 Lime, quick 0.843 
 
 Limestone ...... 3.180 
 
 Logwood 0.913 
 
 Magnesium 1.750 
 
 Mahogany . . . . 0.56 to 0.852 
 
 Maple 0.755 
 
 Marble 2.720 
 
 Mercury , . 13.596 
 
 Milk 1.032 
 
 Molasses ....... 1.426 
 
 Mortar, average .... 1.700 
 
 Naphtha 0.848 
 
 Nitric acid . . . . 1.38 to 1.559 
 
 Oak, American red . . . 0.850 
 
 Oak, American white . . 0.779 
 
 Oak, live, seasoned . . . 1.068 
 
 Oak, live, green . . . . 1.260 
 
 Oil, castor . . . . . 0.970 
 
 Oil, linseed ...... 0.940 
 
 Oil, olive 0.915 
 
 Oil, turpentine 0.870 
 
 Oil, whale ...... 0.923 
 
 Paraffine . , . . 0.824 to 0.940 
 
 Petroleum 0.836 
 
 Phosphorus 1.830 
 
 Pear-tree 0.660 
 
 Pine, red, dry 0.590 
 
 Pine, white, dry .... 0.554 
 
TABLES FOE REFERENCE. 
 
 363 
 
 Pine, yellow, dry . . . . 0.461 
 
 Pine, pitch 0.660 
 
 Pitch 1.150 
 
 Platinum wire 21.531 
 
 Poplar, common .... 0.389 
 
 Porcelain, china . . . . 2.380 
 
 Potassium 0.865 
 
 Quartz 2.650 
 
 Rock-salt 2.257 
 
 Saltpetre 2.100 
 
 Sand, quartz 2.750 
 
 Sand, river 1.880 
 
 Sand, fine 1.520 
 
 Sand, coarse 1.510 
 
 Silver, cast . . 10.424 to 10.511 
 
 Slate 2.880 
 
 Sodium 0.970 
 
 The above table gives the weight in grammes of 1 ccm. 
 of the substance. It should be considered as giving only 
 approximations, as most of the densities vary between wide 
 limits in different specimens. 
 
 GASES AIVD VAPORS AT O C., BAROMETRIC PRESSURE 
 
 OF 76 CM. 
 
 Steel, uuhammered . . . 7.816 
 
 Sugar, cane ...... 1.593 
 
 Sulphur, native .... 2.033 
 
 Sulphuric acid ... .1.840 
 
 Tallow ....... 0.940 
 
 Tar .... . 1.015 
 
 Tin, cast ....... 7.290 
 
 Tourmaline, green . . . 3.150 
 
 Vinegar . 1.026 
 
 Water, at 100 C 0.958 
 
 Walnut ... ... 0.680 
 
 Water, sea 1.027 
 
 Wax, white 0.970 
 
 White metal, Babbitt . . 7.310 
 
 Willow 0.585 
 
 Zinc, cast 7.000 
 
 Acetic acid vapor . . . 2.0800 
 
 Air 1.0000 
 
 Alcohol vapor 1.6138 
 
 Ammonia ...... 0.5967 
 
 Benzole vapor .... 2.7290 
 
 Carbonous oxide .... 0.9670 
 
 Carbon dioxide .... 1.5241 
 
 Chlorine 2.4501 
 
 Coal-gas . . . 0.340 to 0.6500 
 
 Cyanogen 1.8060 
 
 Ether vapor 2.5630 
 
 Hydrochloric acid . . . 1.2780 
 
 In the above table the unit adopted is the quantity of matter 
 in 1 ccm. of air under the standard conditions. 
 
 Hydrogen disulphide 
 Hydrogen . . . . 
 Hydriodic acid . . 
 Marsh ga" . . . 
 Mercury vapor . 
 Nitrogen . . . . 
 Nitrogen binoxide . 
 Nitrogen monoxide . 
 
 Oxygen 
 
 Sulphurous acid . 
 Water vapor . . . 
 
 1.1912 
 0.0693 
 4.3737 
 0.5540 
 6.9207 
 0.9714 
 1.0392 
 1.5241 
 1.1057 
 2.2113 
 0.6225 
 
364 
 
 PliA CT1CAL PHYSICS. 
 
 Table III. 
 LIMIT OP ELASTICITY. 
 
 Cast steel, drawn 
 
 . . 55.6 
 
 Platinum, drawn . . 
 
 . . 2(1. 
 
 " " annealed 
 
 . . 5.0 
 
 " annealed 
 
 . . 14.5 
 
 Copper drawn 
 
 12 
 
 Steel, drawn .... 
 
 42.5 
 
 " annealed . . 
 
 . . 3.0 
 
 " annealed . 
 
 . . 15.0 
 
 Iron, drawn .... 
 
 . . 32.5 
 
 Silver, drawn 
 
 . . 11.25 
 
 " annealed . . . 
 
 . . 5.0 
 
 " anneale'l 
 
 , . 2.75 
 
 Lead, drawn .... 
 
 . . 0.25 
 
 Tin, drawn . . . 
 
 . 0.45 
 
 " annealed . 
 
 . . 0.2 
 
 " annealed . . . 
 
 . . 0.20 
 
 The above table gives the weight in kilogrammes necessary 
 to cause permanent elongation in wires 1 mm. in diameter at 
 the ordinary temperature. 
 
 Table IV. 
 ELECTRICAL CONDUCTIVITY. 
 
 
 4 24 
 
 Lead pressed 
 
 7 67 
 
 Aluminium, annealed 
 Bismuth, pressed . 
 Brass 
 
 . 51.64 
 . 1.15 
 26 22 
 
 Mercury, liquid . . . 
 Nickel, annealed . . . 
 Platinum, annealed 
 
 . 1.58 
 . 12.07 
 . 16.61 
 
 Cadmium 
 Copper, annealed . . 
 German silver .... 
 Gold, annealed . 
 
 . 22.37 
 . 94.19 
 . 7.14 
 . 71.83 
 
 Silver, annealed 
 Sodium ...... 
 Tin, pressed . . . . 
 Zinc, pressed 
 
 100.0 
 . 72.43 
 . 11.39 
 . 26.73 
 
 The above table expresses the conductivity of the substances 
 relatively to silver at C. 
 
TAULES FOE REFERENCE. 
 
 365 
 
 Table V. 
 
 APPROXIMATE ELECTRO-MOTIVE FORCE OF 
 PRIMARY BATTERIES. 
 
 DanielFs, amalgamated zinc, H 2 SO 4 -f- 4Aq. , Cu SC-4, con. sol. 1.079 volts. 
 
 " " -j-12 " " 0.978 " 
 
 " " -j-12 Aq., Cu NOs, " 1.000 " 
 
 " equi-dense solutions of Zn 864, and Cu SC>4 plates 
 
 of pure Zn and Cu 1.104 " 
 
 Bunsen, amal. zinc, H 2 SC>4 -\- 12 Aq., and HNO 3 , carbon . . 1 964 " 
 
 Grove, " -j- ^Aq. , HNOs, platinum 1.95G " 
 
 Leclanche, zinc in saturated solution of NH 4 Cl . . . . 1.32 " 
 
 Potassium bichromate 2.00 " 
 
 Table VI, 
 
 ELECTRICAL RESISTANCE, DIAMETER, CROSS-SECTION, 
 ETC., OF PURE COPPER WIRE, BIRMING- 
 HAM GAUGE, TEMPERATURE 15 C. 
 
 
 DIAMETER. 
 
 AREA OF CROSS-SEC. 
 
 RESISTANCE. 
 
 WEIGHT. 
 
 No. 
 
 Ins. 
 
 Cms. 
 
 Sq. Iiis. 
 
 Sq. Cms. 
 
 Ohms, 
 per Yd. 
 
 Ohms, 
 per M. 
 
 Lbs. per 
 Yd. 
 
 Grrns. 
 per M - 
 
 0000 
 
 .454 
 
 1.1530 
 
 .1620000 
 
 1.0444000 
 
 .000152 
 
 .000167 
 
 1.884000 
 
 934.700 
 
 000 
 
 .425 
 
 1.0790 
 
 .1420000 
 
 .9150000 
 
 .000174 
 
 .000190 
 
 1.651000 
 
 819.100 
 
 00 
 
 .380 
 
 .9650 
 
 .1130000 
 
 .7320000 
 
 .000217 
 
 .000238 
 
 1.320000 
 
 654.800 
 
 
 
 .340 
 
 .7620 
 
 .0908000 
 
 .5860000 
 
 .000272 
 
 .000297 
 
 1.056000 
 
 524.200 
 
 1 
 
 .300 
 
 .7210 .0707000 
 
 .4560000 
 
 .000349 
 
 .000382 
 
 .822000 
 
 408.100 
 
 2 
 
 .284 
 
 .7210 
 
 .0693000 
 
 .4090000 
 
 .000389 
 
 .000425 
 
 .737000 
 
 365.800 
 
 3 
 
 .259 
 
 .6580 
 
 .0527000 
 
 .3400000 
 
 .000468 
 
 .000512 
 
 .613000 
 
 304.200 
 
 4 
 
 .238 
 
 .6050 
 
 .0445000 
 
 .2870000 
 
 .000554 
 
 .000606 
 
 .518000 
 
 256.900 
 
 5 
 
 .220 
 
 .5590 
 
 .0380000 
 
 .2450000 
 
 .000649 
 
 .000709 
 
 .442000 
 
 219.500 
 
 6 
 
 .203 
 
 .5160 
 
 .0324000 
 
 .2090000 
 
 .000762 
 
 .000833 
 
 .377000 
 
 186.900 
 
 1 
 
 .180 
 
 .4570 
 
 .0254000 
 
 .1640000 
 
 .000969 
 
 .001060 
 
 .296000 
 
 146.900 
 
366 
 
 PRACTICAL PJ/YtilVS. 
 
 No. 
 
 DIAMETER. 
 
 AREA OP CROSS-SEC. 
 
 RESISTANCE. 
 
 WEIGHT. 
 
 Ins. 
 
 Cms. 
 
 Sq.Ins. 
 
 Sq. Cms. 
 
 Ohms, 
 per Yd. 
 
 Ohms. 
 perM. 
 
 Lbs. per Gnus. 
 Yd. per M. 
 
 8 
 
 .165 
 
 .4190 
 
 .0214000 
 
 .1380000 
 
 .001150 
 
 .001260 
 
 .249000 
 
 123.5000 
 
 9 
 
 .148 
 
 .3760 
 
 .0172000 
 
 .1110000 
 
 .001430 
 
 .001570 
 
 .200000 
 
 99.3000 
 
 10 
 
 .134 
 
 .0*00 
 
 .0141000 
 
 .0910000 
 
 .001750 
 
 .001910 
 
 .164000 
 
 81.4000 
 
 11 
 
 .120 
 
 .9806 
 
 .0113000 
 
 .0730000 
 
 .002180 
 
 .002380 
 
 .132000 
 
 65.5000 
 
 12 
 
 .109 
 
 .2770 
 
 .0093300 
 
 .0602000 
 
 .002640 
 
 .002890 
 
 .109000 
 
 53.9000 
 
 13 
 
 .095 
 
 .2410 
 
 .0070900 
 
 .0457000 
 
 ,003480 
 
 .003800 
 
 .082500 
 
 40.9000 
 
 14 
 
 .083 
 
 .2110 
 
 .0054100 
 
 .0349000 
 
 .004560 
 
 .004980 
 
 .063000 
 
 31.2000 
 
 15 
 
 .072 
 
 .1830 
 
 .0040700 
 
 .0263000 
 
 .006060 
 
 .006620 
 
 .047400 
 
 23.5000 
 
 16 
 
 .065 
 
 .1650 
 
 .0033100 
 
 .0214000 
 
 .007430 
 
 .008130 
 
 .038600 
 
 19.2000 
 
 17 
 
 .058 
 
 .1470 
 
 .0026400 
 
 .0170000 
 
 .009330 
 
 .010200 
 
 .030700 
 
 15.3000 
 
 18 
 
 .049 
 
 .1240 
 
 .0018900 
 
 .0122000 
 
 .013100 
 
 .014300 
 
 .022000 
 
 10.9000 
 
 19 
 
 .042 
 
 .1070 
 
 .0013900 
 
 .0089400 
 
 .017800 
 
 .019600 
 
 .016100 
 
 8.0000 
 
 20 
 
 .035 
 
 .0889 
 
 .0009620 
 
 .0062100 
 
 .025600 
 
 .028000 
 
 .011200 
 
 5.5600 
 
 21 
 
 .032 
 
 .0813 
 
 .0008040 
 
 .0051900 
 
 .030700 
 
 .033500 
 
 .009360 
 
 4.6400 
 
 22 
 
 .028 
 
 .0711 
 
 .0006160 
 
 .0039700 
 
 .040000 
 
 .043810 
 
 .007160 
 
 3.5500 
 
 23 
 
 .025 
 
 .0635 
 
 .0004910 
 
 .0031700 
 
 .050200 
 
 .054900 
 
 .005710 
 
 2.8300 
 
 24 
 
 .022 
 
 .0559 
 
 .0003800 
 
 ,0024500 
 
 .064900 
 
 .070900 
 
 .004420 
 
 2.1900 
 
 25 
 
 .020 
 
 .0508 
 
 .0003140 
 
 .0020300 
 
 .078600 
 
 .085800 
 
 .003670 
 
 1.8200 
 
 26 
 
 .018 
 
 .0457 
 
 .0002540 
 
 .0016400 
 
 .096900 
 
 .106000 
 
 .002960 
 
 1.4700 
 
 27 
 
 .016 
 
 .0406 
 
 .0002010 
 
 .0013000 
 
 .123000 
 
 .134000 
 
 .002340 
 
 1.1600 
 
 28 
 
 .014 
 
 .0356 
 
 .0001540 
 
 .0009930 
 
 .160000 
 
 .175000 
 
 .001790 
 
 0.8890 
 
 29 
 
 .013 
 
 .0330 
 
 .0001330 
 
 .0008560 
 
 .186000 
 
 .203000 
 
 .001540 
 
 .7660 
 
 30 
 
 .012 
 
 .0305 
 
 .0001130 
 
 .0007320 
 
 .218000 
 
 .288000 
 
 .001320 
 
 .6530 
 
 31 
 
 .010 
 
 .0254 
 
 .0000785 
 
 .0005070 
 
 .314000 
 
 .343000 
 
 .000915 
 
 .4540 
 
 32 
 
 .009 
 
 .0229 
 
 .0000636 
 
 .0004100 
 
 .388000 
 
 .424000 
 
 .000746 
 
 .3670 
 
 33 
 
 .008 
 
 .0203 
 
 .0000503 
 
 .0003240 
 
 .491000 
 
 .536000 
 
 .000585 
 
 .2900 
 
 34 
 
 .007 
 
 .0178 
 
 .0000385 
 
 .0002480 
 
 .641000 
 
 .701000 
 
 .000442 
 
 .2200 
 
 35 
 
 .005 
 
 .0127 
 
 .0000196 
 
 .0001270 
 
 1.260000 
 
 1.370000 
 
 .000229 
 
 .1130 
 
 36 
 
 .004 
 
 .0102 
 
 .0000126 
 
 .0000811 
 
 1.960000 
 
 2.150000 
 
 .000146 
 
 .0720 
 
TABLES FOR REFERENCE. 
 
 367 
 
 Table VII. 
 ACCELERATION DUE TO GRAVITY. 
 
 Berlin, lat. 5230' . 981.25 cm. Washington, lat. 3854' . 980.06 cm. 
 
 Greenwich," 5129' . 981.17 " Lat. of 45 980.61 " 
 
 Paris, " 4850' . 980.94 " Equator 978.10 " 
 
 New York, " 4043 f . 980.19 " Pole , 983.11 " 
 
 Table rill. 
 
 HEAT, ABSORBING, CONDUCTING, RADIATING, 
 REFLECTING POWER. 
 
 Substance. 
 
 ,0 
 
 II 
 
 <1 
 
 Conduct- 
 ing. 
 
 i* 
 
 "S3 
 
 J 
 
 Substance. 
 
 Absorb- 
 ing. 
 
 Conduct- 
 ing. 
 
 IB 
 
 1* 
 
 fT 
 
 
 
 1.8 
 
 
 
 Lead white... 
 
 100 
 
 
 100 
 
 
 
 
 33.1 
 
 7 
 
 100 
 
 
 
 
 
 
 
 
 77.6 
 
 7 
 
 
 Palladium .... 
 
 
 63 
 
 
 
 
 
 
 90 
 
 10 
 
 Paper 
 
 
 
 98 
 
 
 Gold polished . . 
 
 
 53.2 
 
 3 
 
 
 
 
 8 4 
 
 17 
 
 
 Indian Ink 
 
 85 
 
 
 85 
 
 13 
 
 
 
 2.8 
 
 
 
 
 
 
 
 
 Shellac 
 
 72 
 
 
 72 
 
 
 Isinglass 
 Lampblack 
 Lead polished . . 
 
 91 
 
 100 
 
 8 5 
 
 80 " 
 100 
 19 
 
 
 60 
 
 Silver, polished 
 Steel 
 Tin 
 
 
 100 
 12.0 
 14 5 
 
 3 
 12 
 
 90 
 70 
 
 " tarnished . 
 
 
 
 45 
 
 
 Zinc 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 In the table of absorbing powers the standard adopted is 
 lampblack and the source of heat is copper at 100 C. In con- 
 ducting powers, silver is the standard. In radiating power, 
 lampblack is taken as the standard. The initial temperatures 
 
868 
 
 PRACTICAL PHYSICS. 
 
 of the substances compared is 100 C. 
 polished brass is taken as the standard. 
 
 In reflecting powers, 
 
 Table IX. 
 BOILING POINTS OF SUBSTANCES AT BAR. PRES. 76 CM, 
 
 Acetic acid . . 
 \cetone 
 
 . . 119.00 C. 
 56 28 
 
 Petroleum . . . 
 
 40 to 70.0 ( 
 290 
 
 
 . -. 78.39 
 
 Sulphur 
 
 . . 448 4 
 
 Aldehyde . . . 
 Ammonia . . . 
 Amylic alcohol . 
 4.niline . . . 
 
 . . 20.78 
 . . 39.00 
 . . 131.00 
 183 70 
 
 Sulphuric acid 
 Suphur dioxide . 
 Turpentine . . 
 Water distilled 
 
 . . 338.0 
 . . 8.0 
 . . 159.3 
 100 
 
 Benzine . . . 
 Benzole 
 
 90 to 110.00 
 80 44 
 
 Water, saturated 
 NaCl . . 
 
 with 
 102 
 
 Bromine . . , 
 Carbon dioxide . 
 Carbon disulphide 
 Ether 
 
 . . 63.00 
 
 . . 78.00 
 . . 48.00 
 34 90 
 
 Water, saturated 
 KNO 3 . . . 
 Water, saturated 
 Ko CO 3 
 
 with 
 . . 116.0 
 witli 
 135 
 
 Iodine .... 
 
 . . 200 00 
 
 Water, saturated 
 
 with 
 
 Mercury 
 
 350 00 
 
 CaCl 2 .... 
 
 . . 179.0 
 
 Nitrous oxide 
 
 . . 92.00 
 
 Zinc 
 
 . . 1040.0 
 
 Methylic alcohol 
 
 . . 65.5 
 
 
 
 Table X. 
 
 COEFFICIENTS OF EXPANSION FOR 1< 
 AND 100 C. 
 
 . LINEAR. 
 
 BETWEEN 
 
 Aluminium .... 0.00002221 
 
 Antimony .... 0.00000980 
 
 Bismuth ..... 0.00001330 
 
 Brass ...... 0.00001875 
 
 Bronze 0.00001844 
 
 Copper 0.00001866 
 
 Ebonite 0.00008420 
 
 Glass . . , . . . 0.00000861 
 
 Gold 0.00001466 
 
 Graphite 0.00000786 
 
 Iron, cast .... 0.00001125 
 
 " wrought . . . 0.00001220 
 
 Lead 0.00002799 
 
 Marble 0.00000786 
 
 Paraffine 0.00027854 
 
 Pine 0.00000496 
 
 Platinum 0.00000886 
 
 Sandstone, red . . . 0.00001174 
 
 Silver 0.00001943 
 
 Sulphur 0.00006413 
 
 Steel, tempered . . 0.00001322 
 
 " untempered . 0.00001095 
 
 Tin 0.00002730 
 
 Zinc 0-00002976 
 
TABLES FOR REFERENCE. 
 
 369 
 
 Air, cons, vol., 0-100 , 
 
 " cons, pres., 0-100 
 
 Alcohol, ethyl. 0-50 . 
 
 " methyl. 0-61 . 
 
 CUBICAL. 
 
 0.003663 Ether, 0-63 .... 0.002100 
 0.003667 Mercury, 0-100 . . . 0.000181 
 0.001080 Sulphuric acid, 0-30 . 0.000489 
 0.001358 Turpentine, 9-106 . 0.001050 
 
 Benzine, 11-81 . . . 0.001385 Water, 4-100 .... 0.000449 
 
 Table 
 
 LATENT HEAT OF LIQUEFACTION AND VAPORIZATION. 
 
 LIQUEFACTION. 
 
 Beeswax 97.22 
 
 Bismuth 12.64 
 
 Lead. . 5.37 
 
 Mercury ...... 2.83 
 
 Phosphorus 5.03 
 
 Platinum .27.18 
 
 Potassium nitrate . , . 47.37 
 
 Silver 21.07 
 
 Sodium nitrate .... 62.97 
 
 Sulphur 9.37 
 
 Tin 14.25 
 
 Water 79.24 
 
 Zinc . 28.13 
 
 VAPORIZATION. 
 
 Alcohol, ethylic .... 202.4 
 
 " methylic .... 264 
 
 Acetic acid ...... 102 
 
 Bromine ....... 45.6 
 
 Carbon disulphide ... 86.7 
 
 Ether 90.4 
 
 Mercury 62.0 
 
 Oil of turpentine .... 74.0 
 
 Water. , 535.9 
 
 Table XII. 
 
 MELTING POINTS 
 
 Antimony 425 C. 
 
 Beeswax 62 
 
 Bismuth 270 
 
 Brass 1020 
 
 Bromine 24.5 
 
 Butter 33.0 
 
 Copper . . 1064.0 to 1200 
 
 German-silver . . . 1093 
 
 Gold ...... 1250.0 
 
 Ice . 0.0 
 
 Iridium . . . . . 1950.0 C. 
 Iron . . 1500.0 to 1600 
 
 Lard 33.2 
 
 Lead 334 
 
 Margaric acid . . . 59.9 
 
 Mercury 38.8 
 
 Paraffine .... 38-52 
 Phosphorus .... 44.2 
 Platinum. . 1775 to 2000 
 Potassium 02.5 
 
370 
 
 PRACTICAL PHYSICS. 
 
 Rose's metal .... 94 C. 
 
 Silver 1000 
 
 Sulphur 115 
 
 Sodium 97.6 
 
 Stearic acid .... 69.9 
 
 Stearine 60 
 
 Spermaceti .... 49 
 
 Tallow (fresh) ... 43 O. 
 
 Tin . . . . 
 
 Turpentine . 
 Wax, white . 
 Wood's metal 
 Zinc 
 
 235 
 
 27 
 
 65 
 
 68 
 
 433 
 
 Table XIII. 
 SPECIFIC HEAT. 
 
 Alcohol at 0.5475 
 
 Aluminium 0.2122 
 
 Antimony 0.0486 
 
 Bismuth 0.0298 
 
 Brass, hard 0.0858 
 
 Carbon disulphide . . . 0.2352 
 
 Copper 0.0933 
 
 Ether at 0.5290 
 
 Glass, thermometer . . . 0.1980 
 
 Glycerine 0.5550 
 
 Ice 0.5040 
 
 Iron 0.1124 
 
 Lead . , 0.0315 
 
 Mercury 0.0335 
 
 Nitrogen 0.2438 
 
 Olive oil 0.310 
 
 Oxygen 0.2175 
 
 Platinum 0.0323 
 
 Silver 0.0559 
 
 Salt . 0.173 
 
 Sulphur 0.1844 
 
 Steel 0.118 
 
 Tin 0.0559 
 
 Turpentine at . . . . 0.4106 
 
 Wood spirit 0.645 
 
 Zinc . , 0.0935 
 
 Table XIT. 
 INDICES OP REFRACTION. 
 
 Air 000294 
 
 Aqueous lens, eye . . .357 
 
 Alcohol, ethyl 361 
 
 Benzine 49 
 
 Canada balsam ... .54 
 Carbon disulphide . . .626 
 
 Crown glass 515 
 
 Crystalline lens, eye . . .384 
 Diamond . . . 2.47 to 2.75 
 
 Ether 1.354 
 
 Flint glass . . . 1.57 to 1.71 
 
 Glycerine 
 
 Ice 
 
 Iceland spar, ordinary ray 
 " " extra, ray . 
 
 Quartz, ordinary ray . . 
 " extra, ray . . 
 
 Rock salt . . . . . 
 
 Ruby 
 
 Vitreous lens, eye . . . 
 
 Water . 
 
 .47 
 
 .310 
 
 .654 
 
 .483 
 
 .544 
 
 .553 
 
 .550 
 
 .779 
 
 .339 
 
 .332 
 
 These indices are given for the mean D lino. 
 
TABLES FOE EEFEEENCE. 371 
 
 Table XV. 
 MENSURATION RULES. 
 
 Area of triangle = base X h altitude. 
 
 " parallelogram = base X altitude. 
 
 " trapezoid = altitude X h sum of parallel sides. 
 Circum. of circle = diameter X 3.1416. 
 Diameter of circle = circum. X .3183. 
 Area of circle = diameter squared X .7854. 
 Area of ellipse = product of diameters X .7854. 
 Area of reg. polygon = sum of sides X i apothem. 
 Lat. surface of cylinder = cir. base X alt. 
 Contents of cylinder = area base X alt. 
 Surface of sphere = diameter X circum. 
 Contents of sphere = diameter cubed X .5236. 
 
 Surface of pyramid > 
 
 > = cir. base X h slant height. 
 " " cone } 
 
 Contents of cone = area base X J alt. 
 Surface of frustum of pyramid or cone = 
 
 sum of cir. of bases X h slant height. 
 Contents of frustum of pyramid or cone = 
 
 J alt. X sum of areas of bases and sq. rt. of product of these areas. 
 
 Table XVI. 
 LENGTH OF SECONDS' PENDULUM. 
 
 Greenwich, lat. 51 29' 99.413 cm. 
 
 Paris, 48 50' 99-390 " 
 
 New York, 40 43' . . . . 99.317 " 
 
 Washington, 38 54' 99.306 " 
 
 Lat. 45 00' 99.356 
 
 Equator 99.103 
 
 Pole .......... 99.610 
 
372 
 
 PRACTICAL PHYSICS. 
 
 Table XVII. 
 VELOCITY OF SOUND AT O C. 
 
 Air ... 
 Ash .... 
 
 Brass . . . 
 Caoutchouc 
 Carbon monoxide 
 Carbon dioxide 
 Cedar . . . 
 Chlorine . . 
 Copper . . . 
 Elm .... 
 Ether . . . 
 Fir .... 
 Glass .... 
 Gold . 
 
 per sec. 
 
 1,093 ft. 
 15,314 
 
 Hydrogen . . per se 
 Iron . " 
 
 c., 4,163ft 
 17 822 
 
 10 885 
 
 Lead " 
 
 4 030 
 
 197 
 1,106 
 
 Maple . . . . " 
 Oak " 
 
 13,472 
 12 622 
 
 856 
 16 503 
 
 Oxygen . . . . " 
 Pine " 
 
 1,040 
 10 900 
 
 677 
 11,666 
 
 Silver . . . . 
 Steel ....." 
 
 8,553 
 17 182 
 
 13,516 
 3,801 
 15,218 
 16,488 
 5,717 
 
 Tallow . . . . " 
 Turpentine at 24 " 
 Walnut . . . . " 
 Water at 8.1 . " 
 Wax . 
 
 1,170 
 3,976 
 15,095 
 4,708 
 2.811 
 
 Tnhle XVIII. 
 
 ELASTICITY OF TRACTION. 
 
 No. of kilos, required to double the length of a wire 1 sq. 
 mm. in section. 
 
 Brass ....... 9,000 
 
 Copper 12,400 
 
 Glass, plate 7,015 
 
 Iron, wrought 19,000 
 
 Lead 1,800 
 
 Platinum . . . . . . 17,044 
 
 I Silver . . .... 7,400 
 
 Slate. ....... 11,035 
 
 Steel . 21,000 
 
 Whalebone 700 
 
 Wood ....... 1,100 
 
 Zinc . . . . . . . 8,700 
 
TABLES FOft REFERENCE. 
 
 373 
 
 Table XIX. 
 TENACITY. 
 
 Copper, drawn 40.3 
 
 " annealed . . . 30.54 
 
 Iron, drawn 61.10 
 
 " annealed . . . . .46.88 
 Lead, drawn ...... 2.07 
 
 " annealed 1.80 
 
 Platinum, drawn . ... 34.10 
 " annealed . .23.5 
 
 Silver, drawn 29.00 
 
 " annealed . . . .16.02 
 
 Steel, drawn 70.00 
 
 " annealed 40.00 
 
 " cast, drawn . . . .80.00 
 " " annealed . . . 65.75 
 
 Tin, drawn 2.45 
 
 " annealed 1.70 
 
 The above table gives the weight in kilogrammes required to 
 break a wire of the substance 1 mm. in diameter. 
 
 Table XX. 
 TRIGONOMETRICAL FUNCTIONS. 
 
 Angle. 
 
 Sine. 
 
 Tangent. 
 
 Cotangent. 
 
 Cosine. 
 
 Angle. 
 
 
 
 0.000 
 
 0.000 
 
 
 
 
 1.000 
 
 
 90 
 
 
 
 17 
 
 
 17 
 
 
 
 
 
 
 
 1 
 
 0.017 
 
 
 0.017 
 
 
 57.29 
 
 
 1.000 
 
 
 89 
 
 
 
 18 
 
 
 18 
 
 
 
 
 1 
 
 
 2 
 
 0.035 
 
 
 0.035 
 
 
 28.64 
 
 
 0.999 
 
 
 88 
 
 
 
 17 
 
 
 17 
 
 
 
 
 
 
 
 3 
 
 0.052 
 
 
 0.052 
 
 
 19.08 
 
 
 0.999 
 
 
 87 
 
 
 
 18 
 
 
 18 
 
 
 
 
 1 
 
 
 4 
 
 0.070 
 
 
 0.070 
 
 
 14.30 
 
 
 0.998 
 
 
 86 
 
 
 
 17 
 
 
 17 
 
 
 
 
 2 
 
 
 5 
 
 0.087 
 
 
 0.087 
 
 
 11.43 
 
 
 0.996 
 
 
 85 
 
 
 
 18 
 
 
 18 
 
 
 
 
 1 
 
 
 6 
 
 0.105 
 
 
 0.105 
 
 
 9.514 
 
 
 0.995 
 
 
 84 
 
 
 
 17 
 
 
 18 
 
 
 
 
 2 
 
 
 7 
 
 0.122 
 
 
 0.123 
 
 
 8.144 
 
 
 0.993 
 
 
 83 
 
 
 
 17 
 
 
 18 
 
 
 
 
 3 
 
 
 8 
 
 0.139 
 
 
 0.141 
 
 
 7.115 
 
 
 0.990 
 
 
 82 
 
 
 
 17 
 
 
 17 
 
 
 841 
 
 
 2 
 
 
 9 
 
 0.156 
 
 
 0.158 
 
 
 6.314 
 
 
 0.988 
 
 
 81 
 
 
 
 18 
 
 
 18 
 
 
 643 
 
 
 3 
 
 
 10 
 
 0.174 
 
 
 0.176 
 
 
 5.671 
 
 
 0.985 
 
 
 80 
 
 
 
 17 
 
 
 18 
 
 
 526 
 
 
 3 
 
 
 11 
 
 0.191 
 
 
 0.194 
 
 
 5.145 
 
 
 0.982 
 
 
 79 
 
 
 
 17 
 
 
 19 
 
 
 440 
 
 
 4 
 
 
 12 
 
 0.208 
 
 
 0.213 
 
 
 4.705 
 
 
 0.978 
 
 
 78 
 
 
 
 17 
 
 
 18 
 
 
 374 
 
 
 4 
 
 
 13 
 
 0.225 
 
 
 0.231 
 
 
 4.331 
 
 
 0.974 
 
 
 77 
 
 
 
 17 
 
 
 18 
 
 
 320 
 
 
 4 
 
 
 14 
 
 0.242 
 
 
 0.249 
 
 
 4.011 
 
 
 0.970 
 
 
 76 
 
 
 
 17 
 
 
 19 
 
 
 279 
 
 
 4 
 
 
 15 
 
 0.259 
 
 
 0.268 
 
 
 3.732 
 
 
 0.966 
 
 
 75 
 
 
 
 17 
 
 
 19 
 
 
 245 
 
 
 5 
 
 
 Angle. 
 
 Cosine. 
 
 
 Cotangent 
 
 
 Tangent. 
 
 Sine. 
 
 
 Angle. 
 
374 
 
 PRACTICAL PHYSICS. 
 
 Angle. 
 
 Sine. 
 
 Tangent. 
 
 Cotangent. 
 
 Cosine. 
 
 Angle. 
 
 16 
 
 0.276 
 
 
 0.287 
 
 
 3.487 
 
 
 0.961 
 
 
 74 
 
 
 
 16 
 
 
 19 
 
 
 216 
 
 
 5 
 
 
 17 
 
 0.292 
 
 
 0.306 
 
 
 3.271 
 
 
 0.956 
 
 
 73 
 
 
 
 17 
 
 
 19 
 
 
 193 
 
 
 5 
 
 
 18 
 
 0.309 
 
 
 0.32o 
 
 
 3.078 
 
 
 0.951 
 
 
 72 
 
 
 
 17 
 
 
 19 
 
 
 174 
 
 
 5 
 
 
 19 
 
 0.326 
 
 
 0.344 
 
 
 2.904 
 
 
 0.946 
 
 
 71 
 
 
 
 16 
 
 
 20 
 
 
 157 
 
 
 6 
 
 
 20 
 
 0.342 
 
 
 0.364 
 
 
 2.747 
 
 
 0.940 
 
 
 70 
 
 
 
 16 
 
 
 20 
 
 
 142 
 
 
 6 
 
 
 21 
 
 0.358 
 
 
 O.S84 
 
 
 2.605 
 
 
 0.934 
 
 
 69 
 
 
 
 17 
 
 
 20 
 
 
 130 
 
 
 7 
 
 
 22 
 
 0.375 
 
 
 0.404 
 
 
 2.475 
 
 
 0.927 
 
 
 68 
 
 
 
 16 
 
 
 20 
 
 
 119 
 
 
 6 
 
 
 23 
 
 0.391 
 
 
 0.424 
 
 
 2.356 
 
 
 0.921 
 
 
 67 
 
 
 
 16 
 
 
 21 
 
 
 110 
 
 
 7 
 
 
 24 
 
 0.407 
 
 
 0.445 
 
 
 2.246 
 
 
 0.914 
 
 
 66 
 
 
 
 16 
 
 
 21 
 
 
 101 
 
 
 8 
 
 
 25 
 
 0.423 
 
 
 0.466 
 
 
 2.145 
 
 
 0.906 
 
 
 65 
 
 
 
 15 
 
 
 22 
 
 
 95 
 
 
 7 
 
 
 26 
 
 0.438 
 
 
 0.488 
 
 
 2.050 
 
 
 0.899 
 
 
 64 
 
 
 
 16 
 
 
 22 
 
 
 87 
 
 
 8 
 
 
 27 
 
 0.454 
 
 
 0.510 
 
 
 1.963 
 
 
 0.891 
 
 
 63 
 
 
 
 15 
 
 
 22 
 
 
 82 
 
 
 8 
 
 
 28 
 
 0.469 
 
 
 0.532 
 
 
 1.881 
 
 
 0.883 
 
 
 62 
 
 
 
 16 
 
 
 22 
 
 
 77 
 
 
 8 
 
 
 29 
 
 0.485 
 
 
 0.554 
 
 
 1.804 
 
 
 0.875 
 
 
 61 
 
 
 
 15 
 
 
 23 
 
 
 72 
 
 
 9 
 
 
 30 
 
 0.500 
 
 
 0.577 
 
 
 1.732 
 
 
 0.866 
 
 
 60 
 
 
 
 15 
 
 
 24 
 
 
 68 
 
 
 9 
 
 
 31 
 
 0.515 
 
 
 0.601 
 
 
 1.664 
 
 
 0.857 
 
 
 59 
 
 
 
 15 
 
 
 24 
 
 
 64 
 
 
 9 
 
 
 32 
 
 0.530 
 
 
 0.625 
 
 
 1.600 
 
 
 0.848 
 
 
 58 
 
 
 
 15 
 
 
 24 
 
 
 60 
 
 
 9 
 
 
 33 
 
 0.545 
 
 
 0.649 
 
 
 1.540 
 
 
 0.839 
 
 
 57 
 
 
 
 14 
 
 
 26 
 
 
 57 
 
 
 10 
 
 
 34 
 
 0.559 
 
 
 0.675 
 
 
 1.483 
 
 
 0.829 
 
 
 56 
 
 
 
 15 
 
 
 25 
 
 
 55 
 
 
 10 
 
 
 85 
 
 0.574 
 
 
 0.700 
 
 
 1.428 
 
 
 0.819 
 
 
 5o 
 
 
 
 14 
 
 
 27 
 
 
 52 
 
 
 10 
 
 
 33 
 
 0.588 
 
 
 0.727 
 
 
 1.376 
 
 
 0.809 
 
 
 54 
 
 
 
 14 
 
 
 27 
 
 
 49 
 
 
 10 
 
 
 37 
 
 0.602 
 
 
 0.754 
 
 
 1.327 
 
 
 0.799 
 
 
 68 
 
 
 
 14 
 
 
 27 
 
 
 47 
 
 
 11 
 
 
 88 
 
 0.616 
 
 
 0,781 
 
 
 1.280 
 
 
 0.788 
 
 
 52 
 
 
 
 13 
 
 
 29 
 
 
 45 
 
 
 11 
 
 
 39 
 
 0.629 
 
 
 0.810 
 
 
 1.235 
 
 
 0.777 
 
 
 51 
 
 
 
 14 
 
 
 29 
 
 
 43 
 
 
 11 
 
 
 40 
 
 0.643 
 
 
 0.839 
 
 
 1.192 
 
 
 0.766 
 
 
 50 
 
 
 
 13 
 
 
 30 
 
 
 42 
 
 
 11 
 
 
 41 
 
 0.656 
 
 
 0.869 
 
 
 1.150 
 
 
 . 0.755 
 
 
 4'J 
 
 
 
 13 
 
 
 31 
 
 
 39 
 
 
 12 
 
 
 42 
 
 0.669 
 
 
 0.900 
 
 
 1.111 
 
 
 0.743 
 
 
 48 
 
 
 
 13 
 
 
 33 
 
 
 39 
 
 
 12 
 
 
 43 
 
 0.682 
 
 
 0.933 
 
 
 1.072 
 
 
 0.731 
 
 
 47 
 
 
 
 13 
 
 
 33 
 
 
 36 
 
 
 12 
 
 
 44 
 
 0.695 
 
 
 0.966 
 
 
 1.036 
 
 
 0.719 
 
 
 46 
 
 
 
 12 
 
 
 34 
 
 
 36 
 
 
 12 
 
 
 45 
 
 0.707 
 
 
 1.000 
 
 
 1.000 
 
 
 0.707 
 
 
 45 
 
 Angle. 
 
 Cosine. 
 
 
 Cotangent 
 
 
 Tangent. 
 
 
 Sine. 
 
 
 Angle. 
 
TABLES FOE REFERENCE. 
 
 375 
 
 Table XXI. 
 SOME USEFUL NUMBERS. 
 
 7t = 3.1415926. 
 Dyne in grammes = .00102. 
 Poundal in dynes = 13825. - 
 Erg in gramme-centimetres = 
 
 .00102. 
 Foot-pound in kilogramme-metres 
 
 = .13825. 
 
 Kilogramme-metre in foot-pounds = 
 7.23308. 
 
 Foot-poundal in ergs = 421390. 
 \/~2~ = 1.4142. 
 A/IT 1.7320. 
 \/T~ = 2.2361. 
 A cubic foot of water at 4 C. 
 
 weighs in pounds '= 62.425. 
 A cubic foot of water at 16f C. 
 
 weighs in pounds = 62.321. 
 
 A cubic foot of air at C. 
 
 weighs in pounds = 0.080728. 
 1 litre of H. at C., 760 mm., 
 
 weighs 0.08969 g. 
 1 Paris foot = 0.32484 metres. 
 1 " line = 2.2588 mm. 
 1 Eng. foot = 0.30479 m. 
 1 Ger. mile = 7.4204 kilom. 
 1 Eng. mile = 1.60929 kilom. 
 1 Rhenish ft. = 0.31385 m. 
 1 metre = 3.2809 Eng. ft. 
 
 1 kilometer = 0.62138 Eng. mile. 
 1 litre = 0.22017 gal. 
 
 1 " = 1.76133 pints. 
 
 1 kilogramme = 2.20462 Ibs. avoir. 
 1 gramme =15.43235 grains. 
 1 metre =39.37 in. 
 
 1 U. S. gal. =231 cu. in. 
 
 Table XXII. 
 WEIGHTS AND MEASURES. 
 
 MEASURES OF LENGTH, ENGLISH. 
 1 mi. = 8 fur. = 320 rods = 1760 yd. = 5280 ft. = 63360 in. 
 
 MEASURES OF LENGTH, FRENCH. 
 1 kilo. = 1000 m. = 10000 dcm. = 100000 cm. = 1000000 mm. 
 
 MEASURES OF SURFACE, ENGLISH. 
 1 acre = 4840 sq. yd. = 43560 sq. ft. 
 
 MEASURES OF SURFACE, FRENCH. 
 
 1 sq. H km. = 10 sq. P km. = 100 sq. m. = 1000 sq. dcm. = 10000 sq. cm. 
 = 100000 sq. mm. 
 
 1 are = 100 sq. metres. 
 
876 PRACTICAL PHYSICS. 
 
 MEASURES OF VOLUME, ENGLISH. 
 1 cu. yd. = 27 cu. ft. = 46656 cu. in. 
 
 MEASURES OF VOLUME, FRENCH. 
 1 cu. metre = 1000 cu. dcm. = 1000 litres = 1000000 ccm. 
 
 ENGLISH WEIGHTS. 
 
 1 Ib. avoir. = 16 oz. = 256 dr. = 7000 gr. 
 
 1 oz. = 437.5 gr. 
 
 FRENCH WEIGHTS. 
 1 kilo. g. = 1000 g. = 10000 dcg. = 100000 eg. = 1000000 nig. 
 
 MISCELLANEOUS. 
 
 
 Lineal feet X -00019 = miles. 
 
 Square inches X .007 = sq. ft. 
 
 Cu. inches X .00058 = cu. ft. 
 
 Cu. ft. X 7.48 = TJ. S. gallons. 
 
 Cu. in. X . 004329 =U. S. gallons. 
 
 IT. S. gals. X . 13367 = cu. ft. 
 
 Cu. ft. of water X 62.5 = lbs. avoir. 
 
 Cu. in. of water X .03617 = lbs. avoir. 
 
 Metres X 3.2809 = ft. 
 
 Ft. X 0.3048 = metres. 
 
 Sq. in. X 6.451 = scm. 
 
 Scm. X 0.155 = sq. in. 
 
 Cu. in. X 16.386 = ccm. 
 
 Ccm. X .06103 = cu. in. 
 
 Litres X 61.027 cu. in. 
 
 Oz. avoir. X 28.35 = grammes. 
 
 Lb. X 453.593 = grammes. 
 
 Gr. X 15.432 = grains. 
 
 Kilog. X 2.2046 = Ibs. avoir. 
 
INDEX. 
 
INDEX. 
 
 [The numbers refer to the articles.] 
 
 Aberration, spherical, 537, 548. 
 Absorption, of air by water, 52 ; of 
 
 heat by substances, table, page 
 
 367. 
 Acceleration due to gravity, 131 ; 
 
 table, page 367. 
 Adhesion, 64, 65. 
 Air-pump, experiments with, 152- 
 
 154, 160-162, 178, 185, 251, 
 
 261 ; mercury, 163. 
 Air-thermometer, 240, 258. 
 Amalgam, electric, 614. 
 Amalgamating battery-zincs, 611. 
 Analysis of white light, 551. 
 Aneroid barometer, 159. 
 Angle, critical, 541 ; measurement 
 
 of, 18 ; of prism, 522. 
 Angular currents, laws of, 382, 383. 
 Apparatus for laboratory, list of, 
 
 595. 
 
 Archimedes, principle of, 180-185. 
 Area, measurement of, 18, 19. 
 Ascent of liquids in capillary tubes, 
 
 85 ; between plates, 84. 
 Astatic galvanometer, 358. 
 Astronomical telescope, 585. 
 Athermancy, 264. 
 Atmospheric pressure, 151-162. 
 Attraction, electrical law of, 312; 
 
 magnetic law of, 287; of 
 
 vibrating bodies, 496-498. 
 Atwood's machine, 130. 
 Aurora-tube, 402. 
 
 Balance, beam, how to use, 23; 
 Jolly's, how to make and use, 
 23. 
 
 Barometer, 158-159. 
 
 Baroscope, 185. 
 
 Batteries, care of, 613; connecting 
 together, 369; galvanic, 346- 
 348 ; for laboratory, 595. 
 
 Battery, Daniell's, 358,595; float- 
 ing, 383 ; fluid for carbon, 612 ; 
 Gre let, 595 ; measure electro- 
 motive force of, 371-373; 
 measure resistance of, 367-369 ; 
 secondary or storage, 408-409; 
 table of E. M. F. of, page 365 ; 
 thermo-electric, 406. 
 
 Beam-compass, 15. 
 
 Beats, 459, 460, 462. 
 
 Boiling-point of liquids, 254; in- 
 fluence of substance in so- 
 lution, 255; of pressure, 251, 
 252, 254; on thermometers, 
 246 ; table of, page 368. 
 
 Books of reference for laboratory, 
 594. 
 
 Boyle, law of, 165. 
 
 Branch currents, 375. 
 
 Bridge, Wheatstone's, 358. 
 
 Bunsen's photometer, 516. 
 
 Buoyancy of fluids, 180-185. 
 
 Calibration of galvanometer, 374, 
 376. 
 
380 
 
 INDEX. 
 
 Caliper, inside, 13; micrometer, 1); 
 outside, 12; verniered steel, 6. 
 
 Calorimetry, 269-276. 
 
 Camphor, motion of, 82. 
 
 Candle-power, measurement of, 
 517, 518. 
 
 Capillarity, table of, page 361. 
 
 Capillary action, 77-85; laws of, 
 85 ; measure diameter of tube, 
 34. 
 
 Carbonic acid, testing room for, 
 231 ; velocity of sound in, 435. 
 
 Cartesian diver, 184. 
 
 Cements, 607. 
 
 Centre of mass, 117-119; of oscil- 
 lation, 139 ; of percussion, 141. 
 
 Charge of Leyden jar, not in metal, 
 340 ; residual, 335. 
 
 Charging Leyden jars, 335-340. 
 
 Chemical effects of electrical cur- 
 rents, 353-355. 
 
 Chladni's plates, 491. 
 
 Chromic acid solution for batteries, 
 612. 
 
 Circuit, divided, law of, 375. 
 
 Cleavage, 70. 
 
 Coefficient of expansion, 234, 235, 
 241 ; table of, page 36S. 
 
 Coercive force, 298. 
 
 Cohesion, 61-71; figures, 80; of 
 liquids, 64; of solids, 61, 62. 
 
 Coil, induction, 394 ; resistance, 
 358. 
 
 Cold, artificial production of, 277- 
 283. 
 
 Collision of bodies, 113-116. 
 
 Color, 557-566 ; complementary, 
 561-566; mixed, 561, 562; pro- 
 duced by diffraction, 578, 579 ; 
 by pressing two plates together, 
 516; by polarized light, 590- 
 
 593; simple, 551-552; un- 
 equally refrangible, 553. 
 
 Commutator, to make, 347. 
 
 Compound microscope, 584; po- 
 larizing attachment, 592. 
 
 Concave lenses, 546-548; mirrors, 
 532, 534, 535, 537. 
 
 Condensers, 332-340. 
 
 Conduction of heat, 215-223, page 
 367; electricity, 318, page 364; 
 of sound, 428-432. 
 
 Conductometer, 217, 219. 
 
 Conductors, distribution of electri- 
 fication on, 325-331. 
 
 Cone, volume of frustum of, 22. 
 
 Controlling magnet for galvanom- 
 eter, 365. 
 
 Convection of heat, 225-231. 
 
 Convex lenses, 545, 547-549; mir- 
 rors, 533, 534, 536. 
 
 Cooling, affected by character of 
 surface, 265 ; Newton's law of, 
 267. 
 
 Corks, boring holes in, 595. 
 
 Critical angle, 541. 
 
 Crova's disk, 439. 
 
 Crystallization, 66-70; increase of 
 volume due to, 242-244. 
 
 Cube, Leslie's, 258. 
 
 Current electricity, 345-356 ; extra, 
 395 ; induced, 386-397. 
 
 Curved mirrors, 532-537. 
 
 Curvilinear motion, 125-127. 
 
 Cylindrical jar, to measure, 13. 
 
 Daniell's battery, 358, 595. 
 
 Dark lines of solar spectrum, 568, 
 
 569. 
 Density, determination of , 187-198; 
 
 of ice, 244 ; table of, page 361. 
 Deviation, angle of, 540. 
 
INDEX. 
 
 381 
 
 Diagonal scale, 2. 
 
 Dialyzer, 101. 
 
 Diameter of wires, table of, page 
 
 365. 
 
 Diapason, 459. 
 Diathermancy, 264. 
 Differential thermometer, 258. 
 Diffraction of light, 578-581. 
 Diffusion, 95-106; fountain, 102. 
 Dip of needle, 306. 
 Direction of current, 347, 348. 
 Discharger, jointed, 335. 
 Discord, 487-489. 
 Dispersion of light, 551. 
 Distillation, 256. 
 Distribution of electrification, 324- 
 
 331; of magnetism, 301. 
 Divided currents, 375. 
 Dividers, 2; proportional, 1(1. 
 Divisibility of matter, 44-47. 
 Double refraction, 589. 
 Drop-size of liquids, 63. 
 Duration of electric spark, 344. 
 Dust figures, 425. 
 
 Elasticity, 73-76 ; table of limits of, 
 page 364; of traction, table, ' 
 page 372. 
 
 Electric amalgam, 614 ; attraction I 
 and repulsion, 309-314; con- ! 
 ductivity, 318; motor, 388. 
 
 Electrical condensers, 333-340; 
 conductivity, 318, page 364 ; 
 conductivity affected by heat, 
 364; urrents, direction of, j 
 347, 348; currents, division of , I 
 376 ; currents, effects of, 350- 
 356; distribution, 325-331; ! 
 machines, cleaning, 615; meas- I 
 urements, 358-376 ; pistol, 352 ; 
 resistance, table of, page 365. 
 
 Electricity, 308-409; current, 345- 
 356; developed by chemical 
 action, 346-348 ; developed by 
 friction, 308-342 ; developed by 
 heat, 406 ; developed by in- 
 duction, 343, 344, 386-397. 
 
 Electrification detected, 315-317. 
 
 Electrolysis, 353-355. 
 
 Electrodynamics, 378-384; magnet, 
 382 ; magnetism, 378-384. 
 
 Electro-motive force. 370-373 ; table 
 of, page 365 
 
 Electrophorus, 343. 
 
 Electroscope, 315. 
 
 Equilibrium of forces, 109-112; of 
 liquids, 169; of bodies, 120- 
 122. 
 
 Erdmann's float, 20. 
 
 Expansion, coefficient of, 234, 239, 
 241; cubical, 235, 239, 241; 
 table of, page 368 ; on crys- 
 tallization, 242-244; of gases, 
 240, 241 ; of liquids, 238, 239 ; 
 of gases producing cold, 207, 
 281 ; by heat, 233-244. 
 
 Extra current, 395. 
 
 Evaporation, cold due to, 279, 280. 
 
 Eye, model of, 583. 
 
 Falling bodies, law of, 133; inde- 
 pendent of mass, 133. 
 
 Films, soap, 81, 577. 
 
 Fire-syringe, 201. 
 
 Flask, specific gravity, 190. 
 
 Flexure, elasticity of, 75. 
 
 Float, Erdmann's, 20. 
 
 Floating battery, 383. 
 
 Flotation, principle of, 183. 
 
 Fluids, buoyant force of, 181-185; 
 mechanics of, 149-198; pres- 
 sure in, 150-163. 
 
382 
 
 INDEX. 
 
 Focal distance of lenses, 545-546; 
 of spherical mirrors, 535-536. 
 
 Force, acceleration due to con- 
 stant, 129-131; buoyant, 180- 
 185; coercive, 298; electro- 
 motive, 371-373 ; lines of mag- 
 netic, 300, 379, 381; measure 
 effect of a, 132. 
 
 Forces, composition of, 109-112; 
 parallel, 112. 
 
 Fountain, Hero's, 177; intermit- 
 tent, 176 ; in vacuo, 162. 
 
 Fraunhofer's lines, 568, 569. 
 
 Freezing mixtures, 277, 278, 283. 
 
 Friction, 142. 
 
 Frictional plate machine, 342. 
 
 Fusion, latent heat of, 275. 
 
 Galilean telescope, 586. 
 
 Galvanometer, calibration of, 374, 
 376 ; resistance of, 365 ; simple, 
 to make, 347 ; tangent, to make, 
 358. 
 
 Gases, cold produced by expansion 
 of, 207, 281; compressibility 
 of, 165 ; density of, page 363 ; 
 endosmose of, 102-106 ; ex- 
 pansibility of, 160 ; thermal 
 conductivity of, 261 ; velocity 
 of sound in, 434-436. 
 
 Gassiot's cascade, 403. 
 
 Glass, bending tube, 602 ; cutting, 
 600 ; closing end of tube, 603 ; 
 drawing on, 606 ; drawing out 
 tube, 604 ; drilling holes in, 
 605 ; silvering, 608 ; smoothing 
 end of tube, 601. 
 
 Graphic method, 598; study of 
 sound, 500, 501. 
 
 Grating, Nobert's, 578-579. 
 
 Gravitation, 129-131; acceleration 
 due to, 131 ; table, page 367. 
 
 Haldat's apparatus, 168. 
 
 Hardness, Mohr's scale, 71. 
 
 Harmony, 487-489. 
 
 Heat, 199-283 ; absorption of, 263, 
 264 ; capacity of substance for, 
 271-274; capacity of water for, 
 269, 270; conduction of, 215- 
 223; convection of, 224-231; 
 converted into mechanical mo- 
 tion, 207-210; due to chemical 
 action, 212-214; due to electric 
 currents, 350-352 ; due to me- 
 chanical motion, 207-210; ex- 
 pansion by, 233-244; law of 
 reflection of, 262; latent, of 
 water, 275; latent, of steam, 
 276; radiant, 258-267; radi- 
 ation of, affected by surface, 
 265 ; radiation of, affected by 
 temperature of surrounding air. 
 267; specific, 272-274; table 
 of absorbing, conducting, radi- 
 ating, reflecting power, page 
 367 ; table of latent, page 369 ; 
 table of specific, page 370. 
 
 Hemispheres, Magdeburg, 154. 
 
 Hero's fountain, 177. 
 
 Holtz machine, 344. 
 
 Hydrometer, Beaume's, 196; Nich- 
 olson's, 193, 195. 
 
 Images, after, 563-566 ; formed by 
 lenses, 548; formed by mir- 
 rors, 528-531, 534; multiple, 
 530, 531; through small aper- 
 tures, 511, 512. 
 
 Impenetrability, 36-42 
 
 Inclined plane, 148 
 
INDEX. 
 
 383 
 
 Indestructibility, 58, 59. 
 
 Index of refraction, 539, 540 ; table 
 
 of, page 370. 
 Induction, coil, 391, 394; current, 
 
 386-397 ; current on itself, 395 ; 
 
 earth, 397; magnetic, 291, 292, 
 
 307 ; statical, 320-323. 
 Inelastic bodies, 113. 
 Interference of light, by diffraction, 
 
 578-579; by reflection, 57(5, 
 
 577, 581; of sound, 457-462, 
 
 492-494. 
 
 Intermittent fountain, 176. 
 Irregular reflection, 523, 524. 
 
 Jar, Leyden, 335-340. 
 
 Jet, height of, 170, 175, 177. 
 
 Jet-tube, to make, 604. 
 
 Jolly's balance, 23. 
 
 Juriirs laws of capillarity, 85. 
 
 Konig's manometric flames, 502. 
 Kundt's method of measuring ve- 
 locity of sound, 437. 
 
 Laboratory note-book, 597; oper- 
 ations, 600-615 ; physical, 594- 
 599; room, 594; rules, 599; 
 work, conducting, 596. 
 
 Lantern, magic, 509. 
 
 Latent heat, of steam, 276 ; of 
 water, 275 ; of liquefaction and 
 vaporization, table, page 369. 
 
 Lateral jets, 150. 
 
 Lenses, foci of concave, 546; foci 
 of convex, 545 ; effect on 
 pencils of light, 547 ; magnify- 
 ing power of, 549; spherical 
 aberration, 548. 
 
 Leslie's cube, 258. 
 
 Lever, 144-145. 
 
 Leyden jar, charging, 335,337-339 ; 
 charging by induction coil, 396 ; 
 connecting two or more to- 
 gether, 336 ; discharging, 335 ; 
 to make, 336; office of coat- 
 ings, 340; residual charge, 335; 
 spangled, 399. 
 
 Liebig's condenser, 256. 
 ! Light, 598-593; amount of light 
 reflected, 525, 526; diffused 
 reflection of, 523, 524; dis- 
 persion of, 550-556 ; double 
 refraction of, 538-543; inter- 
 ference of, 575-581 ; law of 
 intensity of, 515, 516; multiple 
 reflection of, 530, 531 ; polari- 
 zation of, 588-593 ; rectilinear 
 propagation of, 510-513; re- 
 flected, amount of, 525, 526; 
 reflection of, 519-526; re- 
 fraction of, 538-543; regular 
 reflection of, 520-522; single 
 refraction of, 538-543; total 
 reflection of, 541-543. 
 
 Linear expansion, coefficient of, 
 234 ; table, page 368. 
 
 Liquids, buoyancy of, 180-184; 
 conductivity of heat by, 222, 
 223; diffusion of, 95-101; 
 equilibrium of, 169 ; expansion 
 of, 228, 229; manner of heat- 
 ing, 225, 226 ; pressure inde- 
 pendent of shape of vessel, 168 ; 
 specific heat of, 274 ; transmit 
 pressure, 167. 
 
 Lissajou's curves, 503. 
 
 Loudness of sound, 447-456. 
 
 Luminous effects of electric dis- 
 charge, 344, 393, 398-404. 
 
384 
 
 INDEX. 
 
 Machines, electrical, 341-344; 
 simple, 144-148. 
 
 Magic lantern, 509; slides, 606. 
 
 Magnetic effects of electric cur- 
 rents, 356 ; field, 300-304 ; field 
 around conductors carrying 
 current, 378, 379, 381; in- 
 duction, 291, 292, 307; trans- 
 parency, 289, 290. 
 
 Magnetism, 284-307; nature of, 
 294-296; terrestrial, 306,307. 
 
 Magnetizing, by currents, 356, 382 ; 
 by divided touch, 301; by 
 earth, 307; by induction, 292. 
 
 Magnetoscope, Coulomb's, 301. 
 
 Magnets, effects of heating, 296 ; 
 effects of jarring, 295; electro, 
 382; induction by, 291, 292; 
 polarity of, 286-288 ; to make, 
 285, 301. 
 
 Magnify ing-power, 549, 587. 
 
 Manometric flames, 502. 
 
 Mass, centre of, 118, 119; esti- 
 mation of, 23-34. 
 
 Matter, properties of, 1-106. 
 
 Measurement, angular, 17, 18; 
 linear, 2-17 ; of candle-power, 
 517, 518; of electro-motive 
 force, 370-373; of effect of 
 force, 132; of focal distance, 
 535, 536, 545, 546; of magni- 
 fying-power, 549, 587; of 
 mass, 23-34; of resistance, 
 357-369 ; of surface, 18, 19 ; of 
 velocity of sound, 434-437 ; of 
 vibration-number, 472, 473 ; 
 of volume, 20-22. 
 
 Mechanics, of fluids, 149-198 ; of 
 solids, 107-148. 
 
 Melde's experiments with vibrating 
 strings, 477. 
 
 Melting-point of substances, 253, 
 table of, page 369. 
 
 Mensuration rules, table of, page 
 371. 
 
 Mercury, cleaning, 609. 
 
 Micrometer caliper, 9. 
 
 Microphone, 390. 
 
 Microscope, 584. 
 
 Mirrors, curved, 532-537 ; effect on 
 pencils of light, 532, 533 ; plane, 
 528-531 ; measure focal dis- 
 tance of concave, 535 ; measure 
 focal distance of convex, 536. 
 
 Mixtures, freezing, 283. 
 
 Motion, laws of, 108-116; accel- 
 erated, 129-131 ; curvilinear, 
 124-127; reflection of, 116; 
 wave, 411-417. 
 
 Multiple images, 530, 531. 
 
 Needle, dipping, 306. 
 
 Newton's color disk, 344, 561 ; law 
 of cooling, 267; rings, 576. 
 
 Nicholson's hydrometer, 193, 195. 
 
 Nicol prism, 591. 
 
 Nobert's grating, 579. 
 
 Nodes of organ pipe, 485, 486 ; of 
 vibrating plates, 491 ; of vibrat- 
 ing strings, 481. 
 
 Norremberg's doubler, to make, 
 591. 
 
 Note-book, laboratory, 597. 
 
 Oersted's parallelogram, 347. 
 
 Ohm's law, 358. 
 
 Optical instruments, 582-587 ; Ltudy 
 
 of sound, 502, 503. 
 Optics, 508-593. 
 Osmose, 99-105. 
 Overtones, 478-481. 
 
INDEX. 
 
 385 
 
 Paradox, 122, 168, 252. 
 
 Parallel forces, 112. 
 
 Parallelogram of forces, 109-11 1. 
 
 Pascal, law of, 167-170. 
 
 Pendulum, Blackburn's sand, 504 ; 
 law of, 137-141; table of 
 lengths of seconds, page 371. 
 
 Percussion, heat developed by, 200. 
 
 Photometry, 514-518. 
 
 Pitcli of sound, 471-473. 
 
 Plates, ascension of liquids between, 
 84; Chladni's, 491; tourmaline, 
 590; vibration of plates, 491- 
 494. 
 
 Point, boiling, 254 ; affected by 
 pressure, 251-254; affected by 
 substances in solution, 255 ; 
 located on thermometer, 246. 
 
 Polariscope, to make, 591; micro- 
 scope attachment, 592. 
 
 Polarity of magnets, 285-288. 
 
 Poles, strength compared, 302. 
 
 Polygon, measure area of, 19. 
 
 Porosity, 49-54. 
 
 Porte lumiere, to make, 509. 
 
 Powders, density of, 192. 
 
 Pressure, depends on depth, 150, 
 155 ; effect on boiling-point, 
 254 ; elasticity manifested by , 
 73; exerted by atmosphere, j 
 151-163; exerted in every di- 
 rection, 154, 155, 167; inde- 
 pendent of form of vessel, 
 168 ; on a body in a fluid, 180- 
 185. 
 
 Principle of Archimedes, 179-185. 
 
 Prism, measure angle of, 522 ; make 
 carbon disulphide, 551 ; meas- 
 sure refraction of, 540 ; Nicol, 
 591, 
 
 Projectiles, 134, 135. 
 
 Proof-plane, 316. 
 
 Propagation of sound, 439. 
 
 Protractor, 17. 
 
 Pulley, 146; mass determined, 130. 
 
 Pump, air, 152-154, 160-1G2, 178, 
 
 185, 251, 261; mercury, 163; 
 
 suction, 178. 
 Pyrometer, 209, 234. 
 
 Radiant heat, 257-267; causes 
 which modify, 263-266; in- 
 tensity of, 259 ; law of reflec- 
 tion, 262. 
 
 Radiating power, causes which 
 modify, 265-267. 
 
 Radiometer, 210. 
 
 Rainbow, project on screen, 556. 
 
 Reflection, laws of, 116, 262,521; 
 irregular, 523-524 ; regular, 
 519-522; of heat, 262; of 
 light, 519-526 ; of sound, 440- 
 443. 
 
 Refraction, double, 589; index of, 
 539, 540; single, 538-543; of 
 sound, 440-446; table of in- 
 dices, page 370. 
 
 Residual charge, 335. 
 
 Resistance, coils, 358 ; of batteries, 
 367-369 ; of conductors, 358- 
 364 ; of galvanometers, 365. 
 
 Resonating air-columns, effect of 
 diameter on length of, 454. 
 
 Resonators, 455, 456. 
 
 Resultant of forces, 109-112. 
 
 Rheostat, 358. 
 
 Rider, 23. 
 
 Rings, Newton's, 576. 
 
 Rods, law of vibrating, 475; meas- 
 ure length of, 6. 
 
 Rumford's photometer, 517. 
 
386 
 
 INDEX. 
 
 Scale, accuracy tested, 15; copy a, 
 14 ; diagonal, 2 ; of hardness, 71. 
 
 Sciopticon, 509. 
 
 Secondary batteries, 408, 409. 
 
 Shadows, 513. 
 
 Shunt, 374-370. 
 
 Singing flame, 426. 
 
 Siphon, 172-177. 
 
 Siren, 472. 
 
 Soap-film, colors of, 577; solution, 
 to make, 80; strength of, 81. 
 
 Soldering, 610. 
 
 Solenoid, action of currents on, 
 382 ; of magnets on, 382. 
 
 Solubility, 87-93. 
 
 Sonometer ; 476. 
 
 Sound, 410-507 ; attending magne- 
 tization and demagnetization, 
 356 ; graphic and optical study 
 of, 499-504 ; interference of, 
 457-462, 492, 493 ; loudness of, 
 447-456 ; pitch, 471-473 ; propa- 
 gation of, 438, 439 ; reflection 
 of, 440-443 ; refraction of, 444- 
 446; sources of, 418-426; 
 transmission of, 427-432 ; ve- 
 locity of, 433-437; table of 
 velocities, page 372. 
 
 Sounding air-columns, 482-486. 
 
 Spar, Iceland, 589. 
 
 Specific heat, 272-274; table of, 
 page 370. 
 
 Spectroscope, 522; to make, 569. 
 
 Spectrum, absorption, 571-573; an- 
 alysis, 567-574; bright line, 
 570, 574; colors, pure, 552; 
 color unequally refrangible, 
 553; dark line, 568, 571-573; 
 diffraction, 578-580; mapping, 
 569 ; solar, to project on screen, 
 551. 
 
 Sphere, measure diameter of, 12. 
 Spherical aberration, 537, 548. 
 Spherometer, 11. 
 Sprengel's air-pump, 163. 
 Springs, intermittent, 176. 
 Stability, 120-123. 
 Stable equilibrium, 120, 121. 
 Storage batteries, 408, 409. 
 Strength of substances, 62. 
 Strings, laws of, 476, 477. 
 Suction pump, 178. 
 Surface tension, 78-82. 
 Sympathetic vibrations, 463-470. 
 Syringe, fire, 201. 
 
 Table, laboratory, 594 ; to measure, 
 5; reference, page 361-376. 
 
 Tangent galvanometer, 358. 
 
 Telegraph line, 384. 
 
 Telephone, acoustic, 430; electric, 
 389. 
 
 Telescope, astronomical, 585 ; Gali- 
 lean. 586 ; magnifying power 
 of, 587 ; terrestrial, 585. 
 
 Temperature of boiling-point of 
 water, 247, 251 ; of substances, 
 216, 249. 
 
 Tenacity, 62, 74 ; table of, page 373. 
 
 Terrestrial, gravitation, 129-132; 
 magnetism, 305-307 ; telescope, 
 585. 
 
 Thermal capacity of substances, 
 272-274. 
 
 Thermo-electricity, 406. 
 
 Thermometer, accuracy of location 
 of standard points, 246; air- 
 thermometer, 258 ; comparison 
 with standard, 250; displace- 
 ment of zero, 248. 
 
 Thermometry, 246-256. 
 
 Thermopile, 259. 
 
INDEX. 
 
 387 
 
 Thermoscope, 240. 
 Thickness, to measure, 9-11. 
 Tools for laboratory, 594. 
 Torsion, elasticity of, 76. 
 Tourmaline tongs, 590. 
 Traction, elasticity of, table, page 
 
 372. 
 
 Transmission of sound, 427-432. 
 Triangle, measure, area of, 18. 
 Trigonometrical functions, table of, 
 
 page 373. 
 TyndalFs experiment on specific 
 
 heat, 273. 
 
 Unstable equilibrium, 121, 122. 
 Useful numbers, table of, page 375. 
 
 Velocity of sound, 433-437 ; table, 
 
 page 372. 
 
 Ventilation, 227-231. 
 Vernier, 6. 
 
 Vibrating, bodies, attraction of, 
 496-498 ; plates and bells, 490- 
 
 495; rods, 475; strings, 476, 
 
 477. 
 Vibration, number, to measure, 
 
 472, 473. 
 Vibrations, sympathetic, 463-470. 
 
 Vocal organs, 505-507. 
 
 Volume, of irregular objects, 20; 
 regular objects, 13, 22; sub- 
 stances soluble in water, 21. 
 
 Water-hammer, TyndalPs adhesion, 
 
 65. 
 
 Wave motion, 411-417. 
 Weighing, manner of, 24 ; problems 
 
 in, 25-34. 
 Weights, centigramme, to make, 
 
 33. 
 Weights and measures, table of, 
 
 page 375. 
 
 Wheatstone's bridge, 358. 
 Wheel and axle, 147. 
 Whirling-machine, 125. 
 White light, decomposition of, 551. 
 Wire-gauge, 9 ; measure diameter 
 
 of, 9 ; measure resistance of, 
 
 357-364. 
 Wood, thermal conductivity of, 
 
 221 ; transmission of sound 
 
 by, 429; velocity of sound 
 
 measured, 437. 
 
 Zero, displacement of, 248. 
 Zinc, amalgamation of, 611. 
 
THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 AN INITIAL FINE OF 25 CENTS 
 
 WILL BE ASSESSED FOR FAILURE TO RETURN 
 THIS BOOK ON THE DATE DUE. THE PENALTY 
 WILL INCREASE TO SO CENTS ON THE FOURTH 
 DAY AND TO $1.OO ON THE SEVENTH DAY 
 OVERDUE. 
 
 FEB 11933 I RECEIVED 
 
 ,^. 70-JIPM 
 OCT 7 1937 
 
 
 '"' 
 
 V331 
 
 r 
 
 DEC 3 0)969 
 
 LD 21-50m-8,-32 
 
Y.C 95384 
 
 797967 
 
 cr 
 
 UNIVERSITY OF CALIFORNIA LIBRARY