LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA 
 
 GIFT OF^ 
 
 Macmillan & Cor 
 
 Received 
 Accession No. ~ ciaxsNo. 
 
PRACTICAL PHYSICS 
 
PEACTICAL PHYSICS 
 
 FOR 
 
 SCHOOLS AND THE JUNIOK STUDENTS 
 OF COLLEGES 
 
 BY 
 
 BALFOUK STEWAKT, M.A., LL.D., F.E.S. 
 
 LATE PROFESSOR OF PHYSICS, VICTORIA UNIVERSITY, 
 THK OWENS COLLEGE, MANCHESTER 
 
 AND 
 
 W. W. HALDANE GEE, B.Sc. (LOND.) 
 
 DEMONSTRATOR AND ASSISTANT LECTURER IN PHYSICS 
 AT THE OWENS COLLEGE 
 
 VOL. I. 
 
 LECTRICITY AND MAGNETISM 
 0* THl' 
 
 ILonfcon 
 
 MACMILLAN AND CO. 
 
 AXD NEW YORK 
 
 1888 
 
 All rights reserved 
 
PREFACE 
 
 IT has frequently been a matter of remark that while many 
 schools are provided with fully equipped chemical labora- 
 tories, yet very few have any appliances for teaching 
 Practical Physics. The reason is certainly not to be found 
 in any fundamental unsuitability of Practical Physics as a 
 training for the mind, inasmuch as the subject is universally 
 acknowledged to be of ver.y great importance in this 
 respect. There are several causes which have militated 
 against the introduction of Practical Physics, the chief, 
 perhaps, being the want of properly trained teachers, the 
 absence of organised methods, and the difficulty of obtain- 
 ing suitable apparatus. We venture to think that, as the 
 importance of the subject comes to be realised, there will 
 be no lack of good teachers, each of whom will be capable 
 of controlling a system of instruction suitable to the boys 
 under his charge. Again, we think that instrument makers 
 are becoming more alive to the requirements of elementary 
 students, their strength hitherto having been mainly 
 directed towards the manufacture of instruments suitable 
 for commercial purposes and scientific research. 
 
 It was represented to us by several teachers that ab- 
 stracts of our Elementary Lessms in Practical Physics might 
 be made the basis of good school courses. We have accord- 
 ingly tried the experiment with Electricity and Magnetism, 
 so that the present volume largely consists of simple experi- 
 
viii PREFACE 
 
 ments and measurements in Electrostatics, Magnetism, and 
 Current Electricity, the principles of which are at the same 
 time explained to the student. We have, however, pre- 
 pared something more than an abstract. Chapter I. has 
 been supplemented by several new lessons. Chapter II. 
 has been largely rewritten, new instruments have been 
 devised, and a number of new engravings have been pre- 
 pared. In the Appendix will be found plans of certain 
 typical school laboratories, a list of apparatus, tools and 
 materials, and other information that should be of value 
 to the teacher. 
 
 Furthermore, to make the volume complete in itself, 
 we have given, at the commencement, a series of Introduc- 
 tory Measurements, with which it is essential the student 
 of Electricity and Magnetism should be familiar. 
 
 The greater part of our course should be easily within 
 the range of schoolboys, whilst sixth -form boys should 
 find the more difficult portions a good introduction to ad- 
 vanced work. 
 
 Our thanks are due to Professor T. H. Core for looking 
 over the proofs, and to Messrs. Henry Holden, B. Sc. ; 
 C. H. Lees, B.Sc.; and K. W. Stewart, for help in prepar- 
 ing the new lessons. 
 
 THE OWENS COLLEGE, MANCHESTER, 
 December 1887. 
 
CONTENTS 
 
 INTRODUCTORY MEASUREMENTS. 
 
 Lesson 
 
 Definition of Standard Yard and Metre . 
 Relation of Metrical to English System 
 of Measures of Length 
 
 Area and Volume 
 
 Exercises 
 
 A. USE OF SCALES ... . 
 
 The Vernier introduced 
 
 B. THE STRAIGHT VERNIER .... 
 
 C. USE OF CALLIPERS THE SLIDE CALLIPER . 
 
 D. THE MICROMETER WIRE-GAUGE . 
 
 The Sheet-Metal Gauge 
 
 E. THE STANDARD WIRE-GAUGE 
 
 The Standards of Mass defined 
 
 F. THE BALANCE 
 
 Weights . ; . . . . 
 
 G. METHOD OF USING THE BALANCE 
 
 Estimation of Density .... 
 Estimation of Time .... 
 Units of Angular Measurement 
 The Dividing of Circles 
 
 H. CoptiNG OF CIRCULAR DIVISIONS 
 The Mirror and Scale . 
 
 Article Page 
 (1) 1 
 
 (2) 
 
 (4) 
 (5) 
 (6) 
 
 (7) 6 
 (7a) 7 
 
 (8) 8 
 
 (9) 9 
 
 (10) 10 
 
 (11) 13 
 
 (12) 13 
 
 (13) 15 
 
 (14) 15 
 
 (15) 15 
 
 (16) 15 
 
 (17) 16 
 
 (18) 16 
 
 1 Space is left in this column for the directions of the teacher a:> to the order ii 
 which the lessons are to be taken, and what articles are to be read. 
 
CONTENTS 
 
 CHAPTER I. 
 
 ELECTROSTATICS. 
 
 Lessoa Article Page 
 
 I. ELECTRIFICATION BY FRICTION AND CONDUCTION 1 17 
 
 Gold-Leaf Electroscope . . . 1 18 
 
 Manipulation of Gold Leaf . . . 1 18 
 
 Electrical Amalgam . . . . 1 19 
 
 Ebonite and Vulcanite . . . . 1 19 
 
 Paraffin Wax ..... . 1 19 
 
 Drying Oven ...... 1 19 
 
 II. ELECTRIFICATION BY INDUCTION ... 2 23 
 
 III. THE ELECTROPHORUS OF VOLTA ... 3 27 
 
 IV. FARADAY'S ICE PAIL EXPERIMENTS 4 29 
 V. ELECTRIFICATION BY FRICTION (continued) . 5 32 
 
 VI. EFFECT OF A CONDUCTING ENCLOSURE . . 6 34 
 
 Summary of Laws ..... 7 36 
 
 Fundamental Quantitative Law . . 8 37 
 
 Definition of Electrostatic Unit of Quantity 9 37 
 
 Potential Difference of Level . .10 38 
 
 The Foot-Pound, Dyne, and Erg . .11 39 
 
 Comparison of Electricity and Gravity . 12 39 
 
 Equipotential Surfaces . . . .13 41 
 
 Zero of Potential ..... 14 41 
 
 Positive Current only considered . .15 42 
 
 The Units of Density and Capacity . .16 43 
 
 Application of Definitions . . .17 43 
 
 Condensers ...... 18 44 
 
 Definition of Specific Inductive Capacity I8a 45 
 
 Discharge of a Condenser . . .19 45 
 
 Exercises ...... 20 45 
 
 VII. EXPERIMENTS ON POTENTIAL WITH ELECTRO- 
 
 SCOPE ....... 21 46 
 
 VIlA. THE CONDENSER ...... 2la 49 
 
 VIIs. COMPARISON OF CONDENSERS SPECIFIC IN- 
 
 DUCTIVE CAPACITY . . . .216 52 
 
 VIIc. COMPARISON OF CONDUCTING POWERS OF OILS 21c 55 
 
CONTENTS xi 
 
 CHAPTER II. 
 
 MAGNETISM. 
 
 Article Page 
 
 Elementary Definitions ... 22 57 
 
 VIII. FUNDAMENTAL EXPERIMENTS ... 23 58 
 
 IX. THE MAGNETIC FIELD .... 24 62 
 
 X. THE MAGNETIC MERIDIAN . . . 25 64 
 
 XI. THE LAW OF INVERSE SQUARES 26 68 
 
 Lines of Force 27 72 
 
 XII. THE EARTH'S MAGNETIC ACTION 28 74 
 
 XIII. DETERMINATION OF THE DIP . . . 29 77 
 
 Action of One Magnet on Another . 30 87 
 
 XIV. ACTION OF ONE MAGNET ON ANOTHER . 31 90 
 XV. STUDY OF A VIBRATING MAGNET . . 32 92 
 
 XVI. DETERMINATION OF H AND M . . . 33 98 
 The Comparison Magnetometer intro- 
 duced 34 100 
 
 XVII. USE OF A COMPARISON MAGNETOMETER . 35 100 
 
 Distribution of Magnetism . . . 36 105 
 
 XVIII. THE TEST-NAIL METHOD 37 105 
 
 CHAPTER III. 
 
 VOLTAIC ELECTRICITY FUNDAMENTAL LAWS AND 
 
 MEASUREMENTS. 
 
 XIX. FUNDAMENTAL EXPERIMENTS ... 38 108 
 
 Electrolysis introduced . . . 39 122 
 
 XX. THE DANIELL'S CELL AND COPPER PLATING 40 123 
 
 The Galvanoscope introduced . . 41 127 
 
 XXI. THE GALVANOSCOPE . . . . 42 129 
 
 Theory of the Battery . . . . 43 133 
 
 Electromotive Force .... 44 137 
 
 Ohm's Law 45 137 
 
 The Units of Theory and Practice . 46 141 
 
 The Mirror Galvanometer introduced . 47 144 
 
xii CONTENTS. 
 
 Le S ,o,, 
 
 XXII. CONSTRUCTION OF MIRROR GALVANOMETER 48 144 
 
 Use of Box of Coils . . . . 49 150 
 
 Care and Use of the Box of Coils . 50 152 
 
 The Kheostat . . . . . 51 153 
 
 Figure of Merit defined . . 52 154 
 
 XXIII. FIGURE OP MERIT OF GALVANOMETER . 53 154 
 Determination of E. M. F. . . 54 157 
 XXIV. COMPARISON OF ELECTROMOTIVE FORCES 55 157 
 XXV. PROOF OF OHM'S LAW .... 56 158 
 Wheatstone's Bridge Proof of Prin- 
 ciple 57 161 
 
 XXVI. USE OF WHEATSTONE'S BRIDGE . . 58 163 
 
 XXVII. MANUFACTURE OF A ONE-OHM COIL . 59 167 
 
 XXVIII. CALIBRATION OF A GALVANOSCOPE 60 168 
 
 CHAPTER IV. 
 
 THE TANGENT GALVANOMETER. 
 
 Tangent Galvanometer ... 61 170 
 XXIX. PROOF OF LAW OF TANGENTS . . 62 170 
 XXX. PROOF OF LAW OF DISTANCE . . 63 173 
 XXXI. DETERMINATION OF CONSTANTS OF TAN- 
 GENT GALVANOMETER . . . 64 176 
 XXXII. DETERMINATION OF KESISTANCE AND E. M. F. 65 179 
 Additional Exercises on the Use of 
 
 the Tangent Galvanometer . . 66 183 
 The Mirror Galvanometer a Tangent 
 
 Galvanometer . . . . 67 4 
 
 CHAPTER V. 
 
 MEASUREMENT OF RESISTANCE. 
 
 Measurement of Resistance . . 68 185 
 Theory and Use of Shunts . . 69 185 
 
 XXXIII. THE Box OF COILS USED AS A BRIDGE . 70 187 
 
CONT 
 CHAPTER 
 
 THE QUADRANT ELECTROMETER. 
 
 Lesson Article Page 
 
 The Quadrant Electrometer introduced 71 193 
 
 XXXIV. USE OF QUADRANT ELECTROMETER . 72 193 
 
 APPENDIX. 
 
 Article 
 
 A. ADDITIONAL PRACTICAL DETAILS 
 
 1. Switch for Battery . ... 199 
 
 2. Silk for Suspension of Galvanometer Needles . 200 
 
 3. Clamp and Binding Screws .... 200 
 
 4. Soldering '.'.-.. 201 
 
 5. Substitutes for the Mirror Galvanometer . . . 201 
 
 B. PRICE LIST of APPARATUS AND MATERIALS . . 202 
 
 I. General . 203 
 
 II. Electrostatics . ..... .203 
 
 III. Magnetism . , . . . . 204 
 
 IV. Voltaic Electricity . , . . . . .205 
 V. Parts of Apparatus .-.'... . .206 
 
 C. THE PHYSICAL LABORATORY WORKSHOP . . 206 
 
 I. Fittings 206 
 
 II. Lathe and Lathe Tools 206 
 
 III. Joiner's Tools 207 
 
 IV. Mechanic's Tools 207 
 
 V. Materials 208 
 
 D. THE RECORDING AND CALCULATING RESULTS OP EX- 
 PERIMENTS 208 
 
 E. THE REQUIREMENTS OP A PHYSICAL LABORATORY 
 FOR SCHOOLS 
 
 1. The Laboratory Fittings 211 
 
 2. Working Benches for Juniors . . . .215 
 
 F. NOTES ON THE ORGANISATION OF LABORATORY WORK 
 
 1. Mechanical Assistant . . . . . 217 
 
 2. Constructive Work 217 
 
 3. The Collective and Separate Systems . . .217 
 . 4. The Indicator Board 218 
 
 5. Companionships . . ... 218 
 
 INDEX 219 
 
LIST OP TABLES 
 
 PAGE 
 
 a. RELATION OF STANDARDS OF LENGTH ..... 2 
 
 a,. THE ENGLISH STANDARD WIRE-GAUGE 8 
 
 . RELATION OF BRITISH TO METRICAL STANDARDS OF MASS . 10 
 
 A. ORDER OF CONDUCTORS 22 
 
 B. ORDER OF ELECTRIFICATION ....... 33 
 
 C. NAMES OF POLES 57 
 
 D. FORMULAE FOR TANGENT POSITIONS A AND B OF GAUSS . 90 
 
 E. SERIES OF WIRES SUITABLE FOR RESISTANCE COILS 152 
 

 PEAOTICAL PHYSICS FOE SCHOOLS. 
 
 INTRODUCTORY MEASUREMENTS. 1 
 
 LENGTH. 
 
 (1.) Length is measured by comparison with a standard rule or 
 scale. 
 
 In Great Britain the yard is the national standard. The yard is 
 defined to be the distance between the centres of two gold plugs in a 
 bronze bar deposited in the office of the Exchequer, the temperature 
 of the bar being 62 Fahr. 
 
 "When it is convenient to use smaller units of length, the foot, or 
 3 of a yard, and the inch, or T V of a foot, are employed. The inch is 
 most frequently divided into tenths, but sometimes into 8, 16, 32, or 
 64 parts. 
 
 For scientific purposes the standard is the metre, which was in- 
 tended to be the 10,000,000th part of the distance from the earth's 
 equator to one of its poles measured along a meridian. Practically, 
 however, it means the length of a certain rod of platinum at centi- 
 
 frade. The metre is subdivided decimally, each metre containing 
 decimetres, each decimetre 10 centimetres, each centimetre 10 
 millimetres. Its higher multiples, the decametre, hectometre, and 
 kilometre, which are respectively equal 10, 100, and 1000 metres, are 
 seldom required for laboratory work. 
 
 Abbreviations to be 
 metre, m. ; centimetre, cm. ; millimetre, mm. 
 
 Pronunciation. 
 In England it is getting customary to pronounce the names of the 
 
 1 For more complete details relating to these Introductory Measurements see 
 Stewart and Gee's Elementary Practical Physics, vol. i. 
 
 VOL. I & B 
 
2 PRACTICAL PHYSICS FOR SCHOOLS 
 
 French measures as if the words were English. Metre is pronounced 
 meeter. 
 
 TABLE a. 
 RELATION OF METRICAL TO ENGLISH MEASURES OF LENGTH. 
 
 1 metre = 39 '37 inches = 1 '0936 yards. 
 1 inch =25-39 mm. =2 '539 cm. 
 
 Less Exact Values. 
 
 1 metre =A yard and a tenth. 
 
 1 millimetre = ^5- inch. 
 
 1 inch = 25"4 mm. =2 '54 cm. 
 
 A diagram showing the two scales is given on the inner side of the 
 front cover of this book. 
 
 AREA AND VOLUME. 
 
 (2.) The most useful units of area in the laboratory are the square 
 inch and the square centimetre. 
 
 1 sq. cm. = '155 sq. inch. 
 
 To find the areas of regular figures we use the rules of Mensuration, 
 of which we shall need two : 
 
 To find the area of a square or rectangle, Multiply the length by the 
 breadth. 
 
 To find the area of a circle, Multiply the square of the radius by 
 3 '141 6 (or for rough measurements, by -y 2 -). 
 
 The most convenient units of volume are the cubic inch and the 
 cubic centimetre. 
 
 1 cub. inch = 16-386 cub. cm. 
 
 To find the volume of a right prism or cylinder, Multiply the area 
 of the base by the height. 
 
 The volume of liquids is ascertained by means of graduated vessels. 
 These are best divided into cubic centimetres. 1000 cubic centimetres 
 is a litre. Flasks are made to contain a litre, half litre, or quarter 
 litre. 
 
 Exercises. 
 
 1. How many centimetres are in a kilometre? 
 
 2. Reduce 6 '823 decametres to millimetres. 
 
 3. Find the number of centimetres equivalent to 20 metres added to 
 20 inches. 
 
 4. Measure the top of your bench and ascertain its area in square inches 
 and square millimetres. 
 
 5. Find the number of cubic inches and cubic centimetres of wood in 
 the top of your bench. 
 
INTRODUCTORY MEASUREMENTS 
 
 LESSON A. Use of Scales. 
 
 (3.) Exercise. Two small crosses are ruled upon a penny. It is 
 required to measure the distance between the points of intersection. 
 
 Apparatus. A pair of compasses 
 (spring bows are the best, see Fig. 
 a), also several scales, one divided 
 into half millimetres, one into 64ths 
 
 of an inch, a diagonal scale, and a Fifr a> _ SpRING Bows . 
 
 glass millimetre scale. 
 
 Method. Apply the compasses to the penny, so that one of its 
 points may be in the centre of one of the crosses, and the other of its 
 points in the centre of the other, then apply it to the several scales. 
 Convert all measurements into inches. 
 
 The construction and use of the diagonal scale may be understood 
 from Fig. b. There are eleven equidistant horizontal parallel lines 
 running through the whole scale, and dividing it into ten spaces. 
 
 A B 
 
 f~_ 
 
 n 
 
 
 I 
 
 
 
 J 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 / 
 
 
 
 
 1 
 
 
 
 ) 
 
 
 
 
 1 
 
 ! 
 
 J 
 
 J 
 
 
 
 
 \ 
 
 
 ( 
 
 
 
 
 
 
 / 
 
 2 1 
 
 
 
 
 
 1 
 
 
 
 
 
 
 J 
 
 n 
 
 4- 
 
 i 
 
 1 
 
 
 1 
 
 Fig. b, THE DIAGONAL SCALE. 
 
 These are cut at right angles, at distances of half an inch, by vertical 
 lines marked 1, 2, 3, etc., and by this means the whole scale is split 
 up into a number of spaces or regions. 
 
 In the space or region at one end of the scale the lines AB and CD 
 are divided into ten equal parts, and from the points of division dia- 
 gonal lines are drawn, as shown in the figure. There will thus be two 
 terminal triangular spaces, the sides of which are AC and BD, and 
 nine intermediate slanting spaces. To measure a distance by means of 
 the diagonal scale, place one point of the compass at one of the divi- 
 sions, 1, 2, 3, etc., and suppose that the other point falls between two 
 of the slanting diagonal lines, both points being in the bottom hori- 
 zontal line. 
 
 Suppose, for instance, that one point is at 1, and that the other 
 falls between 8 and 9 on the diagonal scale, then the length lies between 
 1-8 and 1'9. To find the length to a second place of decimals slide 
 the compass horizontally up, keeping its right-hand point in the verti- 
 
4 PRACTICAL PHYSICS FOR SCHOOLS 
 
 cal line 1 until the left-hand point meets the intersection of a diagonal 
 with a horizontal line. Suppose, for instance, that when one point 
 is at the star on the line 1, the other is at the star on the diagonal line 
 8 and horizontal line 5, then the measurement will be 1*85 or =0*925 
 inches, the scale being one of half inches. 
 
 The diagonal scale may be used instead of a finely-divided scale. It 
 is ostensibly made to measure to '0025 inch ; but, as ordinarily con- 
 structed of boxwood, it cannot be depended on to this extent. 
 
 In conveying the measurements to the scales an error may be made. 
 This may be avoided by using the glass scale and applying it directly, 
 etched surface downwards, to the penny. Although only divided 
 into millimetres it will be found easy, by this scale, to estimate with 
 the naked eye to the tenth of a millimetre by means of an imaginary 
 subdivision of the millimetre into ten parts. Correctness in this esti- 
 mation, which is one of the first things to learn in Physical Measure- 
 ments, can only be attained by practice. It will be found that, with 
 the unpractised observer, there is a tendency to estimate the '3 too 
 great and the *7 too small. 
 
 Example. A length on a scale, divided into 64ths of an inch, was 
 
 = 422 inch; on a scale divided into half millimetres it was 10*75 
 
 10'75 
 mm. = ' = '423 inch; while on a diagonal scale it was *85 of half 
 
 an inch ='425 inch. 
 
 (4. ) "With ordinary scales under favourable conditions we have seen 
 that it is possible to estimate to ^ millimetre or '004 inch by the 
 naked eye. Greater accuracy may be obtained by using a sliding scale 
 which was invented in 1631 by Pierre Vernier. 1 This device is known 
 by the name of its inventor. The Vernier has in practice entirely 
 superseded the diagonal scale. 
 
 LESSON B. The Straight Vernier. 
 
 (5.) Exercise. To find the length of a rod by means of a scale pro- 
 vided with a Vernier. 
 
 Apparatus. A paper scale, divided into half inches, is mounted on 
 wood, and provided with a Vernier. The Vernier is 9 half inches in 
 length, and is divided into 10 equal parts. 
 
 Method. Place the rod AB (Fig. c) with one end at the zero of the 
 scale, and bring the zero of the Vernier to coincide with the other end 
 of the rod, as in the figure. It will be seen that the rod is between 2 
 and 3 units long. It will likewise be seen that 6 on the Vernier is in 
 coincidence with one of the scale divisions ; and the following simple 
 proof will show that the true length of the rod is 2*6 units. Since 10 
 divisions on the Vernier =9 divisions of the scale, therefore 1 division 
 
 i Pierre Vernier, La Construction, Viisage et les proprictes du quadrant nouveau de 
 Mathematiques. Bruxelles, 1631. 
 
INTRODUCTORY MEASUREMENTS 5 
 
 of the Vernier = T T of a scale division, or each scale division is T V larger 
 than each Vernier division. 
 
 13 12 11 IVt 9 8 7 65 * 
 
 I I I | I | I | 
 
 I I 
 .') S 
 
 1 I 
 
 7 6 15 4 
 
 \ \ I 
 3210 
 
 1. 
 
 Fig. c. THE VERNIER. 
 
 Therefore, since the coincidence is at 6 of the Vernier, the interval 
 between 
 
 7 on the scale and 5 on the Vernier = '1 unit. 
 6 4 = '2 
 
 = 3 
 = 4 
 = 5 
 
 We thus know that the rod is '6 greater than 2, that is, its length is 
 2-6. 
 
 LESSON C. Use of Callipers The Slide Calliper. 
 
 (6.) Exercises (1.) Measure the diameter and thickness of a num- 
 ber of discs of metal, or ordinary coins, 1 and calculate the area and 
 volume of each in metric measure. (2.) Measure the inside and 
 outside diameters of some metal washers, and calculate the area of 
 the annulus. (3.) Measure the inside and outside diameter of a 
 cylinder and its length, thence deduce the volume of liquid it would 
 contain. 
 
 Apparatus and Method. Callipers (Fig. d) are specially employed 
 for measuring the external or internal diameters of curved bodies. 
 The Outside Callipers constitute a compass with 
 curved legs. The points must be set so that they 
 just glide over the cylinder or other body to be 
 measured, and they are then applied to the rule. 
 The Inside Callipers are used in a similar manner 
 to find the internal diameter of a hollow cylinder, 
 hemisphere, etc. The tool is introduced into the 
 cavity and the points set as before. Fig. d shows the two kinds 
 combined in one instrument. In the compass (Fig. a) as well as in 
 the callipers, the distance between the points is adjusted by aid of a 
 Joint. 
 
 The instrument may also be made on the slide principle, and when 
 
 ^ _CALLIPERS 
 
 It is useful to know that the diameter of a halfpenny is exactly one inch. 
 
6 PRACTICAL PHYSICS FOR SCHOOLS 
 
 graduated and provided with a Vernier, we have an instrument far 
 better adapted for accurate measurements than the ordinary workshop 
 tool. Fig. e shows a slide calliper reading to '1 mm. by means of the 
 Vernier V. In using the instrument it is necessary to first ascertain 
 
 iilimliiiil 
 
 illlllllllllllllllllllllllllllllllllllllllllllHlllllllllllllllllimlllllJ 
 
 Fig. e. THE SLIDE CALLIPER. 
 
 that when A and B are in contact the zero of the Vernier corresponds 
 with the zero of the scale. T is a clamp-screw. 
 
 ff- 
 
 LESSON D. The Micrometer Wire-Gauge. 
 
 (7.) Exercise. To measure the diameter of several steel and copper 
 
 wires. 
 
 Apparatus. A wire -gauge to measure to rroir f an inch. The 
 
 wire-gauge (Fig. /) consists of a bent arm ABC, having at C a small 
 cylindrical steel tooth D fixed in its place by a 
 screw capable of adjustment. Attached to A 
 there is a threaded tube F, into which a long 
 screw S accurately fits. This screw is termin- 
 ated by a second steel tooth at E. G is a 
 thimble, fitting over and attached to the upper 
 part of S, with a milled head at H, and having 
 its lower circumference at A divided into twenty 
 parts. At F there is a linear scale, one division 
 of which corresponds to the distance between 
 two threads of the screw. Thus, by means of 
 the linear scale, we can reckon the whole turns 
 of the screw, and by means of the scale of 
 twenty parts we can measure twentieths of one 
 turn. 
 
 The distance between two contiguous threads 
 
 of the screw is usually -Ar of an inch, and as this 
 THE MICROMETER GAUGE. ig capable of ^g ^^ ^ ^^ ^.^ 
 
 r&W of an inch can thus be measured. If the screw had accurately 50 
 threads to the inch the divisions of the linear scale above mentioned 
 would be divisions along a straight line parallel to the line of motion 
 
 Fig. /. 
 
INTRODUCTORY MEASUREMENTS 7 
 
 of the screw ; but the screw may not be absolutely accurate. Any 
 such inaccuracy may, however, be remedied by reading the linear scale 
 not along a straight, but a slightly spiral line, so contrived as to coun- 
 teract the error of the screAV. 
 
 Method. First, find the pitch of the screw. This may be obtained 
 by observing the graduations of the linear scale. The larger divisions 
 of this generally embrace five smaller ones. If these larger divisions 
 are found to be each T V of an inch, it may be taken for granted that 
 one turn of the screw corresponds to ^ of an inch. 
 
 The circular scale is generally divided into twenty parts, so that a 
 circular division represents -^ x T V = Tinnr of an inch. 
 
 Next, screw until the teeth are in contact. If the instrument is 
 correct, both scales should be at the zero point. If this is not the case, 
 alter the adjusting screw which holds D in its place ; or the zero error 
 must be read and afterwards added to or deducted from the measure- 
 ments. 
 
 Thirdly, to measure the diameter of a wire. Place the wire between 
 the teeth, and advance E until the wire is held by the teeth, so that 
 contact may be felt on both sides of the wire. In some gauges, 
 in order that undue pressure may not be exerted, the milled head 
 turns without advancing the tooth further when contact has once 
 taken place. Suppose the reading to be one large and three small 
 divisions on the linear scale, and eight divisions on the circular scale, 
 then 
 
 In. 
 
 One large division on linear, scale = O'l 
 Three small divisions ,, = '06 
 
 Eight circular divisions = '008 
 
 Diameter of wire . . = 0'168 
 
 (7. ) The diameters of wires and the thicknesses of metal plates are 
 in commerce specified by a number known, as the wire-gauge. Until 
 August 1883 there was no legal wire-gauge, so that to know the number 
 of a wire gave but uncertain information of its diameter. The new 
 gauge, however, it is hoped ] will become of general use. On the 
 following page (Table a) we give its values in English and French 
 measure. 
 
 The approximate thickness of a wire may be readily known by 
 using a sheet -metal gauge (Fig. g), which consists 
 of a metal plate with a graduated series of notches, 
 each notch being numbered according to some speci- 
 fied table of wire-gauges. It is only necessary to ascer- 
 tain the number of the notch into which the wire will 
 just fit, and then a reference to the table will give the 
 diameter. Fi s- 0- 
 
PRACTICAL PHYSICS FOR SCHOOLS 
 
 TABLE a lt 
 THE ENGLISH STANDARD WIRE-GAUGE.* 
 
 No. 
 on 
 New 
 wire- 
 gauge 
 
 Diameter. 
 
 Area of 
 cross- 
 section. 
 
 Sq. 
 Centimetre. 
 
 No. 
 on 
 New 
 wire- 
 gauge. 
 
 Diameter. 
 
 Area of 
 cross- 
 section. 
 
 Sq. 
 Centimetre. 
 
 Inches. 
 
 Centimetre. 
 
 Inches. 
 
 Centimetre. 
 
 7/0 
 
 500 
 
 1-270 
 
 1-267 
 
 23 
 
 024 
 
 0610 
 
 00292 
 
 6/0 
 
 464 
 
 1-179 
 
 1-091 
 
 24 
 
 022 
 
 0559 
 
 00245 
 
 5/0 
 
 432 
 
 1-097 
 
 946 
 
 25 
 
 020 
 
 0508 
 
 00203 
 
 4/0 
 
 400 
 
 1-016 
 
 811 
 
 26 
 
 018 
 
 0457 
 
 00164 
 
 3/0 
 
 372 
 
 945 
 
 701 
 
 27 
 
 0164 
 
 0417 
 
 00136 
 
 2/0 
 
 348 
 
 884 
 
 614 
 
 28 
 
 0148 
 
 0376 
 
 00111 
 
 
 
 324 
 
 823 
 
 532 
 
 29 
 
 0136 
 
 0345 
 
 000937 
 
 1 
 
 800 
 
 762 
 
 456 
 
 30 
 
 0124 
 
 0315 
 
 000779 
 
 2 
 
 276 
 
 701 
 
 386 
 
 31 
 
 0116 
 
 0295 
 
 000682 
 
 3 
 
 252 
 
 640 
 
 322 
 
 32 
 
 0108 
 
 0274 
 
 000591 
 
 4 
 
 232 
 
 589 
 
 273 
 
 33 
 
 0100 
 
 0254 
 
 000507 
 
 5 
 
 212 
 
 538 
 
 228 
 
 34 
 
 0092 
 
 0234 
 
 000429 
 
 6 
 
 192 
 
 488 
 
 187 
 
 35 
 
 0084 
 
 0213 
 
 000358 
 
 7 
 
 176 
 
 447 
 
 157 
 
 36 
 
 0076 
 
 0193 
 
 000293 
 
 8 
 
 160 
 
 406 
 
 130 
 
 37 
 
 0068 
 
 0173 
 
 000234 
 
 9 
 
 144 
 
 366 
 
 105 
 
 38 
 
 0060 
 
 0152 
 
 000182 
 
 10 
 
 128 
 
 325 
 
 0830 
 
 39 
 
 0052 
 
 0132 
 
 000137 
 
 11 
 
 116 
 
 295 
 
 0682 
 
 40 
 
 0048 
 
 0122 
 
 000117 
 
 13 
 
 lOt 
 
 26 i 
 
 0548 
 
 41 
 
 0044 
 
 0112 
 
 0000982 
 
 13 
 
 092 
 
 234 
 
 0429 
 
 42 
 
 0040 
 
 0102 
 
 0000811 
 
 14 
 
 080 
 
 203 
 
 0324 
 
 43 
 
 0036 
 
 00914 
 
 0000657 
 
 15 
 
 072 
 
 183 
 
 0263 
 
 44 
 
 0032 
 
 00813 
 
 0000519 
 
 10 
 
 0<i4 
 
 163 
 
 0208 
 
 45 
 
 0028 
 
 00711 
 
 0000397 
 
 17 
 
 056 
 
 142 
 
 0159 
 
 46 
 
 0024 
 
 00610 
 
 0000292 
 
 18 
 
 048 
 
 122 
 
 0117 
 
 47 
 
 0020 
 
 00508 
 
 0000203 
 
 19 
 
 040 
 
 1016 
 
 00811 
 
 48 
 
 ooic 
 
 00406 
 
 0000130 
 
 20 
 
 036 
 
 0914 
 
 00657 
 
 49 
 
 0012 
 
 00305 
 
 00000730 
 
 21 
 
 032 
 
 0813 
 
 00519 
 
 50 
 
 0010 
 
 00254 
 
 00000507 
 
 22 
 
 028 
 
 0711 
 
 00397 
 
 
 
 
 
 LESSON E. The Standard Wire-Gauge, or S.W.G. 
 
 (8.) Exercise. To find the gauge number of a collection of wires by 
 means of the sheet-metal gauge, and to compare the number given in 
 the table with that obtained by direct measurement with the micro- 
 meter wire-gauge. 
 
 Apparatus. Sheet-metal gauge, micrometer wire-gauge, and a num- 
 ber of copper or steel wires. 
 
 Taken from the Board of Trade Circular. 
 
INTRODUCTORY MEASUREMENTS 
 
 ESTIMATION OF MASS. 
 
 (9.) Mass, or the quantity of matter in a substance, is estimated in 
 terms of some standard. The legal standard for Great Britain is a 
 piece of platinum, of which Fig. li shows the exact shape and size. It 
 is taken to represent 7000 grains, or 1 Ib. avoirdupois. The avoirdu- 
 pois ounce is T V of a pound, and is equal to 437*5 grains. 
 
 The standard of mass in the metrical system is the Kilogramme 
 des Archives, which is intended to have the same mass as a cubic 
 
 Fig. n. 
 
 d 
 
 Fig. fc. 
 
 decimetre of pure distilled water at its point of maximum density, 
 reckoned at 4 C. The exact determinations of Kupffer have proved 
 that the true mass of a cubic decimetre of water at 4 C. is 1 "000013 
 kilogramme, so that, for practical purposes, the metrical standard may 
 be taken to agree with the value which the founders of the system 
 wished it to have. A careful copy (see Fig. k) has been taken of the 
 Kilogramme des Archives, which has been accepted in this country 
 under the Act of 1864. The metrical system will almost exclusively 
 be employed throughout these lessons. Its relation to such masses of 
 the British system as are commonly used is seen in the following 
 table : 
 
10 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 TABLE p. 
 KELATION OF BRITISH TO METRICAL STANDARDS OF MASS. 
 
 1 gramme = 15 '4 grains. 
 
 1 kilogramme = 2 '2046 Ibs. 
 
 1 ounce avoirdupois = 28 '35 grammes. 
 
 Less Exact Values. 
 28 g grammes = 1 avoirdupois ounce. 
 454 =1 Ib. 
 
 LESSON F. The Balance. 
 
 (10.) A general view of a 16-inch beam balance, made by Oertling of 
 
 Fig. I. THE BALANCE. 
 
 London, capable of weighing from a kilogramme to half a milligramme, 
 is given in Fig. 1. Its essential parts are 
 
 (1.) The Beam, which is made of brass, in shape like an elongated 
 lozenge, with cross arms, a form calculated to give rigidity com- 
 bined with lightness. At K (Fig. m), the central portion, there 
 
INTRODUCTORY MEASUREMENTS 
 
 11 
 
 is a triangular brass prism with a knife-edge of agate turned 
 downwards. At the ends of the beam there are similar knife- 
 edges turned upwards (see k, Figs, m and ri). Above the 
 central part is fixed a bob of brass, g, called the gravity bob. 
 
 Fig. m. BALANCE BEAM, 
 
 This may be raised or lowered by a slow screw motion. Below 
 the gravity bob is a small vane, v, which, by turning it slightly 
 towards right or left, may be made to correct small deviations 
 from equilibrium. 
 
 Fig. n. END OF BALANCE BEAM. 
 
 (2.) The Pointer, }), which is 321 mm. long, and is attached to the 
 centre of the beam. It moves over a graduated scale, made of 
 ivory, having twenty divisions, the spaces indicated by these 
 divisions being 1'28 mm. 
 
12 PRACTICAL PHYSICS FOR SCHOOLS 
 
 (3.) The Pillar P (Fig. m), which, supports the beam, and is a hollow 
 brass cylinder. At its top is an agate plane, on which the 
 central knife-edge may rest. 
 
 (4.) The Pan-Supports (Figs, m and n\ which consist each of a 
 bent arm attached to a brass bar, bearing on its lower surface 
 an agate plane, a, which rests on the terminal knife-edge k. 
 Each Pan is attached by a hook, H, to the pan-supports. 
 
 (5. ) The Knife-edges and Planes. By the use of these the balance- 
 maker endeavours to reduce friction to a minimum. This 
 involves the necessity of preserving the sharpness of the edges 
 and the smoothness of the planes, and this in its turn involves 
 the condition that the edges and planes shall only be brought 
 into contact when the balance is in use. Accordingly in all 
 delicate balances there is a framework which brings these edges 
 and planes into their required positions when the balance is 
 about to be used. The constancy of this position is secured 
 in a manner which will now be described. 
 
 (6.) The Arrestment, denoted by the shaded framework. It is 
 attached to a central tube, c, which forms an outer covering 
 surrounding the greater part of the pillar the pillar itself 
 being fixed. By means of the large milled head, M, acting 
 outside the balance-case by an eccentric movement, the arrest- 
 ment may be raised or lowered. When the arrestment is at 
 its highest position the central knife-edge is just lifted off the 
 agate planes, and the terminal planes are also raised from the 
 terminal knife-edges. Each pan-support has a hole, h, and 
 slot, s (Fig. n], into which, in the raised position of the arrest- 
 ment, two screws, r and r', with conical points attached to the 
 end of the arrestment (Fig. n), fit, just separating the planes 
 from the knife-edges. At the same time two Y-shaped portions 
 of the arrestment lift the central knife-edge from its plane Y 
 (Fig. m). As much depends on the perfect working of the 
 arrestment, the mechanician endeavours to make the move- 
 ment as smooth as possible. 
 
 (7.) Two arms, d, d, movable from the outside, which can slide along 
 two bars, b, b (Figs. I and m}, fixed above the balance beam, 
 and thus enable a small weight of bent wire, called a Rider, 
 to be placed on any of the graduated positions on the balance 
 arms. The rider generally weighs one centigramme, and there 
 are nineteen graduated positions on the balance beam at regular 
 distances from the fulcrum, so that by this means differences 
 in weight denoting -^ of a centigramme or half a milligramme 
 may be easily estimated. 
 
 The balance has a case with glass doors, so that while there 
 is convenience of access there is at the same time freedom from 
 currents of air. The instrument is supported on four levelling 
 screw r s, and is furnished with two spirit-levels, ss (Fig. I), at 
 right angles to each other. 
 
INTRODUCTORY MEASUREMENTS 
 
 13 
 
 (11.) Weights. The wei 
 the following order : 
 
 hts used are arranged in a box (Fig. o) in 
 
 Brass weights. 
 
 Platinum weights. 
 
 Platinum or alu- 
 minium weights. 
 
 1000 grins. 
 
 50 grms. 
 
 5 grms. 
 
 0'5 grm. 
 
 '05 grm. 
 
 500 
 
 20 
 
 2 
 
 0-2 
 
 0-02 
 
 200 
 
 10 
 
 2 
 
 0-2 
 
 o-oi 
 
 100 
 
 10 
 
 1 
 
 o-i 
 
 o-oi 
 
 100 
 
 
 
 
 
 Fig. o. Box OF WEIGHTS. 
 
 The weights '005, '002, '001, being very small, are seldom used. A 
 wire of aluminium or gilt brass (Fig. p), called a centi- 
 gramme rider, which may be placed at different points 
 along the beam in the manner just described, is much 
 more convenient. 
 
 The smaller weights are protected when not in use by 
 a slip of glass placed over the compartments that contain 
 them. The larger weights should always be handled by lg ' p ' 
 means of the forked piece of ivory, and the smaller R? D E R 
 weights by pincers (Fig. o). They should be covered with 
 some metal which is not subject to oxidation. They are often platin- 
 ised. If they are gilt, care must be taken that they do not come in 
 contact with mercury. A similar remark applies to the scale-pans. 
 
 LESSON G. Method of Using the Balance. 
 
 (12.) Apparatus. The balance, which we shall suppose to have 
 been put into good adjustment, a box of weights, a rider, a camel-hair 
 brush, and an object to be weighed. 1 
 
 1 It is a useful exercise to weigh a number of coins. 
 
14 PRACTICAL PHYSICS FOR SCHOOLS 
 
 Method. On the left-hand pan, which may be named the object- 
 pan, place the body to be weighed, and in the middle of the right-hand 
 or weight-pan such weights as are estimated sufficient to counterbalance 
 the body. Suppose that 50 + 20 grins, are used, and that on partially 
 lowering the arrestment the pointer is seen to move towards the object, 
 indicating that these weights are too great. Suppose next that on 
 substituting 10 for 20 grms. the weight is found to be too little. The 
 subsequent steps of the process are as follows : 
 
 50 + 10 + 5, too great. 
 
 50 + 10 + 2, too little. 
 
 50 + 10 + 2 + 2, too little. 
 
 50 + 10 + 2 + 2+ -5, too little. 
 
 50 + 10 + 2 + 2 + -5 + -2, too little. 
 
 50 + 10 + 2 + 2 + '5 + '2 + % still too little, but not far from the truth. 
 005 is next added, which proves too great ; and finally, on substituting 
 '0025 for it, the pointer swings equally on both sides of the central line 
 of the scale. The weight is thus found to be 64 '8025 grms. 
 
 As the student becomes familiar with the balance he will learn to 
 weigh quickly and know from the swinging of the balance how much 
 to add in order to obtain equilibrium. 
 
 During the process of weighing it will be necessary to observe 
 several precautions. For the sake of convenience let us arrange under 
 one head the general course of procedure in using the balance, as well 
 as the special precautions necessary. 
 
 Precautions in Weighing. 
 
 1. See that the rider is in its place on its supporting arm, and not 
 
 likely to touch the beam during the oscillations of the balance. 
 
 2. Brush the pans with a flat camel-hair brush. 
 
 3. Lower the arrestment to see whether the balance swings equally 
 
 on both sides of the scale. If not, adjust the vane carefully 
 until it does so. 1 
 
 4. Do not stop the swinging of the balance with a jerk. It is best 
 
 to stop it when the pointer is at its central position. 
 
 5. Stop the swinging of the balance when weights are to be added or 
 
 taken away. 
 
 6. The position of the observer should be central, so that there may 
 
 be no parallax in observing the position of the pointer. 
 
 7. If the balance is nearly in equilibrium there may be a difficulty 
 
 in getting up a vibration ; in this case gently waft the air over 
 one of the pans. Or the arrestment may be raised and lowered 
 again ; one or two attempts will set up the required swinging. 
 
 1 The frequent adjustment of the vane is objectionable, tending to produce 
 " " 6 balance ; so that when " 
 
 injury of the balance ; so that when a balance is in much use it is better to correct 
 for slight want of balance by adding weight to one arm, or by mak 
 in scale divisions for the deviation of the pointer from the centre. 
 
INTRODUCTORY MEASUREMENTS 15 
 
 8. Place the large weights in the centre of the pan and the smaller 
 
 weights in the order of their denomination. 
 
 9. Final- weighings must be made with the balance-case closed, and 
 
 care must be taken that the pans do not swing. 
 
 10. Do not weigh a body when hot ; the heat causes air-currents, 
 
 which affect the weighing. 
 
 11. All substances liable to injure the pans must be weighed in ap- 
 
 propriate vessels. 
 
 12. Hygroscopic bodies must be weighed in closed vessels, as also 
 
 volatile liquids. 
 
 13. Remove the weights from the pans, the rider from the beam, and 
 
 close the balance when the weighing is finished. 
 
 ESTIMATION OF DENSITY. 
 
 (13.) For our purpose we can best define the density of a substance 
 to be the weight in grammes of a cubic centimetre of the substance. 
 Hence 
 
 Whole weight in grammes = Volume in cubic centimetres multiplied 
 by the density. 
 
 To ascertain the density of a solid, such as a piece of copper wire, 
 it must be weighed in air and then in water. The loss of weight in 
 water divided by its weight in air gives the density. 
 
 ESTIMATION OF TIME. 
 
 (14.) The unit of time is the second. In place of a watch we may 
 substitute a leaden bullet tied to a silken string, so as to form a 
 pendulum. By adjusting the length of the string it may be made to 
 beat seconds. In determining the time of any event two students, 
 A and B, must work together. A, at the beginning of the event, 
 makes a sharp tap on the table ; B then commences to count the 
 swings of the pendulum until A makes a second tap. Use may also 
 be made of a stop-watch. 
 
 ANGULAR MEASUREMENT. 
 
 (15.) Units of Angular Measurement. The ordinary unit is the 
 degree, which is divided into 60 minutes, each minute being again 
 divided into 60 seconds. The degree is the angle formed by two radii 
 of a circle which enclose -g-^ part of the whole circumference. De- 
 grees, minutes, and seconds are written thus, 83 15' 32". 
 
 (16.) The Dividing of Circles. Most instruments for measuring 
 angles are provided with a graduated circle. To graduate a circle it 
 is generally first of all divided into six equal parts of 60 each. Each 
 
16 PRACTICAL PHYSICS FOR SCHOOLS 
 
 of these is then twice bisected, giving intervals of 15, which are 
 ultimately divided by a method of trial and error into degrees. As 
 far as laboratory practice is concerned, we shall assume that it is 
 always possible to make use of a circle already graduated, the question 
 being to copy its divisions by the method given in the following lesson. 
 
 LESSON H. Copying of Circular Divisions. 
 
 (17.) Exercise. To divide into degrees a circle of cardboard. 
 Apparatus. The apparatus to be used (Fig. q) consists of a brass 
 circle divided into degrees, and having a radial arm capable of turning 
 
 Fig. q. GRADUATION OF CIKCLE. 
 
 about the centre of the circle. One edge of this arm is bevelled, and 
 this edge moves exactly as a radius of the circle. Cardboard, drawing- 
 pen, Indian ink, etc., are likewise necessary. 
 
 Method. Remove the radial arm, and fix the stout pin about which 
 it revolves through the centre of the cardboard circle. Replace the 
 arm, which now has the circle beneath it, and by means of drawing- 
 pins prevent the circle from moving. Now bring the radial arm close 
 to the zero of the brass scale, leaving just room for the drawing-pen ; 
 then, whilst the arm is held firmly, rule a division on the cardboard. 
 In this way the divisions of the outer brass circle are transferred, the 
 5th, 10th, etc., divisions being made somewhat longer than the others. 
 The success of the operation depends upon keeping the relative position 
 of the drawing-pen and the ruler the same at each ruling. 
 
 (18.) Very small angular movements are measured by means of a 
 mirror and scale in the manner to be afterwards described. 
 
CHAPTER I. 
 
 ELECTROSTATICS ELEMENTARY PHENOMENA AND 
 LAWS. 
 
 LESSON I. Electrification by Friction and 
 Conduction. 
 
 1. Apparatus. (1.) .Two pieces of glass tubing about 350 
 mm. long by 15 mm. in diameter. Each must be closed at 
 one end by the blowpipe. The tubes must be thoroughly 
 clean and dry. The open end should be closed by a cork to 
 keep out dust. (2.) Several ebonite penholders. (3.) A 
 stirrup of copper wire covered with gutta-percha, suspended 
 by two narrow silk ribbons. 
 Fig. 1 shows the method of 
 making the stirrup. (4.) A 
 pad of good silk- about 150 
 mm. square. (5.) Electrical 
 amalgam mixed with a little ^ __ 
 tallow. (6.) A piece of cat- 
 skin or other fur. (7.) Two 
 
 small gold-leaf electroscopes. Fig. 2 shows a convenient 
 form of these. Here A is a Florence flask of four-ounce 
 capacity, provided with an india-rubber cork, through 
 which passes a short ebonite rod, e. The ebonite rod 
 is perforated so as to admit the passage through it of a 
 brass rod having a brass disc soldered at one end, while 
 VOL. I r- 
 
IS 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 the other end is filed so as to make a knife-edge. Two 
 gold leaves are attached to this end of the brass rod. 
 
 A hole should be drilled through 
 the brass disc at J, to serve for the 
 attachment of wires. The flask 
 must be thoroughly clean and dry. 
 It should be well washed, the final 
 washing being with distilled water, 
 and then dried before the fire. The 
 cork, with its fittings, should be 
 inserted when the instrument is 
 still warm. (8.) A tin can about 
 10 cm. long by 7 cm. wide. (9.) 
 A block of paraffin wax. (10.) 
 Several metres of No. 32 B. W. G. 
 copper wire. (11.) Several metres 
 of silk thread. (12.) A piece of 
 glass tubing mounted for study of 
 conduction. 
 
 Fig. 2. 
 GOLD-LEAF ELECTROSCOPE. 
 
 NOTES. 
 
 Manipulation of Gold Leaf. To supply the electroscope 
 with gold leaves is a comparatively easy process when we are 
 provided with the following materials as used by the gilder : 
 (1.) A cushion, this consists of a board 8. inches by 5 inches, 
 which is first covered with baize and then with buff leather, 
 tightly stretched. At one end is a raised edge of parchment to 
 protect the cushion from accidental winds. (2.) A gilder's Jcnife, 
 which is a kind of palette knife with a long flexible blade, hav- 
 ing an edge not sufficiently sharp to cut the leather of the 
 cushion. (3.) A tip or large flat brush of squirrel's hair for 
 taking up and placing the gold leaf. (4.) A powder of burnt 
 talc, which is dusted upon the cushion to prevent the gold leaf 
 from sticking to it. The leaf is transferred by means of the 
 knife to the cushion, and then cut by pressure of the knife. The 
 cut leaf may then be lifted by the tip, very slightly greased. 
 
ELECTROSTATICS 
 
 10 
 
 Electrical Amalgam. This consists of an alloy of equal parts 
 of tin and zinc which has been amalgamated with its own weight 
 of hot mercury. Instead of this amalgam mosaic gold is often 
 substituted. Mosaic gold is a bisulphide of tin. 
 
 Ebonite and Vulcanite. These materials consist of a mixture 
 of india-rubber and sulphur that has been heated under pressure. 
 The only difference between ebonite and vulcanite is in the 
 colouring materials used. It is necessary to protect ebonite from 
 the action of the light, which causes the sulphur to become 
 superficially oxidised, when, for electrical purposes, the substance 
 becomes useless. 
 
 Paraffin Wax. This is a white solid hydrocarbon, having 
 a melting point at 54 C. When heated above this temperature 
 its insulating properties are greatly diminished. 
 
 The following experiments must either be conducted in 
 
 Fig. 2a. DRYING OVEN. 
 
 a room where there is a fire, or an air bath of tin similar 
 to that shown in Fig. 2a should be used, on the top of 
 
20 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 which may be placed the rubbers of silk and fur, and inside 
 the electroscopes and glass rods. The air bath is heated 
 by a Fletcher's burner (F), supported on a brick (B). 
 
 Experiment L Electrification ly Friction. Warm both 
 of the glass tubes, and rub one with dry warm silk on 
 which amalgam has been spread. In absence of amalgam 
 dry warm silk alone will answer, but not so well. The 
 tube so rubbed must be placed so that it is supported at 
 the middle by the stirrup. Next, take the other glass tube 
 and rub it in the same way. On approaching the rubbed 
 portion of the second tube to the rubbed portion of the first 
 the latter will be repelled. All this must be done quickly, 
 otherwise- the charge may be lost. Next, rub or excite an 
 ebonite penholder by means of warm dry fur or warm dry 
 flannel, and replace the glass tube on the stirrup by this 
 penholder. Excite another penholder in the same way. 
 On approaching the excited portion of the second pen- 
 holder to the excited portion of the first the latter will be 
 repelled. 
 
 It thus appears that excited glass repels excited glass, 
 while excited ebonite repels excited ebonite. In a pre- 
 cisely similar manner it may be shown that excited glass 
 attracts excited ebonite, and excited ebonite excited glass. 
 We thus see that the state produced in the ebonite by ex- 
 citation is different from that produced in the glass. Ex- 
 cited glass is said to be positively and excited ebonite 
 negatively electrified. Here the words positive and negative 
 are merely convenient expressions, and do not imply that 
 there is anything essentially positive in the physical state 
 of excited glass, or essentially negative in that of excited 
 ebonite. 
 
 Experiment II. Electrification ly Conduction. Place the 
 tin can on the block of paraffin, then connect the tin can 
 with the plate of the electroscope by means of a copper 
 wire about two metres in length (see Fig. 3, where the 
 electroscope is shown supported on a wooden stand). The 
 
i ELECTROSTATICS 21 
 
 wire must not touch anything as it passes from the one 
 vessel to the other. Excite an ebonite penholder and rub 
 it upon the tin can. The two gold leaves of the distant 
 electroscope will immediately repel each other and fly apart. 
 
 Fig. 3. ELECTRIFICATION BY CONDUCTION. 
 
 Here the electroscope becomes electrified by conduction, the 
 copper wire being a conductor of electricity. Next, sub- 
 stitute a silk thread for the copper wire, and it will be 
 found that the electroscope will now remain unaffected, the 
 silk being an insulator or non-conductor. Wet the silk with 
 water and repeat the experiment. The wetted silk will 
 now be found to be a conductor. In using the electroscope 
 care must be taken that it does not receive too great a 
 charge, for in this case the leaves might be torn. 
 
 If we examine a sufficiently large number of bodies we 
 shall find that there is no essential difference between con- 
 ductors and insulators, the difference being rather inihe degree 
 of conducting power which the various substances possess ; 
 for it will be found that by electrifying the tin can suffici- 
 ently strongly after a little time, even with a good insulator 
 connecting the can and the electroscope, the leaves of the 
 latter will begin slowly to diverge. 
 
 Experiment III. Study of the Conducting Power of Glass. 
 Glass is so much used for the construction of electrical 
 apparatus that it will be well for us to learn the conditions 
 
22 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 under which it is an insulator. Take a piece of glass rod 
 about 80 mm. long and about 5 mm. diameter. Mount it 
 as shown in Fig. 3a, where e and e' are ebonite rods sup- 
 ported by a wooden base, gg' is the glass tube supported 
 by copper wires w and w' from the ebonite. Connect the 
 end w with an electroscope, and the end w' with the gas 
 or water pipe. Now warm gg' by a Bunsen burner, and 
 
 Fig. 3a. 
 
 it will be found that when the electroscope is electrified it 
 either remains charged or loses its charge slowly. Next 
 make gg' very hot; the glass now loses its insulating power. 
 Allow the glass to cool slowly, and observe when it again 
 becomes an insulator. The glass having reached an in- 
 sulating condition, breathe upon it, so that it becomes 
 covered with a layer of moisture, and the glass will no 
 longer be insulating. 
 
 Note. A better form of apparatus than the one figured has two brass 
 forks in place of the wires w and w', upon which different materials 
 may be readily placed and tested. 
 
 The following table gives a list of substances in their 
 approximate order of conductivity : 
 
 Good Conductors 
 Semi-Conductors 
 
 Non- Conductors 
 (or Insulators) 
 
 TABLE A. 
 
 ORDER OF CONDUCTORS. 
 
 Metals, carbon, acids, saline solutions, water. 
 
 The body, cotton, dry wood, paper. 
 fOils, porcelain, wool, silk, sealing-wax, sul- 
 phur, resin, gutta-percha, india-rubber, 
 ( shellac, paraffin, ebonite, glass, dry air. 
 
i. ELECTIIOSTATICS 23 
 
 Experiment IV. All Substances of a Different Nature 
 may be Electrified by being rubbed together. In order to 
 electrify a metallic substance or other conductor it must 
 be furnished with an insulating support. Place, for in- 
 stance, the tin can on the block of paraffin, and connect 
 the former with the electroscope by means of a copper 
 wire. Beat the tin can with warm dry fur. The leaves 
 of the electroscope will diverge, showing that the tin can 
 has been excited. 
 
 LESSON II. Electrification by Induction. 
 
 2. Apparatus. That of the previous lesson with the 
 addition of the following: Two brass knobs (ordinary 
 
 Fig. 4. INDUCTION APPARATUS. 
 
 door handles will do very well) mounted on ebonite pen- 
 holders, supported by wooden stands (see Fig. 4). 
 
 Experiment I. Use of Electroscope. When an electrified 
 body is brought near the gold-leaf electroscope the leaves 
 separate. This shows that electrification may be produced 
 by the influence of an electrified body acting through the 
 air. This is called electrification hj induction. Let us pro- 
 ceed to study this phenomenon as it appears in the electro- 
 scope, learning at the same time the correct mode of using 
 that instrument for testing the nature of an electric charge. 
 
24 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 (1.) Let us first of all give the electroscope a positive 
 charge by touching the brass plate with a stick 
 of excited glass, which we then withdraw. 
 
 Note. Sometimes when the brass plate of the electroscope 
 has been rubbed or even touched with a not too highly 
 positively charged glass rod the leaves diverge with negative 
 electricity. This is caused by the friction of the glass and 
 brass causing the latter to take a negative charge. 
 
 certain divergence of the gold leaves will be caused 
 by this charge. Now, if we bring from above 
 towards the plate of the electroscope either this 
 charged stick of glass or another similarly excited, 
 it will be noticed that the leaves diverge more 
 and more widely as the positively charged glass 
 continues to approach the plate. 
 
 (2.) If we next cause a stick of excited ebonite to 
 approach the plate of the positively charged 
 electroscope, we shall find that the negative 
 charge which the ebonite has will cause the leaves 
 to collapse. If, however, this negative charge be 
 very strong, on bringing it still nearer, the leaves 
 will again open out. When such a charge is 
 quickly brought near the electroscope it is pos- 
 sible that the first collapse of the leaves may 
 escape the notice of the observer. 
 
 (3.) If a conducting body, such as the hand, be ap- 
 proached towards the plate of the charged electro- 
 scope, the gold leaves will tend to collapse. 
 We see from this experiment that the slow approach 
 to the plate of the charged electroscope of a similarly 
 charged body will cause the leaves to open out, while 
 the slow approach of a body charged with the opposite 
 electricity will cause the leaves to fall together, and, 
 if it be strong enough, as the approach is continued, 
 afterwards to open out. 
 
 We see also that the approach of a neutral conductor 
 
I ELECTROSTATICS 25 
 
 whose parts are at varying distances from the plate will 
 tend to make the gold leaves collapse. 
 Experiment II. Charging by Induction. 
 (1.) Having discharged the electroscope, excite a stick 
 of ebonite and bring it near to the plate; the 
 leaves will separate. Whilst the ebonite is kept 
 in this position (near the plate) touch the plate 
 for a moment, and then withdraw the finger; 
 the leaves will now fall together. Remove the 
 ebonite, and the leaves will again open. If we 
 test the character of the charge it will be found 
 to be positive, or opposite to that of the ebonite. 
 (2.) Had we employed a stick of glass instead of one of 
 ebonite, the charge would have been negative. 
 This method of charging an electroscope is called 
 charging ly induction, and is usually better than 
 the other method, or that by conduction, for the 
 reason given in the above note. 
 
 Experiment III. Study of Induction. Let us now pro- 
 ceed to inquire further into the nature of induction. 
 
 (1.) Take the two brass knobs mounted on ebonite 
 penholders, and place the edges of the knobs in 
 contact with each other. Then bring an electri- 
 fied rod, for instance, an ebonite rod charged with 
 negative electricity, near one of the knobs, but 
 not touching it. Whilst the ebonite rod is in 
 this position, separate the knobs from one another 
 and test their charges. They will be found to 
 be charged with opposite kinds of electricity, the 
 one that was nearest the electrified ebonite rod 
 being positively charged. 
 
 (2.) Repeat the experiment, but, when the electrified 
 ebonite rod is near, instead of separating the knobs, 
 touch either of them momentarily with the finger ; 
 both knobs will now be found to have a positive 
 charge. 
 
26 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 (3.) Make the experiment as in (2), but instead of 
 touching the knobs with the finger touch them 
 with the plate of the electroscope ; the electro- 
 scope will be found to have received a negative 
 charge. 
 
 We learn from these various experiments that when 
 electrification by induction takes place, both kinds of 
 electricity are produced, or rather separated from each 
 other, in the neutral conductor, that of the same name 
 as the charge of the inducing body having a tendency 
 to escape. It is therefore said to be unbound or free, whilst 
 that of the opposite name is said to be bound as long as the 
 inducing charge is present. 
 
 Note. To assist the student in under- 
 standing the following explanations he 
 should make drawings in his note-book" 
 representing the successive steps of the 
 experiments. For positive use the sign 
 + and for negative the sign - ; or use 
 blue and red pencils. Fig. 4 a shows 
 the kind of sketches that should be 
 made. 
 
 Explanation of Experiments. 
 The student should now be able 
 to understand the induction ex- 
 periments with the electroscope. 
 . 4a . For instance, in Experiment I., 
 
 we see why the slow approach to 
 
 the plate of a charged electroscope of a similarly charged 
 body should cause the leaves to open out, inasmuch as the 
 approaching body may be imagined to decompose the 
 neutral electricity of the electroscope, attracting or bind- 
 ing that of an opposite name to itself, and thrusting that 
 of the same name as far away as possible that is to say, 
 to the leaves which consequently diverge. 
 
 For similar reasons the slow approach of a body charged 
 with the opposite electricity will cause the leaves to fall 
 
I ELECTROSTATICS 27 
 
 together, and to open out afterwards with an opposite 
 charge as the approach is continued. 
 
 When a neutral body, such as the hand, is placed near 
 the plate of a charged electroscope, the leaves will tend to 
 collapse, because the electricity of the instrument will act 
 upon the hand, decomposing (as it were) its neutral 
 electricity, pulling that of the opposite name as near to it 
 as possible, and thrusting that of the same name through 
 the body to the earth. In this manner part of the charge 
 will become bound, and, being withdrawn from the gold 
 leaves, these will tend to collapse. 
 
 Again, it is manifest that when the electroscope is 
 charged by induction, the office of the finger when it 
 touches the plate is to take away the free electricity, or 
 that of the same name as the charge of the inducing body. 
 What is then left is the charge of this body, and a nearly 
 equal amount of electricity of the opposite name in the plate 
 of the electroscope. Both these are practically bound, and 
 therefore do not influence the gold leaves ; withdraw, how- 
 ever, the inducing body, and the electricity of the electro- 
 scope is now free, and acts therefore upon the leaves. 
 
 LESSON III. The Electrophorus of Volta. 
 
 3. Apparatus. (1.) A simple electrophorus (Fig. 5). A 
 convenient form 'consists of an ebonite disc the plate 
 about 60 mm. in diameter, having a metal disc, termed the 
 sole, of the same size screwed to its under surface. The 
 upper surface of the ebonite is well polished. A separate 
 brass disc with smooth edges, somewhat smaller than the 
 plate, is provided with a rod of ebonite as a handle, and 
 forms the lid of the instrument. An electrophorus con- 
 structed in this manner is a very satisfactory instrument. 
 A simpler variety may be made by melting ordinary seal- 
 ing-wax in the lid of a round tin canister, so as to form a 
 
28 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 Fig. 5. ELECTROPHORUS. 
 
 smooth plate. A disc of tin, with a handle of sealing-wax, 
 will serve as a lid. (2.) An electroscope. (3.) Fur or 
 flannel. 
 
 Use of the Instrument. The 
 plate must first be excited. A 
 few whisks with the fur of a cat 
 will serve to electrify the polished 
 ebonite or sealing-wax strongly. 
 If this cannot be procured, any 
 other kind of fur or a piece of 
 hot flannel will do instead. Next 
 place the lid upon the plate, and 
 touch the metal of the lid moment- 
 arily with the finger. On raising 
 the lid it will be found to be 
 charged and capable of giving a 
 spark. As often as this process is 
 repeated the lid becomes charged, provided that the plate 
 is freshly excited occasionally. The electrophorus thus 
 forms a simple electrical machine. The labour of touching 
 the disc may be avoided if a metal pin be passed through 
 a hole in the plate, so that when the lid is in position 
 the sole may be in connection with the lid. 
 
 Theory of the Instrument. This may be studied by per- 
 forming the following experiments : (1.) Find the nature 
 of the charge of the ebonite ; this will be found to consist 
 of negative electricity. (2.) Find the nature of the charge 
 of the lid after it has first been touched and then removed 
 from the electrophorus; this will be found to consist of 
 positive electricity. (3.) Place a charged electrophorus, 
 with its lid (untouched), upon the plate of the electroscope ; 
 on touching the lid the gold leaves will fly apart, and will 
 be found to be charged with positive electricity. (4.) Now, 
 retaining the arrangement of (3), withdraw the lid from 
 the electrophorus, when the gold leaves of the electro- 
 scope will immediately collapse. 
 
i ELECTROSTATICS 29 
 
 The electrophorus thus acts by means of induction. The 
 ebonite, when struck with the fur or flannel, is negatively 
 electrified, and this negative electricity decomposes the 
 neutral electricity of the sole, pulling the positive to itself 
 and thrusting the negative into the earth. The action of 
 the positive of the sole upon the negative of the ebonite 
 serves to bind the latter into the substance of the ebonite. 
 When the lid is put on, the electricity of the ebonite is not 
 communicated by contact to the lid, the ebonite being a 
 non-conductor, and only touching the lid in a few points. 
 On the other hand, the lid is acted on inductively by the 
 negative electricity of the plate, and when it is touched 
 with the finger the free negative of the lid is thrust 
 through the body of the operator into the earth, and, at the 
 same time, this releases the bound positive electricity of 
 the sole. The lid, if carried away, will' thus be found to 
 be positively electrified. 
 
 When the electrophorus is placed upon an electroscope, 
 and in that position the lid is touched, the positive electri- 
 city of the sole, being released, is permitted to go to the 
 gold leaves, which, in consequence, diverge. When, how- 
 ever, the lid is carried away, this positive is recalled into 
 the sole, and the gold leaves collapse. 
 
 LESSON IV. Faraday's Ice Pail Experiments. 
 
 4. Apparatus. (1.) Two tin cans, one 10 cm. deep by 7 
 cm. wide, the other 7 cm. deep by 5 cm. wide. The larger 
 can has a layer of paraffin wax covering the bottom ; 
 the smaller is furnished with an ebonite penholder 
 as a handle (Fig. 6). (2.) A block of paraffin to serve as 
 an insulating support. (3.) A small electrophorus. (4.) 
 Two electroscopes. (5.) Connecting wires. (6.) It may 
 be convenient to use an electrophorus lid smaller than 
 that mentioned in the previous lesson, such, for in- 
 
30 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 stance, as a halfpenny attached to an ebonite penholder 
 (Fig. 7). 
 
 Note. The student should make sketches in his note-book of the 
 following experiments. 
 
 Experiment I. Place the larger 
 tin can on the block of paraffin, 
 and connect the tin with an 
 electroscope. Charge the lid of 
 the electrophorus, and lower it 
 into the tin can, without allow- 
 ing it to touch the latter. The 
 electroscope leaves will diverge 
 as the lid is lowered, but when 
 it is a little way inside the can 
 this divergence will reach a 
 maximum, and then remain un- 
 altered. Now make the lid to 
 touch the metal near the bottom 
 of the can ; no alteration will be 
 produced by this in the amount of divergence of the 
 electroscope leaves. The charge of the electroscope will 
 be found to be of the same kind as was that of the 
 electrophorus lid. Remove the lid, and test it by a second 
 electroscope ; it will be found to be perfectly discharged. 
 
 Experiment II. Repeat the previous experiment, but 
 when the lid is near the bottom of the can (not having 
 been in contact with the metal), touch the outside of the 
 can with the finger, so as to withdraw the external charge. 
 The leaves of the electroscope will now collapse, but if the 
 electrophorus lid be removed without allowing it to touch 
 the can, the leaves will again separate to as great an extent 
 as before. Test the charge of the electroscope, and it will 
 be found to be of the kind opposite to that of the electro- 
 phorus lid. 
 
 Experiment III. Place the smaller tin within the larger, 
 
 Fig. 6. 
 
 Fig. 7. 
 
r ELECTROSTATICS 31 
 
 so as to make it rest upon the layer of paraffin at the 
 bottom of the latter. Introduce within the smaller tin 
 the positively electrified electrophorus lid. This will give 
 rise to a condition of electrification in which the inner 
 sides of the two tins will be negatively and the outer sides 
 positively charged. 
 
 Now make contact between the two cans by the aid 
 of the insulating handle of the smaller. The inner 
 surface of the inner can will now be negatively and the 
 outer surface of the outer can positively electrified. Next 
 let the lid be removed, but not discharged, the inner vessel 
 removed and discharged, and then both replaced. The 
 outer vessel may now be made to have a double charge 
 by repeating the above process, and a small initial electrifi- 
 cation may thus be multiplied as many times as we please. 
 
 Note. The student should grasp the following explanation with 
 the aid of the sketches he has made. 
 
 Explanation of these Experiments. When the charged 
 electrophorus lid has been lowered sufficiently far into the 
 can (as in Experiment I.), it acts inductively upon the can, 
 attracting to the inside a quantity of electricity equal in 
 amount but opposite in character to that of the lid, and 
 repelling to the outside a quantity equal in amount but 
 similar in character to that of the lid. When the lid 
 touches the inside of the can its electricity combines with 
 that equal and opposite charge which has been induced on 
 the inside, leaving the outside electrification altogether 
 unaffected. The lid will now be found to have no charge, 
 because (see Lesson VL) it has come from being in contact 
 with the interior of a conductor, the charge of which clings 
 to the outside. 
 
 In Experiment II. the touching of the outside of the can 
 carries off to the earth electricity equal in amount and 
 similar in character to that of the lid, thus causing the 
 leaves of the electroscope to collapse. When, however, 
 
32 PRACTICAL PHYSICS FOR SCHOOLS en. 
 
 the charged lid is removed from the inside, the electricity 
 of the inside of an opposite character to that of the lid 
 which was formerly bound by the lid, is now free to influ- 
 ence the gold leaves. 
 
 In Experiment III., after contact has been made be- 
 tween the two cans, the outer one is positively and the 
 inner one negatively charged. If the inner one be now 
 removed, discharged, and then replaced, we shall of course 
 have positive in the outer and nothing in the inner. But 
 if now the charged lid be reintroduced into the inner 
 can, and contact made as before between the two cans, 
 there is no reason why a second positive charge should 
 not be given to the outer can. 
 
 Indeed for this purpose there is no necessity for the 
 two cans, for if the lid, after being discharged, as in Experi- 
 ment I., be recharged and introduced into the can, after 
 contact with the inside, a double charge will be given to 
 the outside. The use of the inner can, however, renders 
 it unnecessary to discharge the lid. 
 
 LESSON V. Electrification by Friction 
 
 (Continued from Lesson /.) 
 
 5. Apparatus. (1.) Glass rod, ebonite, electroscope, etc. 
 (2.) A number of different insulators, such as flannel, seal- 
 ing-wax, paraffin, gutta-percha, etc. (3.) The small electri- 
 cal machine described below. 
 
 Experiment I. Both kinds of Electricity are produced by 
 Friction. The rubber of amalgamed silk or fur is usu- 
 ally not a good insulator, so that its charge is generally 
 lost when held in the hand before its electrification can 
 be tested. To exhibit the electrification of the rubber, 
 place the pad of silk or fur on the cap of the electro- 
 scope, and rub the silk or fur by means of the glass rod 
 or rod of ebonite. Examine the nature of the electricity 
 
i ELECTROSTATICS 33 
 
 with which the electroscope becomes charged. It will be 
 found to be of the opposite kind to that of the glass or 
 ebonite. Test in this manner the quality of the electrifi- 
 cation produced with different materials, and verify the 
 following table, in which the substances are arranged in 
 such an order that any substance in the list becomes 
 negative if rubbed with a body that precedes it, but 
 positive if rubbed with a body that follows it in the list 
 
 TABLE B. 1 
 
 SHOWING ORDER OF ELECTRIFICATION. 
 
 Catskin. Sulphur. Resin. 
 
 Glass. Flannel. Gutta-percha. 
 
 Silk. Cotton. Metals. 
 
 The hand. Shellac. Gun-cotton. 
 
 Wood. India-rubber. 
 
 Additional Practical Exercise. Make a collection of different sub- 
 stances and arrange them, by means of tests made by the electroscope, 
 in the order of electrification. 
 
 Experiment IL Both lands of Electricity are produced ly 
 Friction in Equal Amounts. This may be shown by rubbing 
 two bodies together within an insulated chamber connected 
 with an electroscope. There should then be no external 
 sign of electrification. A simple apparatus, such as is 
 shown in Fig. 8, may be used for this purpose. A is a tin 
 can embedded in a block of paraffin (B) that is protected 
 by the wooden base. Within A is a smaller can (C), not 
 necessarily metallic, but for purposes of convenience made 
 of tin, cemented to the bottom of A by means of paraffin. 
 The inside of C is lined with fur. A metal rod is soldered 
 to the bottom of C. An ebonite cylinder (E) is sup- 
 ported by the metal rod so that the ebonite may easily 
 be rotated, rubbing against the fur as it does so. The 
 
 1 The order in the above table is liable to change, depending upon 
 the exact composition and the nature of the surface of the substance. 
 VOL. I D 
 
34 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 outer tin can is connected with an electroscope by means 
 of the hook S. On rotating E no effect is observed until it 
 is withdrawn to the outside of the outer vessel, when the 
 
 Fig. 8. 
 
 electroscope will indicate positive electricity, for the posi- 
 tive electricity developed on the fur decomposes the neutral 
 electricity of the outer can, pulling the negative to itself 
 and sending the positive away to the electroscope. 
 
 LESSON VI. Effect of a Conducting Enclosure. 
 
 6. Apparatus. (1.) A tin can sufficiently large to con- 
 tain an electroscope. It should be provided with slits, 
 opposite to each other, to enable an electroscope to be 
 observed when placed within. (2.) Two electroscopes. 
 (3.) Block of paraffin, conducting wire, etc. 
 
 Experiment I. There is no Electrification within a Con- 
 ductor. Place the small gold-leaf electroscope within the 
 tin can. Carry a wire from the electroscope to the inner sur- 
 face of the can. The tin must be placed on a block of paraffin 
 
ELECTROSTATICS 
 
 35 
 
 and have its outer surface connected with a second electro- 
 scope (Fig. 9). Now electrify the tin can, when the electro- 
 scope A will immediately show the presence of electricity, 
 while the electroscope B will not be affected. It will be 
 
 Fig. 9. 
 
 found that however intense the electrification of the outer 
 vessel may be, the electroscope B will show no signs of 
 electrification. 
 
 Experiment II. Protection from External Influence. Dis- 
 connect the wire from the inner surface of the tin can. 
 Give the electroscope B a charge by means of an electro- 
 phorus. Now electrify the tin. No further effect will 
 be perceived on the electroscope within the can. In this 
 way it is shown that a body within a metallic enclosure 
 has its electric state uninfluenced by electrifying the en- 
 closure from without. And further, if you bring an 
 electrified body near the outside of the can it can like- 
 wise be shown that the electroscope in the interior 
 will be quite uninfluenced by its inductive action. This 
 has important practical applications, as we shall after- 
 wards see. 
 
36 PRACTICAL PHYSICS FOR SCHOOLS OH. 
 
 SUMMARY OF LAWS. 
 
 7. By aid of the preceding experiments the student 
 has been enabled to illustrate the following laws. 1 
 
 I. " The total electrification of a body or system of bodies 
 remains always the same, except in so far as it receives 
 electrification from or gives electrification to other bodies" 
 
 The more we improve the insulation of a charged body 
 the longer does the charge remain, and it is therefore 
 assumed that an absolutely isolated charge remains con- 
 stant. A charge may be retained for years in a chemically 
 dried, hermetically sealed glass vessel. 
 
 II. " When one body electrifies another by conduction the 
 total electrification of the two bodies remains the same, that is, 
 the one loses as much positive or gains as much negative electri- 
 fication as the other gains positive or loses negative electrification" 
 
 This may be proved by bringing two unequally and 
 differently charged bodies into contact within an insulated 
 enclosure connected with an electroscope, when it will be 
 found that the divergence of the leaves of the electroscope 
 will be the same after contact as before it. 
 
 III. " When electrification is produced by friction or by any 
 other known method, equal quantities of positive and negative 
 electricity are produced." 
 
 This is illustrated by Experiment II., Lesson Y. 
 
 IV. "If an electrified body or system of bodies be placed 
 within a closed conducting surface, the interior electrification of 
 this surface is equal and opposite to the electrification of the 
 body or system of bodies" 
 
 In the case of an electrified body placed in the 
 laboratory or other room where the experiment is per- 
 formed, the floor, walls, ceiling, etc., take a charge equal 
 and opposite to that of the body. 
 
 We see this from the analogy of Experiments I and II., 
 
 1 Elementary Treatise on Electricity, by J. Clerk Maxwell. 
 Clarendon Press. 
 
I ELECTROSTATICS 37 
 
 Lesson IV., in which the inside of the tin can was found 
 to contain electricity opposite in character but equal in 
 amount to that of the electrophorus lid. 
 
 V. " If no electrified body is placed within the hollow con- 
 ducting surface, the electrification of this surface is zero. This 
 is true not only of the electrification of the surface as a whole, 
 but of every part of the surface." 
 
 This is seen from Experiment I., Lesson VI., in which no 
 effect is produced upon the electroscope within a tin can 
 by electrifying the outside of the can. 
 
 8. Fundamental Quantitative Law. If we add to the 
 above five fundamental laws of electric phenomena a sixth 
 quantitative law, the student will be placed in possession 
 of all that is necessary to explain elementary electro- 
 statics. Suppose that at a point A there are m units of 
 positive electricity, and at B m' units of the same kind of 
 electricity, and let the distance between A and B be d 
 centimetres, then it is found that the force / of repulsion 
 may be represented thus, 
 
 If the electrification at A or B be negative, this is in- 
 dicated by putting a minus sign before the symbol of 
 quantity. Thus if A be charged with + 3 units and B 
 with - 6 units at a distance apart of 2 cm., then 
 
 , ( + 3)x(-6) 
 / 2 2 ~" ~ 2' 
 
 A negative sign, therefore, denotes attraction. The direct 
 proof of the very important law in formula (1) is experi- 
 mentally difficult. It was first attempted by Coulomb by 
 using a torsion balance. 
 
 9. Definition of the electrostatic unit of quantity of electricity. 
 The above expression (1) will enable us to define the 
 electrostatic unit of quantity. Let / = 1, d = 1, and 
 
38 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 m = m', then must m=l; in other words, when A and B 
 are each charged with an electrostatic unit of electricity, 
 and are placed unit distance apart, then will these points 
 tend to separate with the unit of force. The unit of force 
 which we shall adopt is the dyne, and this will be after- 
 wards denned. 
 
 FURTHER THEORETICAL NOTES. 
 
 1O. Potential Difference of Level. Every one knows what 
 is meant by difference of level. When we say that the surface of 
 one pond is 100 ft. and that of another pond 50 ft. above the 
 level of the sea we convey perfectly definite information. It 
 will nevertheless be of importance to examine minutely what is 
 and likewise what is not implied in this very simple statement. 
 In the first place it is implied that all parts of the surface of the 
 one pond are at the height of 100 ft., and all the parts of the surface 
 of the other pond at the height of 50 ft. above the zero or sea-level. 
 
 The various parts of each pond are thus in a condition of 
 equilibrium, and there is no rush of water from one part to 
 another of the same pond. 
 
 In the next place, it is not implied that all parts of the same 
 pond have the same depth of water. On the contrary, some portions 
 may be very shallow and others very deep without in the least 
 affecting the equilibrium. 
 
 Again, the one pond may be very different in size from the 
 other, and it may be necessary to take a very large amount of 
 water out of the one in order to reduce its level by 1 ft., while 
 it may be necessary to take only a small quantity out of the 
 other to bring about the same result. 
 
 We may define this difference by saying that the capacity of 
 the first pond is much greater than that of the second. 
 
 In order to simplify our conceptions, let us imagine that the 
 two ponds are the one at the top and the other at the bottom 
 of the same vertical wall, and that on this wall we have a machine 
 by which we may raise water from the lower to the higher level. 
 It is clear that every pound of water so conveyed must be raised 
 50 ft. in vertical height, so that, according to the British termin- 
 ology, 50 foot-pounds of work must be spent in carrying one pound 
 
i ELECTROSTATICS 39 
 
 of water from the lower level to the higher; at least this is 
 what will happen at the beginning of the process, and before we 
 have sensibly affected the level of either pond. 
 
 11. The Foot-Pound, Dyne, and Erg. We may at once gener- 
 alise this statement by asserting that the work which we must 
 spend in conveying m pounds of water from one level to another 
 d feet above it will be md British units of work, or foot-pounds as 
 these units are called. On the other hand, we may open tip a 
 channel between the higher and lower ponds, and the falling 
 water may be made to do useful work ; and here too we may 
 generalise by asserting that m pounds carried down the channel 
 through d vertical feet will do useful work equal to md. 
 
 When we speak of foot-pounds we virtually assume the 
 attraction of the earth for one pound to be our unit of force, and 
 the foot to be our unit of length. Such well-known units are 
 of essential preliminary service in enabling the student to realise 
 a natural force, such as gravity, and to give him a clear concep- 
 tion of energy and work. Nevertheless, it is highly desirable 
 for many reasons, in the various branches of physics to make use 
 of the centimetre, gramme, and second system of units, commonly 
 called the C. G. S. system. 
 
 In this system, while the second still remains the unit of 
 duration, the centimetre is the unit of length, and the gramme 
 the unit of mass. The unit of force, called the dyne, is that 
 which, when acting on unit of mass (one gramme) for unit of 
 time (one second), will generate unit of velocity (that of one- 
 centimetre in one second). 
 
 In this system likewise the attraction of the earth for one 
 gramme will be represented by 981, inasmuch as gravity acting 
 on one gramme for one second will generate in it the velocity 
 of 981 cm. per second. 
 
 Finally, the unit of energy is called the erg, and it represents 
 the energy required to move a body against unit force (the 
 dyne) through unit distance (the centimetre). If, therefore, we 
 raise a gramme through one centimetre of vertical height against 
 gravity we exert an amount of energy = 981 ergs. 
 
 12. Comparison of Electricity and Gravity. Now there may be 
 
40 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 difference of level in the case of electricity just as truly as there 
 is for gravity ; and just as water, when we open up a conducting 
 channel, will run from a higher to a lower level, so in elec- 
 tricity, when we connect together by a wire two electrified 
 bodies at different electrical levels, will there be a rush of elec- 
 tricity from the one to the other. 
 
 But while there is in many respects a very great likeness 
 between gravity and electricity, there are yet features of differ- 
 ence which must be borne in mind. 
 
 In gravity we naturally associate difference of level with 
 difference in vertical height, so that you could not have two 
 reservoirs of water with their surfaces quite close together and 
 yet possessing great difference in level. On the other hand, in 
 electricity (as for instance in the outside and inside coatings of 
 the Leyden jar) you may have two surfaces at very different 
 electrical levels, and yet very close together. In fine, we must 
 entirely dismiss from our minds the idea that the foot-rule will 
 give us the means of measuring differences of electrical level. 
 Even in the case of gravity, the method of measuring differences 
 of level by the foot-rule, although practically convenient, is by 
 no means theoretically perfect. 
 
 As a matter of fact, we cannot leave the surface of the earth, 
 but in imagination we may transport ourselves to a distance ten 
 times as far from the .earth's centre as is our present abode. "We 
 may likewise take with us a pound of water, and at this great dis- 
 tance from the earth's centre raise it up vertically 1 ft., just as 
 we might do on the earth's surface. It will not, however, cost us 
 so much labour to do this at the increased distance as it would 
 at the earth's surface, because at the former position the force of 
 gravity would have only -j-J-^ part of its present or earth-surface 
 value. Hence we might at the increased distance raise the 
 pound of water 100 ft. with the same expenditure of energy 
 that would be required to raise it 1 ft. at the earth's surface. 
 
 So then we see that there may be two ways of measuring 
 differences of level, namely the practical but unscientific method 
 by the foot-rule, and the unpractical but yet eminently scientific 
 method by taking account of the work spent in carrying a pound 
 weight from the one level to the other. 
 
I ELECTEOSTATICS 41 
 
 If we adopt this latter method of procedure, we should regard 
 unit difference of level at the earth's surface to be 1 ft., but at 
 the increased distance 100 ft. 
 
 Viewed in this manner, differences of level are known as 
 differences of potential. Two points therefore may be said to be 
 at unit difference of potential as regards terrestrial attraction 
 when unit of work is spent in conveying unit of mass (the 
 pound) from the one point to the other. It appears that we 
 thus get hold of a general conception which will serve us far 
 above the earth's surface if we agree to measure differences of 
 potential or level by the test of work and not by that of the 
 foot-rule. 
 
 13. EOjUipotential Surfaces. Suppose now that we have a 
 number of points all at the same potential or level, it is clear that 
 no work will be required in order to carry 1 Ib. from one of these 
 points to another. A surface passing through such points is 
 called an equipotential surface. The surfaces of the two 
 sheets of water of which we have been speaking are equipoten- 
 tial surfaces, the potential of the one being, however, different 
 from that of the other by 50 units. Also the potential of the 
 one surface is 50 and that of the other 100 units different from 
 that of the sea surface, which we may call our zero of potential. 
 
 But further, this new way of looking at things will not 
 merely serve us as we go from the earth's surface to distant 
 regions, but it will likewise serve us when we go from one force 
 to another from gravity to electricity, for instance, being just 
 as applicable to the one as it is to the other. 
 
 In gravity, we say that two points are at unit difference of 
 potential when unit of work is spent in carrying unit of mass 
 from the one to the other against gravitating force. So in 
 electricity we may say that two points are at unit difference of 
 electric potential when unit of work is spent in carrying unit of 
 electricity from the one to the other against the force of electric 
 attraction or repulsion. Our readers will remember that unit of 
 electricity has been already denned (Art. 9). 
 
 14. Zero of Potential. Now when we open up, by means of 
 a wire, communication between electrified bodies at different 
 
42 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 potentials, there will be a rush of electricity from the body 
 of highest to that of lowest potential. If, however, we open 
 up a communication between two bodies that are at the 
 same potential, there will be no transfer of electricity between 
 the two. 
 
 And, just as in the case of gravity, we take the sea-level to 
 be the zero or standard level or potential, so in the case of 
 electricity do we take the potential of the earth to be the zero 
 potential. It follows that when a body has a higher positive 
 potential than the earth there will, when communication is 
 opened, be a rush of positive electricity from that body to the 
 earth ; and that when a body has a lower positive potential 
 than the earth there will be a rush of positive electricity from 
 the earth to that body. This last is the same thing as saying 
 there will be a rush of negative electricity from the body to 
 the earth. 
 
 Note. To ascertain the nature of the potential of a body we may 
 further consider whether, when a small imaginary charge of positive 
 electricity is transferred from the body to the earth, this operation is 
 favoured or resisted by electrical force : if the former, the potential is 
 positive ; if the latter, the potential is negative. 
 
 15. Positive Current only considered. We shall not here 
 consider as distinct things this rush of positive electricity from 
 the earth to the body and this rush of negative electricity from 
 the body to the earth ; these may be regarded as merely two ways 
 of viewing the same transfer, and in this science of electricity 
 we shall agree to consider only the flow of positive electricity. 
 
 Note. "We do not intend to discuss whether there are two sorts of 
 electricity or only one sort. But we shall assume, for convenience sake, 
 that the former assumption is the true one. The student must then 
 bear in mind that an isolated body distant from other charged bodies is 
 
 (1.) Of + potential if of + charge. 
 (2.) Of- - 
 
 But if the body is near others, there is no such simple connection 
 between the nature of the charge and the potential. This will be 
 seen in subsequent experiments. 
 
 16. The Units of Density and Capacity. We have thus denned 
 unit quantity of electricity and unit difference of potential or 
 
i ELECTROSTATICS 43 
 
 electrical level, and it will now be very easy to define unit 
 density and unit capacity. If unit of surface of a conductor has 
 on it unit quantity of electricity, then we say that the electrical 
 density of that surface is unity. So that the density is measured 
 by the number of units of quantity that exist on one square 
 unit of surface. 
 
 Again, if it takes unit quantity of electricity to raise the electrical 
 level of a conductor one unit, then that conductor has an electric 
 capacity equal to unity. So that the electric capacity of a con- 
 ductor is measured by the number of units of quantity required 
 to raise it through one unit of potential. 
 
 So in like manner we might say that if it requires unit of 
 mass, or 1 Ib. of water, to raise the level of a vessel of water 1 ft., 
 then the vessel has unit capacity. But if it requires 2 or 3 Ibs. 
 of water to do this, then the vessel has a capacity represented 
 by 2 or 3. 
 
 17. Application of Definitions. The analogy derived from 
 gravity may likewise be used for enabling us to perceive the solu- 
 tion of a great number of electrical problems. Suppose, for in- 
 stance, that we have a vessel of water, the capacity of which is 
 unity that is to say, it requires 1 Ib. of water to raise its contents 
 1 ft, and that it is required to find what expenditure of energy will 
 be necessary in order to fill it, say to the height of 6 ft. Here 
 it will be evident that the first portions of water put into the 
 vessel have only to be raised to a comparatively small height, 
 while the last portion has to be raised to the whole height of 
 6 ft. It follows that the whole energy necessary to raise the 
 level 6 ft. from the bottom will be that necessary to raise 6 Ibs. 
 of water through the average height of 3 ft. that is to say, 
 1 8 foot-pounds or British units of work. 
 
 We may generalise, and say that if we have a vessel whose 
 capacity is C, and if we fill it to a height H, the necessary ex- 
 penditure of energy will be 
 
 CHxf, 
 
 the first, or left-hand factor, representing the whole quantity of 
 water necessary, and the second, or right-hand factor, the aver- 
 
44 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 age height through which this water has to be raised. In like 
 manner, it' we have an electrical conductor of capacity C, and 
 we wish to raise it to the potential or electrical level represented 
 by V, we must expend upon it a quantity of energy repre- 
 sented by 
 
 in which the left-hand factor denotes the whole quantity of 
 electricity required to perform this operation, and the right-hand 
 factor the average height above the earth-level, or zero, through 
 which it has to be raised against the action of electrical forces. 
 
 Our readers might like to know why we have used the letter 
 V to denote electric potential. It is in compliment to Volta, 
 the eminent electrician, V being the initial letter of his name. 
 In like manner C is the first letter of the word capacity, and H 
 the first letter of the word height. 
 
 18. Condensers. Sometimes the word condenser is used in- 
 stead of conductor when speaking of a metallic surface charged 
 with electricity. This word is used more especially to denote 
 an arrangement where we have two metallic plates near one 
 another, with a dielectric, such as air, glass, or ebonite, be- 
 tween. Thus the Leyden jar is a condenser, the internal 
 coating of which may be supposed to be at the potential of 
 the prime conductor of the electrical machine which charges 
 the jar, while the external coating is at zero potential, being 
 held in the hand during the process of charging, and thus 
 having the same electrical level as the earth. A condenser 
 may thus be said to consist of two metallic plates near each 
 other, with a dielectric between, these two plates being at 
 different potentials. It must not, however, be imagined that a 
 system of this kind is essentially different from that which 
 represents an insulated charged conductor. Here in reality we 
 have two conductors, just as truly as in a condensing system, 
 the outer conductor being the metal, human bodies, and other 
 conducting substances which surround the inner insulated con- 
 ductor, the air between acting the part of a dielectric. Hence, 
 if the insulated conductor be charged with a certain amount, 
 
I ELECTROSTATICS 45 
 
 say of positive electricity, we shall have on the surrounding 
 conductors, according to the experiment of Lesson IV., an equal 
 quantity of negative electricity. 
 
 l&a. Definition of Specific Inductive Capacity. The coeffi- 
 cient by which the capacity of an air condenser must be multi- 
 plied in order to represent its capacity when another dielectric 
 is used is called the specific inductive capacity of the 
 dielectric. 
 
 19. Discharge of a Condenser. When we discharge a condenser, 
 such as a Ley den jar, by bringing the opposite plates into com- 
 munication with each other, the energy of electrical separation 
 of the jar is converted into heat; and the amount of heat 
 produced will be represented by the energy that was expended 
 in charging the condenser, which is now discharged. This 
 energy will be, as we have already seen, 
 
 y ay* _(cvy 
 
 UVX 2~ 2 ~ 2C ' 
 
 where C is the capacity of the condenser and V the potential of 
 its inner surface, the outer surface being supposed to be at zero 
 potential. Now the quantity of electricity which has been put 
 into the condenser is CV, and hence we see from the above 
 formula that for the same condenser the heat produced by the 
 discharge will be proportional to the square of the quantity of 
 electricity which has been put into the condenser. 
 
 20. Exercises. 
 
 1. Describe the construction of a gold-leaf electroscope. 
 
 2. Why do the gold leaves of a charged electroscope diverge ? 
 
 3. How would you electrify a gold-leaf electroscope positively by 
 conduction, and how by induction ? 
 
 4. How would you electrify a gold-leaf electroscope negatively by 
 conduction, and how by induction ? 
 
 5. A gold-leaf electroscope is charged and an excited stick of sealing- 
 wax is brought down slowly towards its plate from a distance above. 
 At a certain point the gold leaves collapse, but when the stick is 
 brought still nearer they again diverge. Explain this behaviour. 
 
 6. A charged electrophorus with its lid on is placed on the top of a 
 gold-leaf electroscope. The lid is touched by the finger, when the 
 leaves of the electroscope will be found to diverge. Explain this. 
 
46 PRACTICAL PHYSICS FOR SCHOOLS OH. 
 
 7. An insulated tin can is charged and an insulated conductor is 
 introduced into the interior and there allowed to touch the can. When 
 taken out it is not electrified. Explain this. 
 
 8. An insulated tin can is charged and a conductor connected with 
 the earth is introduced into the interior, and there allowed to touch the 
 can. What will be the result, and how is this result to be explained ? 
 
 9. How many dynes represent the force with which the earth attracts 
 a one-pound weight ? 
 
 10. How many ergs go to represent one foot-pound of energy ? 
 
 11. An electrified point attracts another point oppositely and 
 equally electrified with the force of 8 '5 dynes when the two are 5 '3 
 centimetres apart. How many units of electricity are at one of these 
 points ? 
 
 12. A point is charged with 6 units of positive electricity and another 
 with 4 units of negative electricity, and the two are 7 centimetres apart. 
 With what force will they attract each other ? 
 
 13. A conductor of capacity 5 has been charged up to the potential 
 6. How much energy has been expended upon it in the process of 
 charging ? 
 
 LESSON VII Experiments on Potential with 
 Electroscope. 
 
 21. Apparatus. We shall in the lessons which follow 
 require a special electroscope, which may also be used as 
 a rough electrometer. Fig. 10 shows a form of this instru- 
 ment possessing the advantage of excellent insulation, and 
 of having its leaves protected from electrification of the 
 glass enclosure, a fault to which the electroscopes that 
 we have hitherto used are liable. The present instrument 
 consists of a glass cylinder, provided with a cork C that 
 supports an arm of glass rod gg\ bearing a small block 
 of ebonite e. Through a hole in e there passes a brass 
 wire w stiff enough to be adjustable. This wire bears at 
 one end the gold leaves, which are very narrow, and at the 
 other a small knob k In the cork C is a hole h, much 
 larger than the diameter of the brass wire. Thus w is 
 supported and insulated entirely by the glass rod and 
 ebonite block, and has no contact with the cork C. To 
 keep the glass stem dry, at the bottom of the cylinder there 
 is placed asbestos, a, moistened with strong sulphuric acid, 
 
(UIUVBIISITTJ 
 
 
 i ELECTROSTATICS 
 
 which is kept in place by a perforated leaden sheet /. 
 When the instrument is not in use a small cork S is made 
 to slide down w, and so as to stop the hole in the large 
 cork 
 
 fr 
 
 Fig. 10. GOLD-LEAF ELECTROMETER. 
 
 To shield as much as practicable the instrument from 
 external electrification, a cylinder n of copper wire-gauze, 
 open at the top and bottom, just fits within the electroscope. 
 (In the figure this is shown removed for the sake of clear- 
 ness.) A square window is cut in this gauze for the 
 observation of the leaves, and in order to observe their 
 distance apart a piece of mirror glass m with a scale ss' 
 attached is fastened to the gauze. To enable contact to 
 be made with the gauze a wire w' is provided. 
 
48 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 Note. Another form of the electrometer, made out of a tin canis- 
 ter, 1 is shown in Fig. 10a, which is lettered to correspond with 
 
 Fig. 10. The glass gg passes 
 through an india-rubber cork t. 
 The front of the can is a window 
 D, having cross bars of tinfoil. 
 At a is the asbestos within a 
 ^ e w ' leaden tray. 
 
 The remaining apparatus 
 required is an ebonite rod, 
 catskin, and a block of par- 
 affin. 
 
 Experiment I. Place the 
 electroscope on the paraffin 
 and connect w and w'. Now 
 electrify the knob. No 
 matter what charge is given 
 to this, the leaves will re- 
 main closed. 
 
 Explanation. ( 1 . ) Both 
 leaves and screen are at the 
 same potential, since they are 
 connected together. (2.) 
 Between bodies at the same 
 potential there is no electri- 
 cal force. 
 
 Experiment II. Discon- 
 nect w and w', and connect 
 the screen with the earth, 
 while we leave the knob 
 Fig.iOa.-Goi^L E A F EL E cTKOM ETE R. insulated and discharged. 
 
 Now charge w, the leaves diverge. 
 
 1 The tin canister corresponds to the screen of wire-gauze of Fig. 10. 
 It should be noted that in a theoretically perfect electroscope or electro- 
 meter the screen would wholly surround the leaves, which then would 
 be completely protected from external electrification. Seeing, how- 
 ever, that the instrument is often required to test external charges with 
 which a wire must communicate, such perfect protection is not possible. 
 
i ELECTROSTATICS 49 
 
 Explanation. We raise the potential of the knob and 
 therefore of the leaves by a certain amount above that of 
 the screen. 
 
 Experiment III. Now insulate the screen and charge 
 it by successive small charges of the same kind ; the leaves 
 gradually close. Continue to charge w' ; the leaves again 
 open. 
 
 Explanation. (1.) They collapse, because the series of 
 small charges has brought the potential of the screen equal 
 to that of the leaves. (2.) They open again, because the 
 potential of the screen has been increased, so that now 
 there is a difference between it and the leaves. 
 
 The preceding experiments will have taught the student 
 the true meaning of the indications of the electroscope. 
 
 LESSON VIlA. The Condenser. 
 
 21 a. Apparatus. A well-insulated plate condenser will 
 be requisite. One form is shown in Fig. 1 1 . Here A and 
 B are two brass plates, with rounded edges, supported 
 from glass stems y and y' by means of metal collars b and b'. 
 These stems are kept dry by being surrounded by glass 
 cylinders g and g', containing asbestos and sulphuric acid 
 at a and a'. A block of lead L with a central hole serves 
 to support the glass stem y', which passes through a hole h 
 (but without touching) in the cork C. Two corks 5 and s' 
 keep out dust when the instrument is in use, otherwise 
 they are raised so as to be free from the cylinders. 
 
 Note. In a later and better form of the instrument the plates A 
 and B are vertical and supported on wooden bases. The glass stems 
 are kept dry by asbestos and sulphuric acid contained in annular leaden 
 cups surrounded by glass tubes. This form has the advantage that 
 the plates may be slid any distance apart, whereas in Fig. 11 the 
 upper plate A must either be separately supported, or pieces of ebonite 
 must be used to keep the plates apart. One advantage of the form 
 (Fig. 11) is that the horizontal plate B forms an excellent insulating 
 stand. 
 
 VOL. I E 
 
50 
 
 PKACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 Two gold-leaf electroscopes, which had better be of the 
 type last described. Ebonite rod and fur. Glass rod and 
 silk. Block of paraffin. 
 
 Experiment I. Put the plates nearly in contact, and 
 connect A with the cage and B with the knob (Fig. 11 a) 
 of the electroscope, which should be insulated on a block 
 
 Fig. llo. 
 
 Fig. 11. THE CONDENSER. 
 
 of paraffin. Give a + charge to A until the leaves open 
 a little. Now separate A and B, when the leaves will 
 open more and more widely the farther the plates are 
 asunder. 
 
 Explanation. B, an insulated body within the field of 
 force of A, is at a positive potential. A proof of this will 
 appear from the fact that if B be connected with the earth 
 positive electricity will flow from it to the earth (see next 
 experiment). Also the positive potential of B is greater 
 
ELECTEOSTATICS 
 
 51 
 
 the nearer it is to A, and the potential of A decreases with 
 the approach of B, and hence the difference of potential be- 
 tween A and B increases the farther that they are separated. 
 
 Notes (1.) On B there is both - E and + E, but the whole plate B 
 is nevertheless of one potential. 
 
 (2.) The arrangement A and B is a condenser whose capacity 
 becomes less as A and B are separated. Now the relation Q (quantity 
 of electricity) = CV (see Art. 17) must be fulfilled, and since Q is con- 
 stant, V (the difference of potential between A and B) must increase 
 as they are separated. 
 
 Experiment II. Use two electroscopes, and make the 
 connections of Fig. lib. Give A a + charge. B will be 
 found to have a + potential. 
 
 Explanation. A is of a + potential, B, a body in its 
 field, is likewise of a smaller yet + potential (see Art. 15). 
 
 Experiment III. Touch B so as to connect it with the 
 
 Fig. lie. 
 
 Fig. 116. 
 
 no 
 
 earth. The electroscope, connected with B, shows 
 charge, and that connected with A is deflected less. 
 
 Explanation. The condition of things is as shown in 
 
52 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 Fig. lie. A has a + charge and B a - charge. The charge 
 of B under these conditions is said to be "bound." It 
 cannot leave B, inasmuch as it is at zero potential. But 
 the presence of B in this condition lowers the potential 
 of A. 
 
 Experiment IV. Let B be still earth -connected, and 
 approach it nearer A ; the electroscope of A now shows 
 a diminished deflection. Eemove it farther from A, the 
 deflection increases. 
 
 Explanation. This is left as an exercise. 
 
 LESSON VIlB. Comparison of Condensers by 
 Cavendish's Method 1 Specific Inductive Capacity. 
 
 216. Apparatus. The insulated condensers of Lesson 
 VIlA. Gold-leaf electrometer. Electrophorus. Ebonite in- 
 sulating supports. Two cylindrical condensers, each consist- 
 ing of a tin can within an outer can, from which it is 
 insulated. The interspace in the case of one of the cans 
 is filled with paraffin. Graduated scale for measuring the 
 distance apart of the condenser plates. Block of paraffin 
 for insulation. 
 
 MetJwd and Theory. It will be necessary for two students 
 to work together in order that the connections may be 
 made and broken without the use of pulleys, etc., as em- 
 ployed by Cavendish. The operations are : 
 
 1st, Make connections as in Fig. 12, where A and B 
 are the condenser plates, C and D the inner and outer cans 
 of the cylindrical condenser, a and 5 ebonite rods for hold- 
 ing the connecting wires. Give to A several sparks by 
 means of the electrophorus. Now since there exists the 
 same difference of potential (V) between the coats of the 
 
 1 The student is referred to The Electrical Researches of the Honour- 
 able Henry Cavendish, F.JR.S. Edited by J. Clerk Maxwell. This 
 interesting record of important scientific work, done with crude appar- 
 atus, should find a place in every scientific library. 
 
ELECTROSTATICS 
 
 53 
 
 two condensers, if we call K the capacity of the plate con- 
 denser and K' that of the cylindrical condenser, then the 
 
 S A 
 
 *a BE 
 
 H 
 
 Fig. 12. 
 
 amount of electricity (Q and Q') with which each condenser 
 is respectively charged is 
 
 ' = K'V. 
 
 2nd, Now alter the connections to those of Fig. 120. 
 
 Fig. 12a. 
 
 What will then happen? The quantity of electricity Q 
 will mix with that on C, which is of quantity Q' but of 
 
54 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 opposite sign to that on A. If + Q = - Q' the neutralisa- 
 tion will be complete, and on bringing an electroscope, by 
 means of an insulating rod c, to touch the wire connecting 
 A and C, there then should be no residual charge. Sup- 
 posing that a charge is obtained, then the condenser AB 
 is of less capacity than CD. 
 
 3rd, Lessen the distance between A and B, and repeat 
 the operations until the residual charge becomes zero, 
 in which case the condensers are of equal capacity. 
 Measure the distance between A and B. 
 
 4th, Substitute for CD the other cylindrical condenser 
 mentioned above, containing paraffin, and again adjust 
 the plate condenser, and measure the distance apart of A 
 and B. 
 
 If we divide the distance apart of the plates in the 
 first case by that in the case where the cylindrical con- 
 denser contained paraffin, the result will denote the ratio 
 of the capacities of the two cylindrical condensers, and 
 the same number will be the specific inductive capacity 
 of paraffin. 
 
 Note. We have assumed that the distance apart of the plates is 
 inversely proportional to the capacity of the condenser. This is not 
 strictly the case, but if the distance apart is not great, it is suffici- 
 ently true for our experiments. 
 
 Example. Source of charge one spark from large elec- 
 trophorus. 
 
 CYLINDRICAL CONDENSER WITH PARAFFIN. 
 
 Distance apart of Plates. Reading of Electrometer. Result. 
 
 12-5 mm. -50 Plates least. 
 
 10 , .30 
 
 7-5 , -20 
 
 J i -16 
 
 3 , +2 ,, greatest. 
 
 2-5 , +10 
 
 Capacity = that of plates 3 mm. apart nearly. 
 
ELECTROSTATICS 55 
 
 CYLINDKJCAL CONDENSER WITH AIE. 
 
 15 mm. - 40 Plates least. 
 
 12-5 -25 
 
 7'5 -14 
 
 5 +12 ,, greatest. 
 
 6 +1 
 Capacity = that of plates 6 mm. apart nearly. 
 
 Hence, specific inductive capacity of paraffin 
 
 LESSON VIIc. Comparison of Conducting Powers 
 of Oils. 
 
 21c. Apparatus. Condenser. Gold-leaf electrometer. 
 An ebonite cup to hold oils, provided with two binding 
 screws. Electrophorus. 
 
 Method. When a charged condenser has its plates 
 connected through a bad conductor, the condenser slowly 
 discharges itself. If an electrometer be connected with 
 the condenser, and the times observed that the condenser, 
 with different bad conductors, takes to fall from a given 
 potential to a lower given potential, then their conducting 
 powers will be in the inverse ratio of the observed times. 1 
 
 The requisite connections are shown in Fig. 12 for the 
 experiment, which requires two observers. The plates 
 A and B of the condenser are placed very near together. 
 The cup of ebonite e at first must be empty. A charge is 
 given to A, and then one observer watches the leaves of 
 the electrometer, his eye being in such a position that their 
 reflected images are covered by the leaves. (This is neces- 
 sary in order to avoid the error called parallax.) When 
 the deflection reaches a certain amount, the electrometer 
 observer makes a sharp tap on the table, and the second 
 observer notes down the time to a second. The first 
 
 1 For the complete formula see Elementary Practical Physics, vol. 
 ii. p. 438. 
 
56 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. I 
 
 observer continues to watch the leaves, and when the 
 deflection reaches about half the first value a second time- 
 signal is made, and the second observer will now know the 
 time that the condenser has taken to leak from the higher 
 to the lower potential. If the period is a long one, it 
 
 Fig. 12b. 
 
 shows that the insulation of the apparatus is satisfactory, 
 and the cup may be filled with oil. On repeating the 
 experiment the leakage will be found much greater, so 
 great, in fact, that the leakage without oil in the same 
 time may be considered quite negligible. In the same way 
 various oils should be tested. 
 
 Example. Leakage from 40 to 20 divisions. 
 
 Olive Oil. 
 15 seconds. 
 15 
 61 
 15 
 15 
 14 
 
 No. of Experiment. Paraffin Oil. 
 
 1 
 
 32 seconds. 
 
 2 
 
 35 
 
 3 
 
 30 
 
 1 
 
 4 
 
 38 
 
 
 5 
 
 33 
 
 j 
 
 6 
 
 33 
 
 
 Mean, 33 '5 seconds. Mean, 15 seconds. 
 
 Hence 
 
 Conducting power of olive oil _33'5 _ 9 . 9 
 Conducting power of paraffin oil ~~ 15 
 
CHAPTEK II. 
 
 MAGNETISM. 
 
 22. A MAGNET, for the purpose of this work, may be 
 considered to be a piece of steel or iron that is cap- 
 able of attracting steel or iron. Every magnet has two 
 poles, where the magnetism appears strongest. The line 
 joining these is called the magnetic axis. A freely-sus- 
 pended magnet balanced so as to swing horizontally sets 
 itself in such a manner that its axis will lie in a direction 
 known as the magnetic meridian. This direction makes, 
 at a given place and time, a definite and generally small 
 angle with the geographical meridian. With refer- 
 ence to this position assumed by the magnet, that pole 
 which points nearly north is generally called the north 
 pole, and that which points nearly south the south pole ; 
 but other names have been given to these poles, as will be 
 seen from the following table : 
 
 
 TABLE C. 
 
 
 NAMES OF POLES. 
 
 Pole that points 
 to the North, or 
 North-seeking. 
 
 Pole that points 
 to the South, or 
 South-seeking. 
 
 North 
 Austral 
 Marked 
 Red 
 True South 
 Positive ( + ) 
 
 South 
 Boreal 
 Unmarked . 
 Blue . 
 True North 
 Negative C ) . 
 
 Ordinary usage. 
 
 French usage. 
 
 Faraday. 
 
 Sir G. Airy. 
 
 Sir Wm. Thomson. 
 
 Mathematical usage. 
 
58 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 We shall in this volume use the letter N or the sign -t- 
 to denote the north-seeking, and the letter S or the sign 
 to denote the south-seeking pole of the magnet. 
 
 LESSON VIII. Fundamental Experiments. 
 
 23. Apparatus. Bar and horse-shoe magnets with their 
 poles marked, some thin knitting needles, pieces of watch- 
 spring, soft iron nails, silk fibre, test tubes with corks, 
 blowpipe, Bunsen's burner, sealing-wax varnish, steel filings, 
 a bar of very soft iron, No. 20 iron wire, a strip of tinned 
 iron, various specimens of steel and iron, and two binding 
 screws. 
 
 First fit up a delicate instrument for indicating the 
 presence of magnets and magnetic bodies. We shall call 
 this instrument the magnetoscope. Let 
 us first heat a piece of watch-spring in 
 the blowpipe flame to bright redness, 
 and then plunge it quickly into a 
 beaker of cold water. The watch- 
 spring will now be found to be hard 
 and brittle. Next break off a piece 
 a little shorter than the breadth of the 
 test tube, and then proceed to mag- 
 netise it by rubbing it always in the 
 same direction on one of the poles of 
 the bar magnet. Fit into the open 
 end of the test tube a cork provided 
 with a glass tube terminating in a 
 crook, as shown in Fig. 1 3. 1 Now pro- 
 ceed to attach a very fine silk fibre to 
 the small piece of magnetised watch- 
 spring, which may be done with the 
 help of a little beeswax. The magnet should hang horizon- 
 tally when suspended by the silk fibre. In order to secure 
 1 Instead of a test tube a bottle may be used. 
 
 Fig. 13. 
 THE MAONETOSCOPE. 
 
ii MAGNETISM 59 
 
 this position a little sealing-wax varnish may be put on one 
 end the varnish serving the double purpose of perfecting 
 the horizontality of the magnet and of distinguishing the 
 one end from the other. Attach the other end of the fibre 
 to the glass hook, and place the suspended system in the 
 test tube. The test tube may be supported by a large cork, 
 through which a hole has been bored to admit the end of 
 the tube. 
 
 With the aid of this instrument and the above materials 
 let the student perform the following experiments : 
 
 Experiment I. Show that like poles repel and unlike 
 poles attract each other the north pole of the experi- 
 mental magnet being that end which points to the north. 
 
 Experiment II. Magnetise a piece of the brittle watch- 
 spring by drawing it across the N. pole of a magnet. 
 Notice that the end of the piece of watch-spring which last 
 leaves the pole of the magnet is a S. pole. Show that 
 when broken into two parts each portion of this remains 
 a perfect magnet. Show also that however often the pro- 
 cess of breaking is repeated, the above result will ensue, 
 each portion remaining a perfect magnet. 
 
 Experiment III. Show that a test tube filled with 
 filings or turnings of hard steel may be magnetised just as 
 if it were a steel bar. Then show that if the turnings are 
 taken out, mixed together, and replaced, they are no longer 
 a magnet. To magnetise the filings a strong magnet 
 should be used. 
 
 Experiment IV. Anneal a piece of soft iron wire by 
 heating it to redness and allowing it to cool slowly, then 
 show that this wire attracts both ends of the magnet. A 
 body which attracts loth ends of the magnet is said to be 
 a magnetic body. 
 
 Experiment V. Attempt to magnetise the soft iron wire 
 by drawing it across the pole of a magnet ; when withdrawn 
 it will be found that at the most only a very feeble magnet 
 is produced. 
 
60 PRACTICAL PHYSICS FOR SCHOOLS en. 
 
 Experiment VL Show, however, that while the soft 
 iron remains in contact with or near the pole of the magnet 
 the former becomes temporarily a magnet, being capable 
 of attracting iron filings. Show also that the portion of 
 the soft iron in contact with, say, the N. pole possesses a 
 S. magnetism, and that portion of it farthest from the 
 magnetic pole a N magnetism. To verify this use a small 
 test needle (A or B, Fig. 14), which you convert into a 
 magnet by rubbing it first on the end n, so that the point 
 of the needle leaves this end last. Then, according to 
 Experiment II., if the bar of soft iron has its poles as 
 marked in the figure, the needle, when drawn across the 
 
 Fig. 14. 
 
 end n from position A to B, will have its point exhibiting 
 south polarity. This is called magnetisation by induction. 
 
 Experiment VII. Magnetise a piece of watch-spring. 
 Wind a piece of wire round it so that the watch-spring 
 may be held in the blowpipe flame, where it should be 
 heated to a bright redness. The piece of watch-spring 
 if tested when cold will be found to be no longer a 
 magnet. 
 
 Experiment VIII. Hold a bar of soft iron in a vertical 
 position and smartly tap the upper end with a hammer. 
 Whilst still vertical test the bar, when it will be found to 
 be a magnet, the lower end being the north-seeking pole. 
 Reverse the bar and repeat the experiment, the polarity 
 will be found to be reversed, the now lower end of the 
 magnet being still the north pole. Here the bar becomes 
 
ii MAGNETISM 61 
 
 magnetised by the inductive action of the earth, which acts 
 like a large magnet. 
 
 Experiment IX. Instead of a bar of soft iron take a long 
 and somewhat wide slip of ordinary tinned iron, and plac- 
 ing it vertical as in the last experiment, bend it back- 
 wards and forwards, causing the iron to make a noise. It 
 will now be a magnet, the lower end being the north pole. 
 If carried gently away and applied to the magnetoscope, it 
 will probably be found to have retained its magnetised state ; 
 but if once more mechanically disturbed when horizontal and 
 pointing east and west it will be found to be no longer a 
 magnet, being now devoid of all polarity. In this state it 
 will of course attract equally both poles of the suspended 
 needle. 
 
 Experiment X. Obtain a large knitting needle and 
 clamp it firmly at the ends by the brass binding screws. 
 Violently twist the wire when in the close neighbourhood 
 of a magnet. The knitting needle will be found to have 
 become permanently magnetised. 
 
 From these experiments we may learn various things. 
 
 In the first place we see that the difference between 
 hard and soft iron consists in this, that the former is cap- 
 able of retaining its magnetised condition when withdrawn 
 from the exciting cause, while, however, the latter is un- 
 able to do so, losing all or nearly all its magnetism when 
 withdrawn. 
 
 Now a body which, owing to molecular rigidity, does 
 not readily lose its magnetisation is, from the same cause, 
 less susceptible of acquiring this condition. To increase 
 its susceptibility in this respect we promote a certain 
 molecular freedom, either by heat or mechanical disturbance, 
 while the body lies in a position favourable to magnetic 
 influence. The magnetisation is thus allowed to enter, 
 and when entered is kept there, for when the body is 
 cooled, or when the mechanical disturbance has ceased, the 
 particles are once more in a rigid state. A kind of trap is 
 
62 PRACTICAL PHYSICS FOE SCHOOLS CH. 
 
 thus laid for the magnetisation, this being invited to enter 
 through an open door, which is immediately shut, so that 
 the guest is converted into a prisoner. This property of 
 hard iron is called coercive force, and from Exps. VIII. and 
 IX. we may gather that soft iron is not entirely devoid of 
 this property, possessing it, however, to a very much smaller 
 extent than hard iron. 
 
 LESSON IX. The Magnetic Field. 
 
 24. Exercise. To obtain and fix magnetic curves. 
 
 Apparatus. Bar and horse-shoe magnets, pieces of soft 
 iron, a piece of ferrotype iron, a paraffin bath, sheets of 
 thin writing paper, iron filings, a piece of fine muslin, and 
 an old saw or sheet of steel. 
 
 Method I. Melt the paraffin wax in the bath, and soak 
 in it a sheet of writing paper. Lift the paper out of the 
 bath by one corner and allow the melted paraffin to drain 
 off. Suspend the paper by one corner until the paraffin 
 has set hard. Coat several sheets in this way. Now place 
 closely over a horizontal bar magnet a sheet of the pre- 
 pared paper, which should be supported so that the surface 
 is level by means of pieces of wood. Scatter through the 
 fine muslin iron filings over the paper from about a foot 
 above it. Tap the paper until the filings set themselves 
 along lines which are called magnetic curves. Next pass the 
 flame of a Bunsen's burner over the paraffin paper so as to 
 melt the paraffin, when the filings will sink into the melted 
 wax. On removing the flame the paraffin will soon solidify, 
 and the filings will be retained permanently in the posi- 
 tion which they occupied before melting that is to 
 say, ranged along magnetic curves. These curves may 
 best be studied by holding the preparations up against 
 the light, when the forms assumed by the particles of iron 
 will be distinctly seen, owing to the translucency of the 
 paper. 
 
ii MAGNETISM 63 
 
 Let the student thus obtain the following curves : 
 
 (a) Curves from simple bar magnet. 
 
 (b) horse-shoe magnet. 
 
 (c) ,,2 bar magnets with like poles to- 
 
 gether. 
 
 (d) ,,2 bar magnets with unlike poles to- 
 
 gether. 
 
 (e) ,, bar magnet with a piece of soft iron 
 
 in its field. 
 
 (/) bar magnet near a thin disc of iron. 
 
 (g) end of bar magnet 
 
 It will thus be seen what is meant by the magnetic 
 field. This expression merely denotes that space all round 
 a magnet through which it is capable of exercising an influence 
 upon soft iron or other magnets. The magnetic curves into 
 which the magnetic field may be mapped out represent, in 
 the first place, ropes or chains more or less continuous, into 
 which the iron filings arrange themselves when they are 
 rendered free to turn by the influence of tapping. Had 
 we used instead of iron filings a series of very small needles 
 free to move, these would have similarly arranged them- 
 selves along the magnetic curves, and the direction of the 
 force acting on any one such needle would be along the 
 tangent to the curve at that point. The needle would, in 
 fact, place itself so that this force would pass along its axis, 
 that is, it would constitute itself a tangent to the curve 
 or be a virtual portion of the curve. A magnetic curve 
 is therefore a line or path such that if we walk along it 
 with a little needle in our hand this needle will always 
 point along the path. 
 
 II. A magnet has not always its magnetism symmetri- 
 cally distributed along its length. To prove this, let us ob- 
 tain a long knitting needle, then, starting at a point J of 
 the whole length from one end, let us draw the N. pole of 
 a magnet several times towards this end. Next, with the 
 
64 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 same pole of the. magnet, and starting from the same point, 
 let us perform the same process towards the other end. In 
 this way consequent points or poles will be produced. These 
 will be revealed when we obtain magnetic curves from such 
 a magnet by the process indicated above. Such a peculiar 
 disposition of magnetism is generally, however, a source of 
 trouble, and our object is to avoid it rather than court its 
 production. 
 
 ///. Using as a pencil one pole of a strong magnet, draw 
 a pattern upon a thin steel plate, such as the blade of a 
 saw, going over the pattern several times. If we then 
 obtain magnetic curves, these may possibly be found to 
 be very complicated. Such figures are known as Haldafs 
 Figures. 
 
 Exercises. (1.) Describe the features of the magnetic 
 curves that you have obtained. (2.) Define magnetic field 
 and consequent points. 
 
 LESSON X. The Magnetic Meridian. 
 
 25. Apparatus. A mariner's compass provided with 
 sights, or the materials for making one. 
 
 Method of making a Mariner's Compass Materials. (1.) Square 
 wooden box 1 about 6 cm. square and 3 cm. deep. (2.) Cardboard. 
 (3.) Glass tubing. (4.) Mathematical drawing instruments. (5.) 
 Sewing needles. (6. ) Stocking needle. (7.) A cement, such as Canada 
 balsam, dissolved in benzine or coaguline. (8.) Corks. 
 
 Operations. (1. ) Cut out a square piece of card so as just to fit the 
 box. Draw on it a dial (see Fig. 15) with the thirty- two points of the 
 compass. Cut out the shaded portion, dividing the dial into a central 
 disc that will form the movable compass card, and an outer portion 
 that will form the fixed index ring. The latter has marked upon it 
 two index arrows, as shown. (2.) Make a glass cap upon which 
 to balance the compass card. To do this draw out a piece of glass 
 tubing (Fig. 16), close up the end by fusion, and cut off the tip of 
 
 1 Boxes of varying size are now made for ordinary post or parcel 
 post purposes. They are extremely convenient for the manufacture of 
 apparatus. 
 
IT MAGNETISM 65 
 
 the tube at ab. This forms the cap of the compass card, and must 
 be inserted in a hole in the centre of the card. (3.) Make four magnets, 
 each 4 cm. long, out of a knitting needle. Fix, by cement, two on 
 either side of the cap, on the back of the compass card, with their axes 
 lying parallel to the NS line (Fig. 17), with the like poles pointing 
 in the same direction. To help in doing this accurately prick two 
 
 Fig. 15. 
 
 holes through the NS line, and draw a line joining them on the 
 back of the card. Support the card on the point of a vertically- 
 placed sewing needle, to test if it is balanced. If not, move the 
 magnets until the card is balanced, taking care to keep the magnets 
 parallel to the NS line. (4.) Fasten a slice of cork by cement to the 
 centre of the bottom of the compass box, arid fit upright 011 it a piece 
 of sewing needle. (5.) Fix slices of cork or pieces of wood inside the 
 box for supporting the fixed index ring, which must be fastened by 
 VOL. I F 
 
PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 cement. (6.) Bore two holes near the top of the box at the middle of 
 the opposite sides, through which two short glass or brass tubes t and 
 t' (Fig. 18) must be passed. (7. ) Place two fine needles nn' (Fig. 15) 
 upright on the NS line, and near its ends. These form the sight needles. 
 
 Fig. 16. 
 
 Fig. r, 
 
 To mark down the Position of the Magnetic Meridian on the 
 Table. Look through one of the sight tubes and turn the 
 compass box until the sight needles can be seen in the 
 
 Fig. 18. FINDING MERIDIAN. 
 
 middle of the tubes. Now support a piece of cardboard 
 by a cork, and make upon it a black vertical line. Move 
 this about until the line lies in the magnetic meridian, that 
 is to say, on looking through the sight tube the black line / 
 
II 
 
 MAGNETISM 
 
 67 
 
 (see Fig. 1 8) lies in the prolongation of the line joining the 
 index needles. Make a mark on the table at the base of 
 the vertical line, which we shall suppose to be at a (Fig. 19). 
 Now move the cardboard back, and obtain a new position 
 at b. The line joining a and b will be in the meridian. 
 
 P \K 
 
 Fig. 19. 
 
 This line should be marked permanently on the table 
 for future reference. 
 
 To find the earing of an Object in the Room. Turn the 
 compass until through the sight tubes the object whose 
 bearing is required can be seen, then the reading of the 
 compass card opposite the fixed mark a (Fig. 20) will be 
 the bearing required. 
 
 Example. Suppose the object to be north-east, then 
 the position of the compass box would be as in B (Fig. 20). 
 
 B. 
 
 Fig. 20. 
 
 To mark down the Geographical Meridian on the Table. 
 Draw a line on the table, making an angle of 20 east of 
 
68 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 the line representing the magnetic meridian. This will 
 very nearly give the geographical meridian. The angle that 
 the one meridian makes with the other is called the magnetic 
 declination. 
 
 To verify the Geographical Meridian. Place a stick up- 
 right when the sun is shining, and note the position of the 
 shadow when this is shortest. 1 The shadow of the stick 
 should now coincide with your geographical meridian line. 
 
 To illustrate the use of the Compass for finding the direction 
 in which a ship is sailing. A compass is fixed on board 
 ship with the line joining a and a' lying fore and aft. 
 Hence, when the ship is travelling due north, as in A, Fig. 
 20, the N of the card lies opposite a. But if the ship is 
 travelling north-east, as in B, Fig. 20, the NE of the card 
 will be opposite a. Thus all that is necessary is to observe 
 the point of the card that is opposite a. 
 
 LESSON XI. The Law of Inverse Squares. 
 
 26. Apparatus. Mathematical drawing instruments, 
 drawing board, etc. A very small compass needle mounted 
 on a pivot and a long thin bar magnet. 
 
 Application of the Law of In- 
 verse Squares. We should find the 
 
 I problem of calculating what action 
 
 one magnet has upon another an 
 exceedingly difficult one if we were 
 not allowed to assume that the 
 magnetism acted as if it were con- 
 centrated at the ends of the mag- 
 ^^^^^^^^^^^_ ne t- Let us agree that this as- 
 N N' g" sumption may be made, at least 
 
 Fig 21. with long and thin magnets, and 
 
 let us consider two such magnets 
 NS and N'S' (Fig. 21), so placed that the S and S' poles 
 
 1 Or use a sundial at noon. 
 
ii MAGNETISM 69 
 
 are sufficiently distant to make their action negligible. 
 The force of repulsion between N and N' will depend 
 upon two things : 
 
 (1.) The strength of each of the poles. 
 (2.) The distance of the poles apart. 
 
 The exact law can be best written down in symbols as 
 follows : 
 
 FUNDAMENTAL LAW. 
 
 If f and f be the magnetic strengths of two 
 poles, and d the distance between them, then the 
 whole force P of mutual repulsion or attraction 
 will be 
 
 the upper sign being used when there is repulsion 
 and the lower sign when there is attraction. 
 
 It is of the very first importance that the reader should 
 grasp the meaning of this fundamental law. We shall give 
 a numerical example of its use. 
 
 Example. Let the strength of one pole be + 8 units 
 and the strength of a second pole be -20, or, in other 
 words, let one be a N pole of strength 8 and the other a S 
 pole of strength 20. Suppose that the poles are 2 units of 
 distance apart, and that we are required to determine the 
 force of attraction or repulsion. Here 
 
 r = ( + 8)x 2 (-20) = 160 = 1Q? 
 
 and the force is an attractive one of 40 units. 
 
 Application of Fundamental Law. The above law supplies 
 the key to explain the magnetic curves. Let the student 
 draw a line NS (Fig. 22) representing the long and thin 
 magnet, and consider the position that a small magnet ns 
 would assume when placed in the field of the magnet at 
 
70 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 the point 0. Now the poles of the little magnet would be 
 acted upon by four forces : 
 
 C 
 
 Fig. 22. 
 
 OA=The attractive force of N upon s, the south pole of the little 
 
 magnet. 
 
 OB =The repulsive force of S upon s. 
 OC =The repulsive force of N upon n, the north pole of the little 
 
 magnet. 
 OD = The attractive force of S upon n. 
 
 To find the lengths of the lines representing these 
 forces we must use our fundamental law. Suppose that 
 the strength of the pole N is + 100 units and that the 
 strength of the pole S is - 100 units, whilst that of n is + 2 
 and that of s - 2 units. We shall further make the assump- 
 
ii MAGNETISM 71 
 
 tions that the little magnet is so small that the distance 
 between its poles need not be considered, and further that 
 ON is 3 and OS 5 units long. The fundamental law 
 
 then gives : 
 
 + 100x -2_ 200 
 
 V A ^~i ;r- " 
 
 _ +100 x +2 200 
 
 3*- f ~9" 
 
 -100x+2_ 200 
 
 ~~&~ ~~25' 
 
 The lengths of OA ; OB, 00, and OD are therefore known. 
 It is quite immaterial what lengths we give to these lines 
 providing that the correct ratio is observed. Now 
 
 Hence OA must be made 25 and OB 9 units long. 
 
 Complete the parallelogram AOEB and draw the diagonal 
 OE, which will represent in magnitude and direction the 
 resultant force. In a similar manner we can find OF, which 
 is equal and opposite to OE. The small magnet at will 
 therefore be in equilibrium, and have no tendency to leave 
 its position. It will, however, set itself along the line OF. 
 The line OF will be a tangent to the magnetic curve or line of 
 force passing through 0. 
 
 Exercises. Follow out the same method of construction 
 to find the position which a small magnet would assume 
 when placed as follows : 
 
 (1.) Above the middle of NS. 
 
 (2.) Vertically over N. 
 
 (3.) On a line which is a prolongation of NS. 
 
 Experimental Verification. In the above investigation 
 we have assumed that 
 
72 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 (1.) The poles were at the end of the long magnet. 
 
 (2.) Its length was great compared with the small 
 magnet. 
 
 (3.) No other forces were acting except those between 
 the two magnets. 
 
 In practice we must therefore take care to secure ap- 
 proximately the first two conditions. The third it would 
 be difficult to secure, for we cannot very well eliminate the 
 action of the earth. But we may proceed as follows : 
 
 Place the small compass needle at and turn the 
 drawing board until the compass needle lies along EF. It 
 will then be at rest under the action of the earth alone. 
 Now place the long magnet at NS, when the needle should 
 still point along EF if the theory is correct. Repeat the 
 process at the other positions. What is done here is to 
 make the direction of the little compass needle at each 
 point coincide with the magnetic meridian, in which case 
 the earth's action does not affect the conditions of equi- 
 librium. 
 
 27. Lines of Force. The curious curves exhibited by iron filings 
 will prepare the student to understand what is meant by lines of force. 
 Lines of force may be regarded as graphical representations of the 
 action of force. A unit of mass or pound may be regarded as falling 
 to the earth very much as if the mass had a string attached to it 
 which an operator at the earth's centre was always pulling with a 
 constant force. Now this mental image of strings as representing the 
 action of terrestrial gravity is capable of advantageous extension. 
 
 We may, for instance, suppose that a very great but yet strictly 
 constant number of such strings passes from the earth's centre to points 
 symmetrically disposed along the earth's surface ; these points being 
 likewise very close together, and that the well-known phenomena of 
 weight are due to such strings (see Fig. 23). 
 
 Now what will happen on this hypothesis if we go to a surface ten 
 times as far from the earth's centre as is our present abode? "Will these 
 strings, or an ideal continuation of them, still represent the action of 
 the earth upon a unit of mass placed at this increased distance from 
 its centre ? Let us see whether or not this will be the case. First con- 
 sider the surface of the earth where we live, and let us suppose that 
 terrestrial gravity acting on unit of mass is really due to a very great 
 but strictly constant number of such strings, each giving the same pull 
 and symmetrically spread over the earth's surface. 
 
ii MAGNETISM 73 
 
 Now at the increased distance, ten times farther off from the earth's 
 centre, if the mental image is to hold good, we can only have the same 
 number of strings that we have here. But these strings, or a continu- 
 ation of them, will now be spread over a surface having a hundred 
 times the area of the earth's surface, so that the number of such strings 
 that will pass through one unit of mass will be a hundred times smaller 
 
 Fig. 23. 
 
 at the increased distance. If, therefore, the analogy is still to hold 
 good, the force at this increased distance must as a matter of fact be 
 diminished likewise in this proportion. Now this is precisely what 
 astronomers find to be the case, for they have proved that the force 
 of gravity varies inversely as the square of the distance, so that (as 
 we have already mentioned in Art. 12) the force at this increased 
 distance will be 10 2 or 100 times less than at the earth's sur- 
 face. It thus appears that at these two distances, and in fine at every 
 distance, the earth's force upon a pound of matter may be regarded as 
 proportional to the number of lines or strings of force which pass 
 through the substance. And it is likewise obvious that when such 
 lines of force are very close together, this denotes a region where the 
 force is very strong, and that when such lines are very far apart this 
 denotes a region where the force is very weak. 
 
 In the above instance, if a small stone be dropped towards the earth 
 it will proceed along one of these lines of force and in a straight line. 
 
74 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 But in the case of a magnet the lines of force are, as we have seen, 
 curved and not straight, and the force which such a magnet will exert 
 upon an exceedingly small compass needle will be directive merely ; 
 that is to say, the small compass needle will not be carried bodily 
 along the line of force which passes through it, but merely made to 
 point so that its length will lie along the line, the one pole being as 
 much attracted as the other is repelled. 
 
 LESSON XII. The Earth's Magnetic Action. 
 
 28. Apparatus. Sewing needle, magnet, vessel of water, 
 mathematical instruments, etc. 
 
 The Earth's Force Directive only. Magnetise the sewing 
 needle, and carefully place the dry needle upon the water 
 in a horizontal position. It will now float, and may be 
 moved about on the surface of the water by means of a 
 magnet. If it is deflected out of the magnetic meridian, 
 it will return to this meridian, with its N pole pointing 
 north, provided there is no magnet near ; but will show no 
 tendency to move as a whole towards the north or south pole 
 of the earth. In other words, the action of the earth is 
 directive only. 
 
 To explain why this should be we must refer to Lesson 
 XI., where we found that a small magnet placed in the 
 field of a large one is under the action of two equal and 
 opposite forces, which can only produce rotation. Thus 
 (Fig. 24), suppose that nOs is a compass needle that is 
 displaced from the meridian MR, so as to make an angle 
 a with this meridian ; it will be acted upon by the equal 
 and opposite forces called the terrestrial magnetic couple, 
 which tend to bring the magnet into the meridian. 
 
 Now as we know nothing about the strength of the 
 earth's poles, or the distance of them from the needle, we 
 shall express the force acting on the n pole of strength / by 
 
 +/H, 
 
 where H is defined to be horizontal component of the earth's 
 magnetic force. 
 
MAGNETISM 
 
 75 
 
 In like manner the force acting on the s pole is 
 -/H. 
 
 These, then, are the two forces constituting the terres- 
 trial magnetic couple. 
 
 The student who is not familiar with trigonometry 
 must now be made acquainted with the meaning of the 
 term sine. Draw the triangle ABC (Fig. 25) with a right 
 angle BOA. 
 
 Let the angle BAC =a 
 
 BC, the side opposite to a . . =o 
 
 AC ,, adjacent to a . . a, 
 
 AB, or the hypothenuse . . . =7t 
 
 Measure o, a, and h. Then the sine of the angle a is 
 
76 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 equal to the ratio of the opposite side o to the hypothenuse 
 h, or, briefly, Q 
 
 sin a = T . 
 n 
 
 Example. Suppose = 8 and 
 h = 1 2, then sin a = ^ = -6. 
 
 We shall presently have to 
 use two other relations, namely, 
 the cosine and tangent. 
 
 cosine a (abbreviated to cos a) = r, 
 tangent a ( 
 
 tan a) = -. 
 
 For the purpose of finding 
 the angle corresponding to a 
 given sine, cosine, or tangent, 
 mathematical tables must be 
 used (see Appendix D). 
 
 Returning now to Fig. 24, if 
 we call A, the half length of the 
 needle, we see that 
 
 or 
 
 also 
 and 
 
 mn \ sin a, 
 
 7n's=Xsin a, 
 
 pn = 2mn = 2X sin a. 
 
 But pn is the perpendicular distance between the forces 
 constituting the couple. In works on mechanics it is 
 shown that the moment of a couple is found by multiply- 
 ing the strength of one of the forces by the perpendicular 
 distance between them. Hence the moment F tending to 
 bring the needle into the meridian is 
 
 F=/Hx2X sin a. 
 The above expression (equivalent to 2A/H sin a) may 
 
ii MAGNETISM 77 
 
 be simplified if we introduce the definition of the moment 
 of a magnet. 
 
 Definition.-* The moment of a magnet is the product of the 
 strength of one of its poles multiplied by the distance between 
 them. 
 
 Call the moment of the magnet ^, then 
 
 /* = 2X/, 
 and 
 
 F=/xHsina, 
 
 or the moment tending to bring the compass needle into the 
 meridian is equal to the united product of the magnetic 
 moment of the needle, the horizontal component of the earths 
 magnetism, and the sine of the deviation from the meridian. 
 The student should fix this formula in his memory. 
 
 Exercises. When A = 4 units, /= 1 unit, H = 6 units, (1) 
 find the turning moment when a is 30 and also when a is 
 45. (2.) Find the moment of a magnet whose half length 
 or A is 6 while the strength of one of its poles is 5. (3.) 
 Find the strength of the earth's magnetism where the 
 moment required to keep a needle of moment 5 deflected 
 30 is 50 units. 
 
 LESSON XIII. Determination of the Dip. 
 
 29. Apparatus. A dip circle and needle, or materials 
 for making these. Fig. 26 shows a form of dip circle 
 especially designed for the work of this lesson. Fig. 2Qa 
 is a simpler form, such as could be made by the student. 
 
 Materials for snaking Dip Circle. (1.) Block of wood 10 cm. square 
 and 2-5 cm. thick. (2.) Four corks. (3.) Glass rod. (4.) Strips of 
 looking-glass. (5.) Sewing needle. (6.) Cardboard. 
 
 Operations. (1.) Make the stand and uprights of dimensions and 
 materials shown (Fig. 26a). The supports for the needle are seen at 
 ab and cd. The ends at b and c are made Y-shaped by heating the glass 
 in the blowpipe and then touching it with the end of a heated file. 
 (2.) Divide a card into degrees and number it in four quadrants in the 
 order 0, 90, 0, 90.. Cut out two sectors ss' stretching from 60 
 
78 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 to 60, and cement two pieces of looking-glass across these openings 
 (3.) Make the needle. A satisfactory needle can be made by any one 
 having the necessary patience in the following manner: (a.) Take a 
 piece of crinoline steel ? cut into shape as exactly as possible by 
 means of shears, (b. ) Drill a central hole just sufficiently large to 
 admit a sewing needle. The strip of steel supported by the sewing 
 needle as a horizontal axis should remain balanced in any position. If 
 this is not so the balance must be made perfect by filing the ends of 
 
 Fig. 26. DIP CIKCLE. 
 
 the strip of steel, (c.) Wrap iron wire round the strip of steel and 
 heat to bright redness in the blowpipe flame. Plunge vertically into 
 cold water. If the blowpipe flame be not sufficiently large to heat the 
 whole of the strip of steel at once, first one end and then the other 
 must be hardened. (4. ) Cut out two wads of cardboard by means of 
 a cork borer. Place one on either side of the strip of steel and thrust 
 a sewing needle, that is to serve as an axis, through the centre of one 
 wad, then through the hole in the strip of steel, and finally through 
 the centre of the other wad. Secure the wads to the steel by balsam 
 cement. The needle should now be put away until the cement sets. 
 Test whether the steel remains balanced, and if not, a final adjustment 
 must be made by grinding on a stone. (5. ) Magnetise the needle by 
 
II 
 
 MAGNETISM 79 
 
 the method of divided touch. On the base of the dip circle a hole h is 
 drilled sufficiently large to admit the pivot of the dip needle and the 
 fixing wad. We must fix, for the purpose of magnetisation, the dip 
 needle flat to the wooden base (with one of its pivots inserted in the 
 hole) by means of a strip of brass provided with a screw S (Fig. 26). 
 We now take a magnet in each hand and place the opposite poles 
 
 WOOD GLASS PAPER CORK STEEL 
 
 near the centre of the needle (Fig. 27), and draw the magnet from 
 the middle to the ends of the needle about twenty times. The 
 needle is then turned over and the process repeated on the other 
 
 side. 
 
 Theory of the Dip Needle. When discussing the earth's 
 magnetic action in Lesson XII., we only considered that 
 part of the earth's magnetic force that tends to bring the 
 compass needle into the magnetic meridian when displaced 
 therefrom. Nothing was said about any tendency of the 
 
80 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 OH. 
 
 needle to tilt due to any vertical force, for such force would 
 be counteracted by the resistance of the supporting cap of 
 the compass needle. By mounting the magnet so as to 
 allow any vertical force to have an evident action, as we 
 do in the dip needle, we may study this vertical force. 
 
 Further, by setting the dip needle so that it may swing 
 with its plane in the magnetic meridian, we may observe 
 the simultaneous action of the horizontal force. Consider, 
 therefore, SN (Fig. 28) to be a dip needle swinging in the 
 meridian. It will come to rest in a position inclined to the 
 horizontal, owing to action of two couples 
 
 (1.) The horizontal magnetic terrestrial couple - H/ and 
 
 + H/._ 
 
 (2.) The vertical magnetic terrestrial couple - V/ and 
 + V'/, and its position will be such that T/ 
 and + T'/, the resultant couple -forces, have no 
 moment, but act merely as two opposite pulls 
 upon the needle. 
 
 The resultant of H and V or of H' and V is called the 
 total magnetic force, and the angle TOB that the needle 
 makes with the horizontal is called the inclination or dip 
 of the needle. Let us call this angle 8. 
 
ii 
 
 MAGNETISM 
 
 81 
 
 Looking at the figure and remembering that 
 
 , side opposite to angle 
 tangent of an angle = -^ 7 ^. pmt : tn Mfflfl ' 
 
 we find 
 
 "side adjacent to angle 
 
 or 
 
 -B 
 
 Fig. 28. 
 
 This is a very important relation, for if we know two of 
 the quantities the third can be found. 
 Again 
 
 cos5=/=^> 
 or v * 
 
 T 
 
 cos 5 
 
 VOL. I 
 
82 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 Exercises. (1.) The horizontal magnetic component was 
 2 unit and the dip was 60. Find the vertical magnetic 
 component. (2.) Find the total magnetic force from the 
 same data. 
 
 Method of Conducting a Dip 
 Observation. Our first object is 
 to set the needle with its plane 
 in the magnetic meridian. The 
 most convenient method will be 
 as follows : 
 
 (a.) Load the dip needle by 
 means of the weighted cork, 
 into which the sharp end of the 
 needle is thrust. 
 
 (b.) Place the needle on its 
 pivots, when it will become 
 vertical. 
 
 (c.) Set the card so that the 
 upper end of the needle points 
 to 90. Whilst setting the card 
 the position of the eye must be 
 such that the end of the needle 
 covers its reflection in the mir- 
 ror glass, for we then avoid the 
 error known as .parallax. 
 
 (d.) Eemove the load at the 
 V bottom of the magnet and turn 
 
 Fig. 29. the stand of the dip needle 
 
 until the needle is vertical. It 
 
 is clear that we have now the needle with its plane at 
 right angles to the meridian, for if we consider Fig. 29, 
 where we see a dip needle in this position, we shall per- 
 ceive that the horizontal couple tends only to raise one 
 end of the pivot of the magnet. The vertical couple 
 is thus left free to bring the magnet into a vertical 
 position. 
 
ii MAGNETISM 83 
 
 (e.) Mark the position that the base occupies when the 
 needle is vertical by running a pencil line round the base, 
 and then turn it through 90. The needle will now be 
 in the desired position with its plane in the magnetic 
 meridian. 
 
 The needle and dip circles are liable to several errors. 
 
 Sources of Error. With regard to the needle there may 
 be (1.) a want of symmetry in mass, that is to say, the 
 centre of gravity of the needle may not coincide with its 
 axis of motion. (2.) A want of symmetry in magnetism, 
 that is to say, the magnetic axis may not be coincident 
 with the axis of figure. (3.) There may be friction or 
 adhesion of the axles as they rest upon their supports. 
 In the next place, with regard to the instrument, the 
 axis of rotation of the needle may not pass through the 
 centre of the vertical circle, and the circle itself may not 
 be properly set. 
 
 The error due to friction must be made as little as 
 possible by keeping the pivots and bearings clean. To 
 eliminate the other errors we must follow the method of 
 observation described below : 
 
 Method of Observation for Determining the Dip. (1.) Pre- 
 suming that the instrument has been set with its plane in 
 the magnetic meridian, and that the pivots and bearings are 
 clean, let us suppose that the face of the instrument (that is 
 to say, the side bearing the graduation marks) is towards 
 the magnetic east. Further, let us suppose that one side 
 of the needle, the face (distinguished by a scratch or letters), 
 is towards the face of the instrument. Read both ends of 
 the needle, estimating to a tenth of a degree. (2.) Now 
 turn the instrument to magnetic west, and again take the 
 readings. (3.) Then reverse the needle and repeat them, 
 and then, keeping the needle reversed, turn the face to 
 magnetic east and repeat the first set of observations once 
 more, with the difference that the back of the needle is 
 now turned to the face of the instrument. 
 
84 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 Of the two extremities of the needle, which are marked 
 say, a and /?, let us suppose that a dips. We have thus 
 made in all eight observations, as follows : 
 
 Upper Lower 
 Extremity. Extremity. 
 Face of instrument east, Face of needle to face 
 
 of instrument . . A a A' a 
 
 west ,, B a B' a 
 
 ,, ,, ,, Back of needle to face C a C' a 
 
 east D a D' a 
 
 (4.) We must now reverse the polarity of the needle by 
 the method of "divided touch," so as to make /3 dip. 
 (5.) We may therefore suppose the needle to be saturated 
 with magnetism, the end @ dipping. Having cleaned its 
 axles with cork, let us now proceed to make with it a 
 series of eight observations, precisely analogous to these 
 already described. Call these 
 
 The observation is now complete, and the mean of the 
 sixteen readings will give us the true dip. 
 
 Theory of the Method of Observation. The various pro- 
 cesses are rendered necessary by the possibly faulty con- 
 struction of the needle and the imperfect placing of the 
 vertical circle. 
 
 A needle, assuming that its axle is truly cylindrical, may 
 yet be imperfect in three ways : 
 
 (a) Its centre of mass may not coincide with its centre 
 of motion as regards the length of the needle. 
 
 (/?) Its centre of mass may not coincide with its centre 
 of motion as regards the breadth of the needle. 
 
 (y) Its magnetic axis may not coincide with its axis of 
 figure. 
 
 Exercise. Draw diagrams representing these several 
 
MAGNETISM 
 
 85 
 
 faults ; cut out models in thin cardboard of needles with 
 these faults. The error ft may be represented by a strip 
 of cardboard gummed to one side of the cardboard 
 needle. 
 
 Again, the axis of motion of the needle may not pass 
 through the centre of the graduated circle. This last 
 error, or that caused by eccentricity, is overcome by read- 
 ing both ends of the needle. 
 
 Exercise. Draw a graduated circle and a radius ON" 
 (see Fig. 30) at an angle of say 45 with 00, also an eccen- 
 
 90 
 
 N 1 
 
 Fig. 30. 
 
 trie diameter N'N" parallel to ON". Now N'N" represents 
 the needle, and the student should verify that the mean 
 of the readings at N' and N" is equal to the reading 
 atN. 
 
 When the needle is reversed in its bearings the action 
 of the needle errors (/3) and (y) will be likewise reversed. 
 The student may assure himself of this statement by mak- 
 ing the model needles transparent by steeping them in 
 paraffin, having previously denoted the magnetic axis by an 
 ink line and the centre of gravity by a dot of ink. It will 
 
86 PRACTICAL PHYSICS FOR SCHOOLS OH. 
 
 at once be seen that if the action of either error is (say) 
 to increase the dip when the face of the needle is towards 
 the observer, it will actjso as to diminish the dip when the 
 needle is reversed. 
 
 When the face of the circle is turned round through 
 180 the extremities of the needle are brought into different 
 quadrants of the vertical circle. If, therefore, the points 
 (90) have been erroneously set, so as to make the needle 
 read too low in the previous position, it will now read too 
 high, and thus by taking a mean of the two the error 
 caused by an erroneous setting of the circle is avoided. 
 Another advantage of this reversal of the vertical circle is 
 that new points of the steel axle are brought in contact with 
 the bearings. 
 
 The only error left uncompensated is (a), for it will be 
 noticed that during all these changes its position with 
 respect to the axis of motion remains unreversed. 
 
 This error is got rid of by reversing the poles of the 
 needle. For if, when the first series was made, the centre of 
 mass should have happened to be below the axis of motion, 
 thus causing a moment tending to increase the dip, after 
 the reversal, the same centre of mass will be above the 
 axis and thus cause a moment tending to diminish the 
 dip. The student may render this point obvious to himself 
 by means of the models steeped in paraffin. 
 
 Having thus described the reason for the various steps 
 of the process, it only remains to state that in the determina- 
 tion of the position of verticality it is obviously unnecessary 
 to reverse the poles of the needle, inasmuch as any dis- 
 placement of the centre of mass of the needle with regard 
 to its length could have no effect in altering its verti- 
 cality. It is only when the needle assumes a non-vertical 
 position that this can be influenced by the error in 
 question. 
 
 Example. 
 
MAGNETISM 
 
 87 
 
 Pole Dipping. 
 
 Pole /3 Dipping. 
 
 A^ A' a mean 
 67*3 67-3 
 67 '3 
 
 ** A 'e 
 
 67'4 67'4 
 
 mean 
 67'4 
 
 68*2 68* 
 681 
 
 67-3 67 : 4 
 
 67 0> 35 
 
 67*8 67'6 
 67'7 
 
 67-9 67-8 
 
 67'85 
 
 67-3 67'3 
 67'3 
 
 671 67-2 
 Mean of means 
 
 6715 
 
 Mean of means . 67 '60 
 
 67'44 
 
 Mean of all the observations, 67 P 52. 
 
 30. Action of one Magnet on Another. We have shown 
 that the couple urging a magnetic needle back to its posi- 
 tion of rest will be 
 
 aX/'Hsina (1) 
 
 where 
 
 X =half length of needle. 
 
 /' = strength of one of its poles. 
 
 H = horizontal strength of earth's magnetism. 
 
 a = deviation of compass from meridian. 
 
 Let us now proceed to study the action of a magnet 
 upon a needle. Suppose that the needle nOs is kept 
 deflected by a powerful horizontally-fixed permanent mag- 
 net NS (Fig. 31), placed with its axis in a line that is 
 perpendicular to the magnetic meridian, and that passes 
 through the centre of suspension of the magnetic needle. 
 Let / be the strength of the poles of the fixed magnet, 
 21 the distance between its poles, and d the distance of its 
 
88 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 centre from the centre of the needle. Also let /' be the 
 strength of the poles of the needle. 
 
 If we suppose A to be very small compared to the 
 distance d, and if the angle a is not great, then the dis- 
 
 JET 
 
 
 
 Fig. 31. 
 
 tance of the pole S from n or 5 will be approximately 
 represented by d - I, while that of the pole N from n 
 or s will be approximately represented by d + 1. 
 
 We thus find (assuming the law of force to be that of 
 the inverse square) 
 
 Attraction of S upon n= - 2 - 
 
 Repulsion of N upon n=, , A a 
 
 Hence total attractive action upon n 
 
 1 l 
 
 (d-lf 
 
II 
 
 MAGNETISM 
 
 89 
 
 In like manner the total repulsive action upon 5 
 _ + iff 'Id 
 
 Bearing in mind that this force makes approximately an 
 angle (90 - a) with the length of the needle, we thus see 
 that the needle is acted upon by a couple whose moment is 
 8/'l\d cos a 
 
 Now this moment must (since there is equilibrium) be equal 
 to that of the earth's magnetic couple ; hence 
 
 
 or 
 
 H 
 
 tan a. 
 
 It will be seen that 2/ is the strength of the one pole 
 of the permanent magnet multiplied by the distance be- 
 tween the two poles; this is called the 
 moment of the magnet. If we designate this 
 moment by M we have 
 
 M (d 2 - 
 H = ~2d 
 
 tana 
 
 (I*) 
 
 and if d be very great compared with I this 
 will become 
 
 M d 3 
 
 H = ~2 ' * * ( ) 
 
 In a similar manner the relation between 
 M and H can be ascertained when the magnet *? 
 is placed broadside on, as in Fig. 32. These 
 two positions we shall call the A and B Tan- 
 gent Positions of Gauss. Fig ' 82t 
 
 In the following table are given the first and second 
 approximations to the value of for the two cases A and B. 
 
90 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 TABLE D. 
 FORMULA FOR THE TANGENT POSITIONS A AND B OF GATJSS. 
 
 Posi- 
 tion. 
 
 B 
 
 1st Approxi- 
 mation (a). 
 
 2d Approxi- 
 mation (6). 
 
 H 
 
 Note. It is very tedious to use formulae like the above unless 
 logarithms are employed. Four-place logarithms are sufficient, and 
 the student should at once be made acquainted with their method of 
 application, which presents no difficulties (see Appendix D). It may be 
 noticed that formula A(&) for purposes of calculation may be written 
 
 2d 
 
 LESSON XIV. Action of one Magnet on another. 
 
 31. Exercise. To prove the formulae of the preceding 
 paragraphs experimentally. 
 
 Apparatus. A compass box with a small magnetic 
 needle (Fig. 33) pivoted at the centre of a card graduated 
 
 Fig. 33. DEFLECTION MAGNETOMETER. 
 
 into degrees. The needle has a pointer pp' of brass wire 
 placed at right angles to the magnetic needle. To avoid 
 
MAGNETISM 
 
 91 
 
 parallax in reading the position of the pointer the bottom 
 of the compass box is provided with a mirror, which is 
 indicated by the shaded ring. The compass box is pro- 
 vided with two arms, A and B, with central grooves formed 
 on one side by a boxwood millimetre scale. A short 
 but powerfully magnetised bar magnet NS will likewise 
 be required. 
 
 Method. Arrange the apparatus for the A position of 
 Gauss. See that both pointers are at zero. Place the bar 
 magnet NS on the east limb of the instrument, with its N 
 
 
 
 
 Fig. 34. 
 
 pole west, and note the deflection produced by means of 
 the pointers. Note at the same time the exact distance 
 between the centres of the two magnets. Then turn the 
 magnet end for end, so that while its centre preserves the 
 same position its south pole is now nearest the needle, and 
 again read the deflected position of the pointers. Next 
 take the magnet to the other limb of the instrument, 
 leaving its distance from the centre of the needle the same 
 as before, and obtain a series of deflections similar to those 
 already described. Fig. 34 shows the various positions. 
 Take the mean of the deflections in order to obtain the 
 angle a. Lastly, repeat the observations with different 
 
92 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 distances, and then calculate the value of g with the aid 
 of the preceding formulae. 
 
 Repeat the experiment for the B position of Gauss. 
 
 Example. 
 
 A POSITION. 
 
 
 Posi- 
 
 Distance of 
 
 
 
 tion. 
 
 Magnet from 
 Compass Box. 
 
 Deflection (a). 
 
 Experiment I. 
 
 
 
 
 
 1 
 
 20 cm. 
 
 ll-25 
 
 
 la 
 
 I 
 
 11-0 Mean, 11-125 
 
 
 2 
 
 it 
 
 11-0 
 
 
 2a 
 
 ii 
 
 ll-25 
 
 Experiment II. 
 
 
 
 
 
 1 
 
 10 cm. 
 
 30 -00 
 
 
 la 
 
 ?j 
 
 30 -00 Mean, 30 '19 
 
 
 2 
 
 j $ 
 
 30 -50 
 
 
 2a 
 
 > j 
 
 30'25 
 
 Experiment III. 
 
 
 
 
 
 1 
 
 5 cm. 
 
 49'00 
 
 
 la 
 
 J) 
 
 53 -00 Mean, 51 '06 
 
 
 2 
 
 
 
 53 -00 
 
 
 2a 
 
 
 
 49 '25 
 
 Length of magnet =10 '5 cm. Diameter of compass box = 18'0 cm. 
 Length of compass needle = 28 '5 mm. 
 
 The difference between the values in Experiment III. 
 would seem to indicate that the magnet was too near the 
 compass box, hence we shall reject the result. 
 
 Exp. I. Exp. II. 
 
 M 
 
 Using Formula (A) . 
 
 H 
 
 = 3949-4 
 
 = 3767-0 
 
 4148-4 
 
 37687 
 
 LESSON XV. Study of a Vibrating Magnet. 
 32. Apparatus. The magnet intended to be put in 
 
MAGNETISM 
 
 93 
 
 vibration should be suspended in a box (Fig. 35) by 
 means of a few fibres of unspun silk. The silk thread is 
 supported by a small hook h held by a boxwood cap c that 
 fits over the top of a glass tube t. The latter is fixed in 
 a hole in the top of the 
 box by the help of the box- 
 wood mounting c'. At the 
 top of the box is a narrow 
 glass window w. A strip 
 of mirror glass is fixed to 
 the bottom of the box, and 
 has an index line ii r across 
 its middle. A stirrup of 
 thin copper s is used to 
 support the magnet, at 
 one end of which a piece 
 of paper with an index 
 mark m is gummed. The 
 front and back of the box 
 are sliding doors of glass. 
 The apparatus may be 
 readily constructed from 
 one of the postal boxes, if 
 
 COrks be Used instead of 
 
 boxwood, and only one 
 sliding door of glass employed. 
 
 Law of a Vibrating Magnet. We proceed to give a for- 
 mula of very great value in magnetic measurements. 
 
 Fig. So. VIBRATION MAGNETOMETER. 
 
 MH 
 
 where t is the time in seconds required for the magnet to 
 make one oscillation (that is to say, a single swing), TT is 
 the ratio of the circumference of a circle to its diameter, or 
 31416 nearly, M is the moment of the magnet, H is the 
 horizontal component of the earth's magnetic force, and I is 
 
94 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 the moment of inertia of the magnet. The meaning of this 
 latter term will require explanation. 
 
 Definition of Moment of Inertia. When a solid body is 
 made to vibrate or rotate (let us say rotate, for this is 
 simpler) it is clear that all the particles of the body are not 
 moving with the same velocity. For those near the axis 
 of rotation will move comparatively slowly, while those at 
 a distance from it will move comparatively fast. Now the 
 energy or work that must be bestowed upon the body in 
 order to start its rotation depends upon the absolute velo- 
 city communicated to these various particles. Thus, for in- 
 stance, suppose that we have a thin steel wire, of which the 
 mass may be 'neglected, and which is made to rotate hori- 
 zontally around an axis at its centre, and furthermore let 
 both arms be loaded with equal masses of lead placed at 
 equal distances from the centre. Then it will require four 
 times as much energy to make the system rotate once in a 
 second, if the lead be placed two decimetres from the 
 centre, as will be necessary if the lead be only one de"ci- 
 metre from the centre ; because in the former case the lead 
 will be constrained to move twice as fast as in the latter 
 and this means a fourfold energy. 
 
 Suppose now that a complicated system, such as a 
 heavy top, is made to rotate say once in a second. There 
 is in any such system a certain distance from the axis such 
 that if we imagine the whole mass of the system to be 
 concentrated at that distance, then will the energy neces- 
 sary to rotate this imaginary system once in a second be 
 the same as that necessary to rotate the actual system at 
 the same rate. This point or distance from the axis at 
 which we have imagined the mass to be concentrated is 
 called the centre of gyration, and the perpendicular distance 
 between it and the axis the radius of gyration. Again, the 
 whole mass multiplied by the square of the radius of gyra- 
 tion is called the moment of inertia, or I ; and if w denote 
 the angular velocity of the body, or velocity at distance 
 
ii MAGNETISM 95 
 
 unity from the axis, then will the whole energy of rotation 
 be denoted by the expression Jo> 2 I ; that is to say, by one 
 half the square of the angular velocity multiplied by the 
 moment of inertia. 
 
 Calculation of Moments of Inertia. The following rules 
 will be useful : Eectangular parallelepiped, axis through 
 centre and perpendicular to the side contained by a and I 
 
 12 
 
 Eight cylinder, of length / and radius of section = r, axis 
 through centre perpendicular to axis of cylinder 
 
 
 where W is the mass of the body. 
 Application of Formula. We have 
 
 =*VSH 
 
 hence 
 
 * 2 = 
 from which 
 
 MH=^ (3) 
 
 or the product MH varies inversely as the square of the 
 time of oscillation. 
 
 Application 1st. If we carry the same magnet to different 
 parts of the earth, taking care that its magnetic moment 
 remains the same by keeping the magnet free from con- 
 cussions and great changes of temperature, then we can 
 ascertain the relative value of H at any two places. Thus 
 at a certain place we may have 
 
 MH'=^ (4) 
 
 where t' is the time of oscillation. 
 
96 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 Hence from (3) and (4) 
 
 H t' 2 
 
 ir=^ (5) 
 
 Exercise. A magnet in London made 135 oscillations in 
 50 seconds, and when in Edinburgh made 127 oscillations 
 in the same time. What is the relative value of the hori- 
 zontal component at the two places ? 
 
 Application 2nd. Magnets of the same shape and weight 
 have the same moment of inertia, hence, if they are vibrated 
 at the same place, we may compare their magnetic moments. 
 Thus with a magnet of moment M' we may have 
 
 hence, from (3) and (6), 
 
 Exercise. Two magnets of equal moments of inertia 
 gave times of vibration 1*23 and 3*69 seconds. Compare 
 their magnetic moments. 
 
 Application 3rd. The magnet under vibration may be 
 of an irregular form, of which it would be difficult to cal- 
 culate the moment of inertia. If we attach to the vibrat- 
 ing magnet a body of definite form made of non-magnetic 
 material, we may then ascertain experimentally the moment 
 of inertia of the magnet, for 
 
 where I' is the calculated moment of inertia of the non- 
 magnetic body, and t' the time of vibration of the combined 
 system. 
 
 Hence, from (3) and (8), 
 
ii MAGNETISM 
 
 therefore 
 
 UKI7EESIT7 
 
 l'~t" 2 -t 2 
 
 or T-F P 
 
 Exercise. A magnet gave t = 4, and when a bar of brass 
 was added to it t' = 8. Find the moment of inertia of the 
 magnet, supposing that the moment of inertia of the brass 
 bar is 50. 
 
 EXPERIMENTAL WORK. 
 
 Exercise I. Compare the magnetic moments of two magnets 
 A and B of the same weight, size, and shape. 
 
 Method. (a.) Place the vibration box so that the line 
 joining the index threads is in the magnetic meridian. The 
 box should likewise be placed at a convenient height for 
 observation by supporting it on a wooden block or stool. 
 (b.) Put the brass bar in the stirrup and allow it to come 
 to rest. If it does not come to rest in the magnetic 
 meridian, this shows that there is torsion in the support- 
 ing thread. Turn then the head C that supports the 
 thread round until the bar lies in the meridian. The 
 thread will now be free from torsion, (c.) Replace the 
 brass bar by the magnet, having previously gummed a 
 strip of paper at one of its ends ; steady the magnet, 
 and, when nearly at rest, cause it to be set into vibra- 
 tion by approaching another magnet. (d.) Proceed to 
 find the time of vibration of the magnet. With his 
 head about two feet above the vibration box, let one 
 observer notice when the middle of the magnet crosses 
 the index line, and let him sharply tap on the table; 
 a second observer should meanwhile be ready to note 
 down as accurately as he is able the time at which the 
 signal is given. Call the time of the first signal the time 
 of the Oth passage. Let the first observer continue to 
 count the number of the passages until the 100th is 
 
 VOL. I II 
 
98 PRACTfCAL PHYSICS FOR SCHOOLS CH. 
 
 reached, when he should again give a sharp tap as a signal 
 to the second observer, (e.) Subtract the time of the Oth 
 passage from the time of the 100th, and divide the result 
 by 100 in order to obtain the time of a single oscillation. 
 (/.) Repeat the process with the magnet B, then apply the 
 
 \T /'2 
 
 formula ^, = -^ 
 
 Example. 
 
 Time of Vibration of A 
 
 h. in. s. 
 
 Time of Otli passage 1 14 10 
 
 100th 1 27 19 
 
 Time of 100 oscillations 13 9 
 
 60 
 
 Therefore time of 1 ,, 100)789 
 
 7 '89 seconds. 
 
 Time of Vibration of B . . . . 8 '00 
 Moment of A 8 2 , 
 
 MoinenFoTB = (7W^ 1>03 nearly " 
 
 Exercise II. To compare the strength of field of the earth 
 with the strength of field produced ly placing a long magnet 
 above the vibration box. 
 
 Method. (a.) Find the time of oscillation of the sus- 
 pended magnet as before, (b.) Place the long magnet with 
 its long axis in the meridian, and with its south pole to the 
 north, and again determine the time of oscillation, (c.) 
 Apply the formula j~, = ^- 
 
 Exercise III. To determine the moment of inertia of a 
 magnet by experiment and calculation. 
 
 Method. (a.) Find the time of oscillation of the magnet 
 by itself, and then with a brass bar fastened to it by silk 
 thread, (b.) Apply the formula I = I'^rp- 
 
 LESSON XVI. Determination of H and M. 
 
 33. Apparatus. The vibration box of the previous 
 lesson and the deflection apparatus of Lesson XIV. 
 
ii MAGNETISM 99 
 
 Theory of Method.' Let us write formula (3), page 95, 
 in a simplified form, so 
 
 MH=A . . . . . (11) 
 
 where A stands for the right-hand member of the equation. 
 Eefer now to page 89, where we obtained a formula 
 
 | = B . . . . . (12) 
 
 where B is the right-hand member of the expression there 
 given. From (11) and (12) we find, by multiplication, 
 
 or 
 
 M=VAB . .,. ' V- ; . (13) 
 
 and by division 
 
 or 
 
 Formulae (13) and (14) thus enable us to find simul- 
 taneously the moment of a magnet and the horizontal 
 component of the earth. 
 
 Exercise. A. = 8, B = 2. Find M and H. 
 
 Practice of Method. This will be sufficiently clear from 
 the following example : 
 
 I. Deflection Observation. 
 
 Position of Magnet. Deflection. 
 
 1 47-25^ 
 
 !! L Mean 46-81=0. 
 
 o 
 
 4 
 
 47 I- 
 47 f j 
 
 46 I 
 
 Distance from centre of magnet to centre of deflection needle, 20'3 cm. 
 = d. Half length of magnet, 5 '1 cm. = I. 
 
 M ^-Z 2 )^ 
 
rOO PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 
 = 3911. 
 //. Vibration Observation. 
 
 a=lQ'2 cm., &=1'4 cm., t = 7'89 seconds. 
 
 i=w ^- 2 = C8 . 6 (io-2n(t^ =6 . 06 neav]y 
 
 ' 
 
 Value of H. 
 
 M = (-9610x 
 
 Since all the measurements have been made in centimetres, 
 grammes, and seconds, the above values are in accordance 
 with the C.G.S. system of units. 
 
 34. By the preceding method we can find in any par- 
 ticular system of units the moment of a magnet. Once 
 possessed of a magnet of known moment, the comparison of 
 this magnet with any other may be made by balancing 
 one magnet against the other. A convenient apparatus for 
 the purpose we shall call a Comparison Magnetometer. 
 
 LESSON XVII. Use of a Comparison 
 Magnetometer. 
 
 35. Apparatus. A comparison magnetometer of the fol- 
 lowing construction : A short hollow cylindrical magnetic 
 needle ns (Fig. 36) is suspended by a fibre of silk within a 
 box similar to the vibration box. Attached to the needle 
 is a pointer pp' of glass or aluminium or thin brass wire, 
 weighted at p', whose movement is observed through the 
 window w. The pointer swings above a short scale a 
 
ii MAGNETISM 101 
 
 attached to a strip of looking glass, and the extent of its 
 swing is limited by two stops t and t'. On either side of 
 the box are two arms, A and B, provided with grooves 
 
 Fig. 36. THE COMPARISON MAGNETOMETER. 
 
 and millimetre scales. These scales are fixed nearly at 
 the same height as ns, and on them the magnets under com- 
 parison, NS and N'S', are placed. To assist in bringing 
 the needle to rest a wire d passes from its centre and dips 
 in a vessel of water placed at the bottom of the box. 
 
 A magnet of known moment will be required for use 
 
102 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 with the instrument, and other magnets and pieces of steel 
 for experimental purposes. 
 
 Method of Using the Instrument. Place the instrument 
 on a steady table or stone slab, and turn it until, on looking 
 through the glass-covered hole w in the roof of the box, 
 the end of the pointer (when covering its image in the 
 looking glass) points to zero of the scale a. Now place 
 on the scales the magnets under comparison, NS and N'S', 
 with their like poles opposing. Then by moving one of 
 the magnets the index can be brought to zero. If D be the 
 distance of the centre of one magnet from the needle, then 
 
 M_D 3 tana 
 H~ 2 ' 
 
 where a is the deflection which one magnet alone will 
 produce; but since the magnet is opposed by the second of 
 moment M' at distance d, then 
 
 M'_d 3 tana 
 H~~~2~ 
 or 
 
 M D* 
 
 M' = ^ (1) 
 
 or the moments of the magnets are directly as the cube of 
 the distances of the centres of the magnets from the needle. 
 As it is a little difficult to obtain the exact distances D 
 and d, it is better to proceed by what is called a difference 
 method. Obtain a balance at new distances D' and d', then 
 
 ^ .....< 
 
 From (1) 
 
 From (2) 
 
 3 _ 
 
 M' ~ d' 
 
ir 103 
 
 hence 
 
 or 
 
 -' 3 ,, 
 
 that is to say that we only require to note the distance 
 each magnet has been moved from the first balancing posi- 
 tion to the second. 
 
 By considering M' as of unit moment and making 
 d - d' = 1 0, the formula simplifies to 
 
 ' 
 
 000 ' ' 
 
 The above formulae give only a first approximation. 
 To obtain more correct results a more complicated formula 
 would be necessary. They give, however, all the necessary 
 accuracy for comparing the moments of magnets that have 
 been magnetised in different ways and then subjected to 
 concussion, change of temperature, etc., as in the examples 
 that will now be described. 
 
 EXAMPLES OF THE USE OF THE COMPARISON 
 MAGNETOMETER. 
 
 /. Comparison of two Magnets A and B of equal length. 
 A on Left. B on Right. 
 
 A at 304 balanced B at 300 
 A at 202-5 B at 200 
 
 moment of A /304-202'5\ 3 101 '5 3 
 
 moment of B 
 
 _/304-202-5\ 3 _101-5 3 
 ~ \ 300 - 200 / ' : 100 3 
 
 II. Study of Magnetisation. (a.) A strip of steel was magnetised 
 by the method of single touch and balanced against a standard magnet. 
 The latter was kept at 435 on the scale. The effect of the successive 
 strokes that the steel had been submitted to is seen below. 
 
104 
 
 PRACTICAL PHYSICS FOE, SCHOOLS 
 
 CH. 
 
 After 1st stroke 
 
 2d 
 
 3d 
 
 4th 
 
 5th 
 10th 
 loth 
 20th 
 30th 
 
 Balanced at 115 
 
 150 
 
 160 
 
 162 
 
 ., 164 
 177 
 
 (b.) The effect of stroking with copper bar. 
 
 Before stroking with copper 
 
 After 1st stroke .... 
 
 , 2d 
 
 167 I Magnetisation 
 170 f unstable. 
 177J 
 
 182 
 175 
 170 
 
 (c.) The same steel strip made as hard as glass and magnetised by 
 single touch. 
 
 Strokes. 
 1 
 2 
 3 
 4 
 
 Readings. 
 148 
 159 
 163 
 167 
 
 Strokes. 
 5 
 
 10 
 15 
 20 
 
 Readings. 
 
 170 
 
 167^ 
 
 175 [-Unstable. 
 
 168J 
 
 (d.) A weight was allowed to fall from a definite height on to the 
 strip of magnetised steel. 
 
 Initial reading . . . . . . . 168 
 
 Weight dropped once . . . . . 160 
 
 ,, ,, twice : 155 
 
 ,, three times . . . strip broken. 
 
 (e.) Study of magnetisation by divided touch. Standard at 435. 
 
 Strokes. 
 1 
 2 
 3 
 4 
 5 
 
 10 
 15 
 
 Readings. 
 180 
 210 
 222 
 230 
 238 
 250 
 252 
 
 Strokes. Readings. 
 
 20 
 30 
 40 
 50 
 60 
 70 
 100 
 
 255 
 261 
 265 
 266 
 268 
 270 
 275 
 
 (/.) The magnet of previous experiment was dropped repeatedly 
 
 from a definite height on to a stone. Standard at 435. 
 
 Initial reading . 275 After 6th drop 
 
 After 1st drop . 250 ,, 7th ,, 
 
 2d ,, . 246 8th ,, 
 
 3d ,, . 241 9th ,, 
 
 ,, 4th ,, . 240 10th ,, 
 5th 228 
 
 225 
 225 
 225 
 218 
 216 
 
ii MAGNETISM 105 
 
 (gr.) Effect of Temperature. Standard at 435. Magnet of previous 
 experiment used. 
 
 Initial reading 216 
 
 Heated to temperature of boiling water . . 214 
 , , , , of melting sealing-wax . 208 
 
 As tlie magnet cooled it was observed to recover a portion of tlie 
 lost magnetism. 
 
 (h.} The magnet of last experiment was inserted within a helix, 
 around which a powerful electric current was circulating. Standard 
 placed at 435, balancing the steel magnetised in this manner at 345. 
 
 In the above experiments, a h, the actual value in 
 C.G.S. units of the moment of the experimental magnets 
 may be readily calculated when the value of that of the 
 standard magnet has been once ascertained. 
 
 36. Distribution of Magnetism. To ascertain the law of 
 distribution along a magnet we may apply several methods, 
 as 
 
 (1.) A Vibration Method. 
 
 (2.) A Deflection Method. 
 
 (3.) A Test-Nail Method. 
 
 The first two methods are simply applications of the 
 principles we have described. The third method will form 
 the subject of the next lesson. 
 
 LESSON XVIII. The Test-Nail Method. 
 
 37. Exercise. To find the distribution of force along a 
 short bar magnet. 
 
 Apparatus. A spring balance in one of its modifications. 
 Fig. 37 shows one suited for the purpose. Here ss' is a 
 spiral spring, having a silk cord attached to its upper end. 
 The silk passes round a pulley mounted so as to rotate 
 stiffly in a collar. At the end of the spiral spring is a 
 small piece of soft iron. When the soft iron rests upon a 
 magnet the force of attraction is measured by the amount 
 of turning that must be given to the milled head m in 
 
106 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 order to detach the soft iron. This is indicated by means 
 of the graduated disc d and the fixed index i. To ensure 
 that the pull from the magnet is vertical the spiral spring 
 
 works within the glass 
 guard tube g. The 
 apparatus is supported 
 from an arm which 
 may be raised or low- 
 ered at pleasure. 
 
 Thwry.IS. S de- 
 notes the strength of 
 the magnet at any 
 point, then the mag- 
 netism induced in the 
 soft iron will be pro- 
 portional to S,or equal, 
 let us say, to KS, and 
 hence the force neces- 
 sary to detach the mag- 
 net must be propor- 
 tional to S 2 , or 
 
 F = constant xS 2 , 
 or S = constant V^\ 
 
 that 
 
 is 
 
 to say, the 
 
 strength at any point 
 is proportional to the 
 square root of the 
 force required to de- 
 tach the soft iron. The 
 method is open to the 
 objection that the 
 amount of magnetism 
 induced depends upon the coefficient of induced magnetism, 
 which may not, however, be strictly constant, but may 
 vary to some extent with S. Again, the presence of the 
 
 Fig. 37. MAGNETIC BALANCE. 
 
MAGNETISM 
 
 107 
 
 soft iron is liable to cause a change of distribution of 
 magnetism in the neighbourhood where it is placed. 
 
 Method. Obtain the zero point of the balance by sub- 
 stituting for the magnet a piece of wood of the same size, 
 turning the milled head until the soft iron just touches the 
 wood. Now place the magnet in position and ascertain 
 the number of divisions through which the milled head 
 must be turned until the soft iron leaves the magnet. The 
 milled head must be turned slowly without any jerks, and 
 a number of observations must be taken at each place, 
 especially near the ends of the magnet, where such observa- 
 tions are most likely to vary. 
 
 Example. Magnet divided into 1 74 equal parts. 
 
 Distance from 
 middle of 
 Magnet = D. 
 
 F. 
 
 V F - 
 
 VF: 
 
 ~TT 
 
 13 
 
 9 
 
 3-0 
 
 23 
 
 23 
 
 21 
 
 4-58 
 
 20 
 
 33 
 
 39-5 
 
 6-28 
 
 19 
 
 43 
 
 70 
 
 8-37 
 
 19 
 
 53 
 
 125 
 
 11-18 
 
 21 
 
 63 
 
 183 
 
 13-52 
 
 21 
 
 73 
 
 308 
 
 17-55 
 
 24 
 
 These results agree approximately with Coulomb's con- 
 clusion that for short magnets, that is to say, for magnets 
 whose length is less than fifty times their diameter, the 
 magnetic strength (between the end and the centre) is 
 directly proportional to the distance from the centre. If 
 
 this had been quite true the value of ^ should have been 
 a constant quantity. 
 
c 
 
 EB III. 
 
 VOLTAIC ELECTRICITY FUNDAMENTAL LAWS AND 
 MEASUREMENTS. 
 
 LESSON XIX. Fundamental Experiments. 
 
 38. Apparatus. Two pint Bunsen's cells placed in a box 
 arranged as shown in plan in Fig. 38. Each cell consists of 
 a cylindrical glazed stoneware jar P, about 10 cm. in dia- 
 
 2 34 
 
 Fig. 38. PLAN OF TWO-CELL BATTERY. 
 
 meter and 15 cm. high. In this jar there is placed a cylinder 
 of zinc Zn, made from a plate of zinc 14 cm. by 20 cm. 
 that has been heated and then bent round until its edges 
 nearly meet. Within the zinc cylinder there is placed a 
 porous potp 14 cm. high and 5 cm. in diameter made of un- 
 glazed earthenware. This porous pot contains a rod of pre- 
 pared carbon C 16'5 cm. in height and 3 '5 cm. by 1'75 cm. 
 in cross-section. The zinc and carbon have attached to 
 
CH. in VOLTAIC ELECTRICITY 109 
 
 them screw clamps a and b. The box for containing the 
 battery is covered inside with pitch in order to prevent 
 the fumes of the acid from acting upon the wood, and is 
 provided with four binding screws numbered 1, 2, 3, 4, 
 each of which has attached to it, inside the box, a thick 
 copper wire covered with gutta-percha for making connec- 
 tions with the clamps. 
 
 The following additional apparatus and materials 
 should be at the disposal of the student : 
 
 Measuring vessels. Nitric acid. 
 
 Glass funnel. Mercury. 
 
 Glass tubing. Caustic soda. 
 
 Stoneware jug with a spout. File. 
 
 No. 18 insulated copper wire. Emery paper. 
 
 No. 20 cotton-covered copper wire. Stiff nail brush. 
 
 No. 30 pure iron wire. 1 3 Carbon rods, 6 to 12 in. 
 
 No. 30 copper wire. l n g> about 2 in. thick. 
 
 Sulphuric acid. India-rubber finger stalls. 
 
 Fitting up of the Battery. This must be done in a draught 
 cupboard or in the open air to prevent the fumes of the 
 acid from affecting the operator. 
 
 Begin by removing all the clamps and clean the con- 
 necting surfaces and screws by means of a file and emery 
 paper. 
 
 Proceed next to the making of mixtures and the 
 amalgamation of the zinc. Into one of the earthenware 
 battery jars put a solution of caustic soda and water (1 of 
 soda to 20 parts of water by weight), and into the other 
 some sulphuric acid diluted with water (1 of acid to 12 of 
 water by weight). In making this last mixture in the jug, 
 pour the water first into the jug, then gradually pour upon 
 it the acid, stirring meanwhile with a glass rod. If the 
 acid be put in first and the water be added to it sufficient 
 heat might be produced by the chemical union to crack_ 
 the jar. Since all the sulphuric acid of commerce contains 
 lead sulphate which is precipitated on dilution with water, 
 
 1 This should be kept in a bottle with quicklime. 
 
110 PRACTICAL PHYSICS FOR SCHOOLS cu. 
 
 the acid mixture will appear milky when first made. As 
 the presence of lead is very injurious to the working of the 
 battery it will be desirable to allow the mixture to settle 
 and then decant off the clear liquid. A quantity of the 
 mixture should thus be prepared and labelled ""Battery 
 sulphuric acid." 
 
 The process of amalgamation is as follows : 
 
 First, Dip the zinc into the solution of caustic soda in 
 order to remove grease, and then wash it under a water-tap. 
 
 Secondly, Place the zinc in the dilute sulphuric acid 
 until effervescence has commenced, then lift it out and lay 
 it down in a flat dish. 
 
 Thirdly Pour mercury that is free from lead and other 
 injurious metals in a thin stream upon the inside of the 
 cylinder, and also on the outside. Eoll the cylinder about 
 until nearly the whole surface of the zinc has a bright 
 appearance. 
 
 Fourthly, Eeplace the zinc in the acid, and rub the sur- 
 face with a stiff brush or with a rag, the fingers being pro- 
 tected in the operation by finger stalls. The whole of the 
 zinc should be now well amalgamated. Remove it from 
 the acid, wash it well with water, and allow it to drain. 
 
 Lastly, Collect any waste mercury and place it in a 
 bottle labelled "Amalgamation mixture." 
 
 Keep also the soda solution in a bottle appropriately 
 labelled. 
 
 The process of amalgamation tends to make the zinc 
 brittle and rotten if too much mercury be used. Napier 
 (Electro-Metallurgy} alloAvs 1 J ounce of mercury for every 
 effective square foot of zinc in the first operation, and half 
 that weight for the second and all subsequent operations. 
 We find that 1 gramme of mercury will thoroughly amal- 
 gamate 100 square cm. of zinc surface. Three times this 
 quantity of mercury may be used in the actual process, of 
 which two-thirds will be recovered by draining off. 
 
 Examination and Preparation of the Porous Pots. The 
 
in VOLTAIC ELECTRICITY 111 
 
 porous pots being thoroughly clean and dry, subject them 
 to the following test : Pour water into each pot, taking 
 care not to wet the outside, and note the time by a watch. 
 Then observe when first an indication of moisture appears 
 on the outside surface of the pot, and again note the time. 
 If the moisture appears immediately, the pot is cracked, 
 and should be rejected. A good pot, if made of red clay, 
 should become moist all over in about two minutes ; if made 
 of white clay, in about double the time. 1 For low resist- 
 ance cells the red-clay pots are to be preferred, but they 
 possess the serious defect of being liable to disintegration, 
 a fault possessed in a much less degree by the white pots. 
 
 Melt some paraffin wax, and plunge the open end of the 
 porous pot vertically into the wax until this has soaked 
 into it through a distance of about a quarter of an inch from 
 the open end. 
 
 This will prevent the acids from creeping up the sides, 
 and will likewise prove especially useful in preventing the 
 sulphate of zinc formed when the battery is in action from 
 becoming concentrated along the rim of the jar, and there 
 crystallising, with the effect of disintegrating the porous 
 material. 
 
 It is an excellent plan to put a flat india-rubber band 
 round the top of the jar. This serves to protect the 
 paraffin and to insulate the pot from the clamp at the top 
 of the zinc, besides enabling the experimenter to handle the 
 pot without staining his fingers with nitric acid. 
 
 Charging the Battery. Fix the clamps upon the carbon 
 and the zinc, and bring the parts of the battery together. 
 Now pour strong nitric acid through a funnel into the 
 porous pot to within about an inch of the top. Next fill 
 up the outer pot with battery sulphuric acid to a level about 
 an inch higher than that of the acid in the inner pot, the 
 reason for this difference of level being that the action of 
 
 1 A good pot should have a minimum leakage of 15 per cent in 
 twenty-four hours, according to the French standard. 
 
112 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 diffusion tends to empty the outer pot. Connect the zinc 
 of one cell to the wire attached to the binding-screw No. 1, 
 its carbon to that of No. 2, the zinc of the other cell to 
 that of No. 3, and its carbon to the remaining screw. 
 
 Finally, tighten all the clamps, and then close and fasten 
 the box, which may now be brought into the laboratory. 
 
 Necessary Precautions with the Battery. The student 
 must once for all be warned that nitric acid batteries may 
 be the source of considerable danger to delicate instruments. 
 Hence it is better that they should not be brought into the 
 laboratory, being only used in a draught cupboard or 
 placed outside a window. Since, however, this arrangement 
 is not always convenient, we may employ a tightly-fitting 
 box, such as we have described, provided this box be not 
 opened in tlie laboratory. The battery should be placed 
 under the experimenter's table or bench in a position 
 where it is not liable to be overturned. 
 
 In some schools it may be considered preferable to use 
 a more simple form of battery in which nitric acid is not 
 used. We shall therefore describe the bichromate battery. 
 
 The Bichromate Battery. An ideal battery should at any 
 desired time be capable of yielding a strong and constant 
 current. No primary 1 battery hitherto invented can be 
 said to have these qualities in a satisfactory manner. The 
 nearest approach is perhaps found in certain forms of the 
 bichromate battery, of which Fig. 39 represents a good type. 
 It has two pots p and P, the former of unglazed (porous) 
 and the latter of well glazed earthenware. Within^ stands 
 an amalgamated plate of zinc Zn, and within P are four car- 
 bon plates fastened together by a band of lead. The cells 
 are provided with a wooden framework having an arrange- 
 ment whereby the zincs may be supported out of the liquid 
 when the battery is not required for use. To charge the 
 
 1 Batteries are divided into two classes, primary and secondary. The 
 latter comprise the storage cells, which require to be charged by means 
 of a current obtained from a dynamo. 
 
in VOLTAIC ELECTRICITY 113 
 
 cell dilute sulphuric acid is placed within p and one of the 
 following mixtures in P : 
 
 Oxidising Mixture. Dissolve 100 grammes of bichro- 
 mate of potash that has been purchased in the form of a 
 
 Fig. 39. THE BICHROMATE BATTERY. 
 
 fine powder in one litre of boiling water. Cool the solution 
 and add 60 c.c. of strong sulphuric acid. This mixture acts 
 chemically in a manner similar to nitric acid, being a strong 
 oxidising fluid, but it is free from injurious fumes. 
 
 Instead of bichromate of potash we may use with much 
 advantage bichromate of soda, for the soda salt does not 
 
 VOL. I I 
 
114 
 
 PRACTICAL TIIYSICS FOR SCHOOLS 
 
 CH. 
 
 give rise to chrome-alums that deposit in the cell. The 
 soda salt when obtained in quantity is much cheaper than 
 the potash salt. 
 
 Chromic acid is likewise now beginning to replace 
 bichromate of potash. 
 
 Preliminary Connections. Connect together binding screws 
 Nos. 2 and 3 (Fig. 38) by means of a short piece of wire, and 
 attach main or leading wires to Nos. 1 and 4. For this pur- 
 pose No. 1 8 gutta-percha-covered copper wire will be found 
 useful. The bared brightened ends of the wire are to be put 
 round the binding-screws, or better still, we may employ a 
 plate of copper (Fig. 40) provided with forked ends. This 
 
 Fig. 40. 
 METHOD OF CONNECTION WITH BINDING SCREWS. 
 
 Fig. 41. 
 SCHEME OF BATTERY. 
 
 plan gives a better contact, and is therefore much to be 
 preferred. Fig. 41 exhibits the manner in which the 
 battery is usually connected. Here the thin vertical lines 
 represent the carbons, the short thick wires the zincs, and 
 the battery is said to be in series. In the diagram there 
 are three cells, supposed to be connected together by wires 
 going from the carbon of one cell to the zinc of the next, 
 and so on. The end of the wire connected with the outer 
 zinc is called the negative pole (written - ), and that con- 
 nected with the outer carbon is called the positive pole 
 (written + ). When these poles are connected together 
 there will be a flow of electricity from the + to the - pole. 
 
in VOLTAIC ELECTRICITY 115 
 
 The battery now described should be used for the 
 following groups of experiments : 
 
 Group I. (a) Bring the free ends of the leading wires 
 together and then separate them ; a spark will be 
 produced. 
 
 (b) Attach a file to one leading wire and rub the other 
 pole along it ; the sparks will now be more brilliant. 
 
 (c) Attach a small piece of carbon rod to each leading 
 
 wire, bring the carbons together and separate them, 
 when a bright light will be produced. Observe 
 that the carbon rods get very hot. 
 
 (d) Twist a piece of thin iron wire round one pole and 
 then touch the free end of the iron wire with the 
 other terminal of the battery ; it will be found that 
 several inches of the wire may thus be kept at a 
 red heat, and if of short length the wire may even 
 be fused. 
 
 (e) Use fine copper wire of the same diameter instead 
 of the iron, and notice that it cannot be heated to 
 redness. 
 
 Group II. Additional Apparatus. Pohl's commutator 
 or instrument for changing the direction of the current 
 (Fig. 42) ; a magnet suspended from a stand ; a wire one 
 metre long stretched between the uprights (Fig. 43) and 
 mounted on a board. With the aid of the suspended 
 magnet set the wire in the magnetic meridian. See that 
 the cups of the commutator contain mercury, and that the 
 ends of the wires dipping into them are well amalgamated. 
 Connect the ends of the wire with the commutator. 
 
 Make connections such as are exhibited in Fig. 43, on 
 which the commutator is denoted by the cross. Trace 
 out these and ascertain the position of the commutator 
 switch that corresponds to a current from north to south 
 along the wire. Call this Position I., and that which gives 
 a current in the opposite direction Position II. Now break 
 
116 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 the current, and then suspend by means of a fibre over or 
 under the wire a short magnetic needle. The fibre should 
 
 S 
 
 Fig. 42. POHL'S COMMUTATOR. 
 
 The cups of the ebonite base contain mercury, and are in connection each with 
 its nearest binding screw. The switch hinged at A and B is moved by the in- 
 sulating handle S. 
 
 When the terminals of the battery are connected at E and F, or C and D, then 
 the ends of the main circuit are placed at A and B, and vice versa. 
 
 In the position shown, if a current entered at E it would ascend the left curved 
 wire, descend the lateral wire to A, pass through the main circuit to B, ascend 
 the right lateral wire and descend the curved wire to F. When the switch is 
 pushed back the current will traverse the horizontal wires and be reversed. 
 
 be attached to a stand so arranged that by means of a tele- 
 scopic joint or otherwise the magnet can be easily raised 
 
 Fig. 43. EXPERIMENT OF AMPERE. 
 
 or lowered. When the magnet is at rest turn the com- 
 mutator into Position I. and note the direction in which 
 
in VOLTAIC ELECTRICITY 117 
 
 the magnet is deflected. Then turn the commutator into 
 Position II. and again note the direction of the deflection 
 which is produced. Proceed in this manner to verify the 
 following table : 
 
 WIRE HORIZONTAL. 
 Position of Magnet. Position of Commutator. 
 
 Above wire . . . North end deflected to west. 
 
 Below wire ... ,, east. 
 
 Level of wire east side . South end dips. 
 
 ,, west side . North end ,, 
 
 II; 
 
 Above wire .... North end deflected to east. 
 Below wire .... ,, west. 
 
 Level of wire east side . . North end dips. 
 west side . South 
 
 WIRE VERTICAL. 
 
 North pole against the wire . . North end deflected to east. 
 South pole ,, ,, . . South end ,, 
 
 II. Current down the Wire. 
 
 North pole , , . . North end deflected to west. 
 
 South pole ,, ,, . . South end 
 
 Exercise. Cut out a cardboard model of a man, and 
 test your results against the following menwria technica. 
 Imagine a man to be swimming against the current, 
 which we may suppose to enter in at his head and leave at 
 his feet, his face being turned towards the needle. Under 
 these circumstances the north-seeking pole of the needle will 
 be deflected towards his right hand. 
 
 Group III. Apparatus. Glass tubing J-inch in diameter, 
 corks, soft-iron nails, iron filings. Experiments. (a) 
 Take a piece of the glass tubing about 3J inches 
 long, bore f-inch holes in two corks each about 1J 
 inch in diameter. Into these holes the ends of the 
 tubing have to be fitted to form reels. 1 Now make 
 
 1 Turned wood reels can be used instead, as shown in the figure. 
 
118 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 Fig. 44. 
 METHOD OF WINDING HELIX. 
 
 a small hole through one of the corks near the inside 
 edge, and inserting through it the 
 end of some No. 20 cotton-covered 
 wire, proceed to wind this on the 
 tube in the direction opposite to 
 that of the hands of a watch, 
 looking at the reel from above. 
 About 6 inches of the wire should 
 be passed through the hole before 
 beginning to wind (see A, Fig. 
 44). Continue winding until four 
 layers of wire are wrapped round 
 the tube, and then bring the other 
 end of the wire through a second hole in the cork 
 (B, Fig. 44). Connect the ends of the wire with 
 the battery. The helix will be found to behave as a 
 magnet, and its polarity must be examined by means 
 of the magnetoscope. Reverse the current and again 
 examine the helix, which will now -be found to 
 have its polarity reversed. 
 
 (b) Make a second helix, but wound in a direction the 
 
 contrary to that of the hands of a watch, and then 
 repeat the preceding experiments. The direction 
 of magnetisation or polarity of this second helix 
 will be found to be the opposite of that of the 
 first. 
 
 (c) Notice that soft iron wires are readily drawn into 
 the helices when the current is passing. Notice 
 also that when the central hollow of the helix is 
 filled up with such wires the magnetic power is 
 greatly increased, the polarity being the same as 
 that of the helix without the iron wires. See also if 
 your results conform with the following rule : Look 
 upon the helix from that end which makes the posi- 
 tive current appear to circulate in the direction of the 
 hands of a watch. This end will be the S. pole and the 
 
in VOLTAIC ELECTRICITY 119 
 
 other the N. pole of the helix. Hence if the helix 
 could be swung freely it would point magnetic north 
 and south, and the positive current would at the N. 
 pole ascend on the west side and descend on the east. 
 (d) Place the helix conveying the current vertical, with 
 a piece of cardboard across its end. Scatter filings 
 over it, and obtain magnetic curves with and with- 
 out a soft-iron core. 
 
 Grroup IV. Dip the two ends of the battery wires into 
 a small beaker containing dilute sulphuric acid, and leave 
 them there several minutes, the terminals not being in con- 
 tact with each other. It will be noticed that one terminal 
 becomes covered with bubbles, which collect and escape to 
 the surface, and that this is the one connected with the 
 negative, 'pole. The other terminal meanwhile becomes 
 cleaner and brighter, as if the acid were dissolving it. 
 That this is really the case will be seen by the liquid be- 
 coming blue, owing to the formation of copper sulphate. 
 If the action be continued sufficiently long the negative 
 terminal will become covered with a brown deposit, which 
 on examination will prove to be pure copper. 
 
 The general explanation of these appearances is as 
 follows : The current decomposes the liquid in which the 
 terminals are placed, that is to say, it decomposes the 
 dilute sulphuric acid, the copper terminal connected with the 
 positive pole taking the oxygen and sulphur, and produc- 
 ing sulphate of copper, while at the negative terminal the 
 free hydrogen, which forms the remaining portion of the 
 decomposed molecule, is allowed to escape. 
 
 When, however, besides free acid there is a sensible 
 quantity of sulphate of copper dissolved in the liquid, the 
 sulphate of copper is electrolytically decomposed, copper 
 is deposited upon the negative terminal, and acid is repro- 
 duced, which in its turn dissolves more copper at the 
 positive terminal or electrode. 
 
 B^vjp 
 
 
120 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 B 
 
 We shall see afterwards what advantage is taken of this 
 action in plating operations. 
 
 Note Draw in your note-book diagrams illustrating the above ex- 
 planations. 
 
 Group V. Proceed now to fit up a Voltameter, or 
 instrument for decomposing water and collecting the pro- 
 ducts, as follows : 
 
 (a) Cut off the shank of a 4-inch glass funnel to within 
 
 half an inch from the top. 
 
 (b) Procure a piece of platinum foil, ABCD, of the size 
 
 represented in Fig. 45, place it upon a brick, 
 and direct the blowpipe flame upon it. 
 Whilst the platinum foil is at a bright 
 red heat lay upon one end of it a short 
 piece of platinum wire, EF, and then 
 by means of a few smart taps with a 
 hammer weld the wire to the foil. 
 Wind the end F of the platinum wire 
 round one end of a piece of No. 20 copper 
 wire about 6 inches long, sprinkle a little 
 resin on the joint, on which a fragment 
 of soft solder has been placed, and pro- 
 ceed to solder it by means of a Bunsen's 
 burner. The electrode will now be fin- 
 ished. Next make a second one of the same size. 
 
 (c) Fit a cork into the end of the funnel, and, piercing 
 
 it with two holes by means of a knitting needle, 
 pass the copper wires through these so that the 
 platinum electrodes may be inside the funnel. 
 Well warm the funnel all round, melt some 
 paraffin wax and pour it in so as to fix the elec- 
 trodes in position and cover the copper wire. 
 (d) Procure two test tubes of exactly the same size. 
 Place the voltameter on a retort stand and pour 
 into it some dilute sulphuric acid (say 1 part of 
 
 1) 
 
 Fig. 45. 
 VOLTAMETER 
 ELECTRODE. 
 
in VOLTAIC ELECTRICITY 121 
 
 acid to 50 of water). Fill the test tubes likewise 
 with dilute acid and invert them over the plat- 
 inum electrodes. Finally connect the terminals to 
 the battery by means of clamp screws (see Appen- 
 dix). The acidulated water will now begin to be 
 decomposed, and the student will note the follow- 
 ing particulars : 
 
 (1) Gases are evolved from both electrodes. 
 
 (2) The gas in the tube connected with the 
 
 negative electrode accumulates twice as 
 rapidly as that connected with the positive. 
 
 (3) The gases respond to the tests for hydrogen 
 
 and oxygen, the relative volumes being 
 those in which these gases combine to 
 form water. 
 
 (4) By collecting both gases in one tube an ex- 
 
 plosive mixture is obtained. 
 
 Here again we have evidence of the decomposing power 
 of the electric current, and the student will observe how 
 peculiar must be that action which gives us all the hydro- 
 gen at the one terminal and all the oxygen at the other. 
 We may perhaps represent to ourselves what takes place 
 by means of the following hypothesis, due to Grotthuss : 
 First of all we may regard oxygen as an electro-negative 
 element and hydrogen as electro -positive. Under these 
 circumstances the oxygen ends of the various molecules 
 will all point to the positive terminal, to which they will 
 be attracted, while, on the other hand, the hydrogen ends 
 will all point to the negative terminal, to which they will 
 be attracted. 
 
 Now if the electric condition of these terminals be 
 strongly enough developed, the positive terminal will at- 
 tract the oxygen particle next it, and the negative terminal 
 the hydrogen particles next it, and these will be given off 
 at the respective terminals. This is the first operation. 
 
122 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 The next will be a change of partners. The hydrogen 
 of the molecule next the positive electrode having lost its 
 partner, will attach itself to the oxygen of the molecule next 
 but one to the electrode, the hydrogen of this to the oxy- 
 gen of the molecule next but two, and so on until the 
 whole line are once more properly paired. This is the 
 second operation. 
 
 They are not, however, yet facing the proper electrodes, 
 for the hydrogen will be facing the positive and the oxy- 
 gen the negative. They will therefore have all to turn 
 round about their centres through 180. This is the 
 third and final operation. After this the same round of 
 operations is repeated. 
 
 Note. Draw in your note-book a diagram illustrating the above 
 hypothesis. 
 
 Discharging the Battery. When we have done with the 
 battery it must be carried to the draught cupboard and 
 there discharged. Remove the clamps, wash and dry them. 
 Pour the nitric acid into a bottle labelled " Old nitric acid 
 for batteries ;" this maybe used again, unless it be of a 
 green colour. Thoroughly wash the porous pots and leave 
 them to soak in water. Notice if any black spots appear 
 on the zincs, and if so reamalgamate such places ; then 
 wash the zincs and leave them likewise to soak in water. 
 By soaking the porous pots and the zincs the zinc sulphate 
 will be removed, which would otherwise tend to block up 
 the pores of the pots and thus disintegrate them, and would 
 likewise crystallise on the surface of the zincs. The sul- 
 phuric acid should be thrown away, for it is sure to con- 
 tain nitric acid, which is very injurious to zinc. 
 
 39. The process of chemical decomposition effected by 
 the electric current is called electrolysis. The experi- 
 ments of Groups IV. and V. of the previous lesson are 
 examples of electrolysis. A very important part of electro- 
 lysis relates to the deposition of metals, hence the next 
 
in VOLTAIC ELECTRICITY 123 
 
 lesson will be devoted to the typical example of copper 
 deposition. 
 
 LESSON XX. The Daniell's Cell and Copper Plating. 
 
 40. Apparatus. A Daniell's cell of the kind exhibited 
 in Fig. 46, which forms a convenient arrangement. It 
 consists of a glazed earthenware pot or outer vessel P, 
 which is 13 cm. high 
 by 9 cm. in diameter. 
 In it stands a cylinder 
 of zinc Z?^, provided 
 with three tags or 
 tongues, a, b, c, and of 
 these the last has a 
 binding screw attached 
 to it. These tags are 
 formed by cutting away 
 portions from the ori- 
 ginal sheet of zinc that 
 has been employed to 
 form the cylinder. The 
 height of the cylinder 
 
 ?/. i ., -,. Fig. 46. DANJ ELL'S CELL. 
 
 is 10 cm., and its dia- 
 meter 8 cm., so that when placed in the earthenware pot 
 the zinc is supported by its tags, and the bottom of the 
 zinc is more than 2 cm. from- the bottom of the pot. 
 Within the zinc cylinder there is a porous potp, 13 cm. high 
 and 5 cm. in diameter, and this contains a cylinder of 
 copper Cu, provided with a single tag, to which a binding 
 screw is soldered. The porous pot has its mouth coated 
 with paraffin after the manner already described. A 
 small flask/, containing crystals of copper sulphate each 
 about the size of a small nut, is placed mouth downwards 
 in the copper cylinder. At the bottom of the outer pot 
 a few pieces of scrap zinc are placed ; this will help to 
 
124 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 decompose any copper sulphate solution that diffuses into 
 the outer pot. 
 
 The other materials required are as follows : Crystals 
 of zinc sulphate and of copper sulphate; some telegraphic 
 binding screws (see Appendix); india-rubber cork, f-inch 
 diameter, with two holes; some plates of copper '05 inch 
 thick ; a graduated measure ; sulphuric acid, caustic soda, 
 nitric acid ; brass wire, No. 28 ; a glass rod, a beaker, a 
 Bunsen's burner, and sundry materials for making solutions. 
 
 Charging the Battery. Place a saturated solution of 
 sulphate of copper in the porous pot. Into the flask already 
 mentioned put crystals of sulphate of copper of about the 
 size of small nuts, and fill it up with a saturated solution 
 of this material, then invert it, and let it stand thus in the 
 porous pot. The flask will now act as a supply reservoir to 
 keep up the strength of the copper sulphate solution. Into 
 the outer pot pour water in which some zinc sulphate has 
 been dissolved (1 part of zinc sulphate by weight to about 
 20 parts of water). The battery will now be ready for 
 use. Next connect the zinc and the copper by means of 
 a short wire and leave the cell thus for some time with 
 the current passing. In this condition it is said to be short- 
 circuited, which process will help to bring the cell to a 
 normal state of working. 
 
 Fitting up a Plating Bath. Fig. 47 exhibits the 
 requisite arrangement. Here ab is an india-rubber cork, 
 having two unconnected holes, an upper hole at the right, 
 and a lower one at the left. Into the hole at b there is 
 passed the shank of a telegraphic binding screw, which 
 serves to support a copper plate A by means of the 
 tag d, and to connect it with the wire from the positive 
 terminal of the battery. This large plate is called the 
 Anode. Into the hole at a passes the shank of a double 
 binding screw, formed by uniting together two ordinary 
 binding screws. This serves to support the plate C, which 
 must be smaller than A, and which forms the mam cath- 
 
VOLTAIC ELECTRICITY 
 
 125 
 
 ode, as well as a small Test Cathode T, and these are to 
 
 be connected with the negative terminal of the battery. The 
 
 whole arrangement is supported 
 
 in a glass battery jar by means 
 
 of brass wire, as shown in Fig. 
 
 47. This jar has to be filled 
 
 with liquid, whose composition 
 
 will be afterwards described. 
 
 We may here mention that when 
 
 in action the copper deposit goes 
 
 from the anode to the cathode, 
 
 and hence the propriety of 
 
 these names. 
 
 Cleansing the Copper Plates. 
 In the first place a scratch brush 
 (Fig. 48) should be made. This 
 can be readily done by driving 
 into a board two long nails 
 about 6 inches apart, and then 
 winding fine brass wire con- 
 tinuously from the one nail to 
 the other. Then bind the strands together by wire, and 
 cut off the ends. The arrangement may now be thrust 
 through a hole in a cork, in order that it may be pro- 
 vided with a handle, and we shall thus have a scratch- 
 
 Fig. 47. PLATING BATH. 
 
 Fig. 48. SCRATCH BRUSH. 
 
 brush with two ends. Secondly, make a lifting hook, which 
 is simply a rod of glass bent into the shape shown in 
 Fig. 49, and provided at one end with a cork handle. 
 Thirdly, prepare the following cleansing liquids, and label 
 them as under : 
 
126 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 No. 1. Alkaline Liquor for Cleansing Copper. 
 1 part by weight of caustic soda. 
 10 parts by weight of water. 
 
 No. 2. Sulphuric Acid Liquor for Cleansing Copper. 
 1 part by volume of sulphuric acid. 
 10 parts by volume of water. 
 
 No. 3. Dipping Liquor for Cleansing Copper. 
 1 vol. of impure nitric acid (residue from battery). 
 1 vol. of water. 
 
 No. 4. Brightening Liquor for Cleansing Copper. 
 Strong nitric acid, with a few drops of strong hydrochloric 
 acid added. 
 
 Enough of these solutions should be prepared to cover the 
 copper plates when they are placed therein. No. 1 should 
 be contained in a porcelain evaporating basin, and 
 the other solutions should be in glass beakers. 
 Fourthly, the copper plates may now be cleansed 
 as follows : (a) By means of the scratch -brush 
 thoroughly clean both sides of the plates, going 
 over the surfaces several times until the striae run 
 into each other ; (b) wash each plate with water 
 under the tap, rubbing it well with the fingers or 
 with a rag ; (c) boil the plate in the alkaline 
 liquor No. 1. This will cause a discoloration, 
 Fig. 49. owing to the formation of an oxide. Remove the 
 I SoSf pl ate by means of the lifter, which should be used 
 throughout the subsequent operations. Wash the 
 plate well under the tap, then carry it to liquor No. 2, in 
 which it should remain sufficiently long to enable the acid 
 to dissolve the dark -coloured oxide. Again wash it with 
 water, and then place it in liquor No. 3 for about 15 
 seconds, after which it must be washed and placed for a 
 few seconds in No. 4, and then quickly washed with distilled 
 water. The plate should be now very bright and clean. 
 If it is not so, the processes must be repeated. Let the 
 
in VOLTAIC ELECTRICITY 127 
 
 plate now be preserved in a dilute solution of copper sul- 
 phate until required for use. 
 
 Deposition of the Copper. The liquid with which the 
 depositing bath must be charged is obtained by dissolving 
 100 grms. of copper sulphate in 500 cc. of water. Let it 
 be boiled in a beaker until all is dissolved, and when cold 
 let 25 grms. of sulphuric acid be added. The liquid should 
 be bottled and labelled " Copper depositing liquid." 
 
 Next place as much of this liquid in the depositing 
 bath as will well cover the plates, and then connect the plates 
 with the proper battery poles, attaching the negative ter- 
 minal wire to the cathode or smaller plate, and the wire 
 from the positive pole to the anode or larger plate. Now, 
 place the apparatus in a place where it will not be disturbed 
 and cover it up to keep out dust and prevent evaporation. 
 The liquid should be stirred occasionally. The progress of 
 the deposition may be ascertained by examination of the 
 test plate. 
 
 In the course of a couple of days a bright copper deposit 
 will be obtained on the cathode, whilst the anode will be 
 found to be covered with a dark substance resembling mud. 1 
 When a sufficient deposit has been obtained, remove the 
 cathode, wash it well, dry, and preserve it for future 
 experiments. 2 
 
 41. The Galvanoscope. The existence of an electric cur- 
 rent may be proved by reference to its (1) heating, (2) 
 lighting, (3) chemical and (4) magnetic effects. An instru- 
 
 1 This substance is of complicated composition. Besides containing 
 disintegrated copper it may contain the impurities of commercial 
 copper, such as tin, antimony, sulphur, nickel, silica, selenium, gold, 
 cobalt, iron, and lead. 
 
 2 For further information the student should consult the various 
 treatises on electro -plating, such as: Practical Guide for the Gold 
 and Silver Electroplater, and the Galvanoplastic Operator, by Dr. 
 Wahl. London: Sampson Low, 1883. Art of Electro -Metallurgy, 
 by Dr. Gore. London : Longman and Co. Muspratt's Chemistry, 
 newed., p. 792, Article " Electro- Metallurgy," etc. 
 
128 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 ment arranged for the exhibition of any of these effects 
 would, properly speaking, be a current-indicator, detector, or 
 Galvanoscope. But as the magnetic effects produced by 
 the direct action of a current on a freely suspended mag- 
 net are by far the most con- 
 venient for observation, galvan- 
 oscopes are almost invariably 
 based upon the observation of 
 the deflection of a magnetic 
 needle. The methods of con- 
 struction of galvanoscopes are 
 extremely various. They may 
 roughly be classified into Verti- 
 cal Galvanoscopes and Horizontal 
 Galvanoscopes. Fig. 50 shows 
 a vertical galvanoscope of the 
 kind largely used by telegraphic 
 engineers, and called by them 
 a Detector. The instrument 
 consists of a vertical coil wound 
 
 at right angles to the plane of the paper, within which is 
 a pivoted magnetic needle. The needle is loaded so as 
 to rest in a vertical position. Fastened to the same axis 
 as the needle is a pointer, which moves over a circle 
 placed between the pointer and coil, graduated into degrees. 
 When a current passes, this needle, with its pointer, tends 
 to place itself in a horizontal position. 
 
 It may be asked how far an instrument such as a 
 detector may be used as a current measurer or Galvan- 
 ometer. If the angle of deflection of the needle were 
 strictly proportional to the current passing through the 
 coil, then the instrument would be of great value in com- 
 parative measurements. But this is by no means the 
 case, nor can the indications be valued by the help of 
 any simple rule. In order, therefore, to render the instru- 
 ment of service, it must be submitted to the process of 
 
 Fig. 50. 
 THE VERTICAL DETECTOR. 
 
in VOLTAIC ELECTRICITY 129 
 
 Calibration. We shall later on describe the necessary 
 process, and meanwhile confine ourselves to the assumption 
 that the greater the deflection the greater must be the 
 current circulating in the coils. This assumption will be 
 made in the next lesson, which deals with some further 
 fundamental experiments made with a horizontal gal- 
 vanoscope. 
 
 LESSON XXI The Galvanoscope; 
 
 42. Apparatus. A simple galvanoscope, or the following 
 materials for fitting one up, will be required : A tooth- 
 powder box about 3 inches in diameter, four binding 
 screws, No. 28 silk or cotton covered wire, 6 inches of 
 J-inch copper strip, wood for making a simple reel, namely, 
 a strip 9 inches by J inch by \ inch, a magnetic needle 2 
 inches long provided with an agate cap, a sewing needle 
 for pivot, galvanometer card or card-board for making it, a 
 piece of common window glass, thin board (g- inch thick) 
 on which to mount the card. 
 
 Making, Winding, and Fitting the Reel. Divide the strip 
 of wood into three equal oblong pieces, and fit them to- 
 gether in order to form a reel. Trim the ends so as to make 
 the reel fit somewhat tightly into the box. Make a small 
 hole at one end of the reel and pass through it 3 inches of 
 wire. Then wind continuously until the reel is nearly 
 filled with wire. Finally, pass the other end of the wire 
 through a second hole in the reel, then fit the reel into the 
 box. Pass the ends of the wire through holes in the lower 
 part of the box, and connect them with binding screws 
 screwed into the box. The bright ends of the wire may 
 be put round the ends of the binding screws, and then 
 firmly held in their place by screwing the binding screws 
 well into the wood. It is better still to make a soldered 
 contact, but if the binding screws are firm this will not be 
 necessary. 
 
 VOL. I K 
 
130 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 Mounting the Card. Gum or glue upon a thin board a 
 card graduated into degrees. Cut the board into a circular 
 shape so as just to fit inside the box. At its centre fix 
 the point of a needle so as to project upwards above the 
 board for about quarter of an inch or less. Upon this point 
 the agate cap of the magnetic needle is supposed to rest. 
 
 Fitting the Lid. Mark off a circle 2 inches in diameter 
 on the lid by means of compasses, and then cut out a hole 
 having the circle marked as its boundary. Take off the 
 rough edges by means of a file and sand-paper. 
 
 Next place the board which has the scale attached to it 
 on a sheet of glass, and cut the glass round its edge by 
 means of a diamond or substitute for a diamond. Snip 
 off the glass with pincers ; the glass ought now just to 
 fit inside the lid. 
 
 Putting the Pieces together. In the first place adjust the 
 card in the box so that the zero line of the graduation 
 shall lie along the direction of the strands of the wire. 
 Put the needle on its pivot, and cover the whole with the 
 box-lid. The instrument is now complete. Before being 
 used it must be placed in such a position that the needle 
 points to zero, in other words, the strands of the wire as 
 well as the needle must lie in the magnetic meridian. G. 
 of Fig. 51 shows the completed galvanoscope. 
 
 Use of Copper Strip. Where strong currents have to be 
 observed, it will be necessary to make use of a copper strip, 
 through which, and not through the wire of the galvan- 
 oscope, the current must be passed. In this case the 
 galvanoscope as above described, being properly pointed, 
 ought to be placed on the wooden block to which the 
 copper strip is fastened. In the arrangement sketched in 
 Fig. 5 1 the strip of copper is bent so as to form the three 
 sides of a square. It is pivoted to the wooden block so as 
 to move stiffly. This is done by screwing the binding 
 screws through holes in the copper into the wood. Accord- 
 ing to the strength of the current the copper strip must 
 
Ill 
 
 VOLTAIC ELECTRICITY 
 
 131 
 
 be turned round its bearings into a plane more or less 
 oblique to that of the block, this obliquity being greatest 
 when the current is strongest, and least when the current 
 is weakest. Or we may, 
 by means of a sliding ar- 
 rangement, place the gal- 
 vanoscope at a greater or 
 less distance from the cop- 
 per strip. In Fig. 52 the 
 copper strip is mounted 
 on a wooden hoop, and the 
 galvanoscope is mounted 
 so as to slide on a gradu- 
 ated platform. By either 
 of these arrangements, or 
 
 by a union of both, We GALVANOSCOPE wira COPPER STRIP. 
 
 can bring the most power- 
 ful currents within the range of the scale of the galvan- 
 oscope. 1 
 
 Fig. 52. SLIDING METHOD OF CHANGING SENSIBILITY. 
 
 Fitting up the Apparatus. The copper strip must be 
 
 1 The former of these arrangements exhibits the principle of Obach's 
 galvanometer, the latter the principle of Thomson's current meter, 
 instruments which are employed in measuring currents of different 
 strengths. 
 
132 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 connected with the battery by means of the appropriate 
 binding screws. When in action the copper strip must 
 lie in the plane of the magnetic meridian. The arrange- 
 ment may, if necessary, be firmly fixed to the table by a 
 wooden clamp. The battery and commutator must be east 
 or west of the galvanoscope (see Fig. 53), and the leading 
 
 Fig. 53. 
 
 wires should remain in a fixed position during the perform- 
 ance of the experiments. Of these the following are ex- 
 amples, which were all made by means of the copper strip : 
 Experiment I. One cell was found to give a deflection 
 
 i 
 
 Fig. 55. CELLS IN MULTIPLE ARC. 
 
 Fig. 54. Two CELLS 
 IN MULTIPLE ARC. 
 
 of 48, whilst two cells in series gave a deflection of 49, 
 or very nearly the same as before. 
 
 Experiment II. The two zinc terminals were connected 
 together, and the two carbon terminals were likewise con- 
 nected together, so as to form one large cell (see Fig. 54). 
 This method of connection is known as that of multiple 
 arc (where many cells have to be arranged in this manner, 
 
in VOLTAIC ELECTRICITY 133 
 
 it is best to place them as shown in Fig. 55). It was found 
 that the two cells in multiple arc gave a deflection of 62. 
 
 Experiment III. A piece of carbon rod, 8 inches long, 
 placed in the circuit reduced the strength, so that one 
 cell now gave only 16, while two cells in series gave 
 28, thereby showing that, when there is a resistance 
 external to the battery, the current is increased by adding 
 to the number of the cells. 
 
 Experiment IV. It was shown that the greater the 
 length of carbon rod in circuit, the less was the deflection. 
 
 Experiment V. Two carbon rods of the same length 
 placed alongside each other gave a greater deflection than 
 one rod alone. 
 
 Experiment VI. A piece of iron wire was coiled in a 
 spiral and placed in the circuit. The deflection was noted, 
 and then the iron was heated by means of a spirit lamp. 
 Thereupon the deflection became less, but when the wire was 
 allowed to cool the needle returned to its previous position. 
 
 43. Theory of the Battery. It may here be desirable to 
 give a short account of the principles of action of the vol- 
 taic battery, premising that in all probability these are not 
 yet fully understood, so that any statement we make must 
 only be regarded as a working hypothesis. If a zinc rod 
 or wire be soldered or closely united to a similar copper 
 rod or wire, an electric separation is produced at and over 
 the joining surfaces, in virtue of which 
 the zinc becomes positively and the 
 copper negatively electrified. This 
 electrical difference is not, however, 
 great, and its existence can only be 
 experimentally verified by means of 
 a delicate electrometer. Imagine now 
 (Fig. 56) a circuit of the following 
 nature, namely a thick semicircular zinc rod soldered or 
 united at two junctions to a similar copper rod. Shall 
 
134 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 we have a current from this arrangement? Unquestionably 
 not. At the upper junction there is no doubt a source of 
 electric irritation, in virtue of which positive electricity is 
 driven to the zinc or left-hand side, and negative electricity 
 to the copper or right-hand side, and if these two elec- 
 tricities could be allowed freely to unite in the remainder 
 of the circuit, we should certainly have a current as long as 
 the electric irritation was kept up. But this is not the 
 case, for the lower junction is a similar source of electrical 
 irritation, and will prevent the union of the two elec- 
 tricities, so that what we shall finally have will be, not a 
 current, but a distribution of statical electricity, in virtue 
 of which the zinc will remain positively and the copper 
 negatively electrified. Before we can get a current we 
 must be able to retain the irritation at the one junction 
 and neutralise it at the other. 
 
 It is this which is accomplished by means of the battery 
 liquid. Suppose that we dispense with the lower junction 
 and allow the rods to swell out into two plates or ter- 
 minals of their own material, which are to be immersed in 
 a vessel containing dilute sulphuric acid (Fig. 57). A mole- 
 cule of this dilute acid may be regarded as being com- 
 posed of two members or parts, one of these containing the 
 oxygen, which we may regard as negatively electric, and 
 the other the remainder of the mole- 
 cule, including the hydrogen, which 
 we may regard as positively electric. 
 The first eifect of the immersion of 
 the electrodes in dilute acid may be 
 regarded as a polarisation or point- 
 ing of these liquid molecules after 
 the manner which we have previously 
 described, namely, the ends containing 
 oxygen pointing to the zinc, and the 
 
 ends containing hydrogen to the copper terminal. Now, if 
 the positive electricity of the zinc terminal be more intense 
 
in VOLTAIC ELECTRICITY 135 
 
 than that of the hydrogen portion of the dilute acid mole- 
 cule, the oxygen portion will leave this hydrogen portion 
 and will unite with the zinc, which will thus be oxidised, 
 and, in like manner, at the other end the hydrogen portion 
 of the dilute acid molecule will go to the copper terminal, 
 carrying its positive electricity with it. By this means 
 negative electricity will constantly be carried to the zinc 
 and positive electricity to the copper terminal, so that the 
 electric difference of these terminals will be neutralised. 
 Meanwhile we may imagine that at the upper junction, the 
 source of electric irritation continuing to exist, a constant 
 supply of positive electricity is carried down the zinc side 
 and a similar supply of negative electricity down the 
 copper side, both of which are, as fast as they descend, 
 neutralised after the manner we have now described. But 
 a current of negative electricity flowing down the right- 
 hand side is equivalent to a current of positive electricity 
 flowing up, so that, taking both sides together, we have 
 virtually a current of positive electricity flowing round the 
 circuit in a direction the opposite to that of the hands of 
 a watch, and passing in the liquid from the zinc to the 
 copper. 
 
 The combination of the zinc with the oxygen, and the 
 solution of the oxide in the liquid, involves of course the 
 gradual wasting away of the zinc, which may be said to be 
 slowly burned in a liquid manner. This burning is the 
 source of energy in the arrangement, to which the zinc 
 serves as fuel, while the peculiar construction of the circuit 
 is adapted to convert this energy into the form of a current 
 of electricity. We have in fact to look for the mechanical 
 equivalent of the energy displayed to the burning of the zinc, 
 and for the peculiar form which this energy takes to the 
 arrangement of the circuit. If we did not amalgamate the 
 zinc there would probably be a difference in hardness and 
 chemical composition, between different parts of the same 
 plate. These differences would give rise to local currents, 
 
136 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 so that the energy due to the combustion of the zinc 
 would be partly spent on these local currents, to the 
 weakening of the main current of the battery, which it 
 is our object to strengthen as much as possible. Thus 
 amalgamation of the zinc, by equalising the chemical com- 
 position all over the plate, prevents the formation of these 
 local currents, so that the whole energy of the combustion 
 is directed towards the main current. But it will be asked, 
 What becomes of the hydrogen which is set free on the 
 copper plate ? It cannot, of course, combine with the 
 copper, and will ultimately no doubt form bubbles and 
 escape to the surface. Meanwhile, however, it may envelop 
 the copper terminal, and, by means of the tendency to send 
 a current in the opposite direction or Polarisation thus 
 produced, act detrimentally upon the production of the cur- 
 rent, which will become quickly enfeebled from this cause. 
 It becomes therefore a matter of importance to prevent 
 this deposition of hydrogen and consequent polarisation, 
 so as to obtain a constant current from our battery. This 
 is done in Bunsen's battery, which we have just been de- 
 scribing. Here, under ordinary circumstances, while the 
 amalgamated zinc would be gradually oxidised by the 
 dilute sulphuric acid, the hydrogen would be deposited on 
 the carbon plate, which plays the part of the copper, and 
 thus polarise it; but this deposition is prevented by im- 
 mersing the carbon plate in strong nitric acid enclosed in 
 a porous cell. By this means the nascent hydrogen is 
 immediately oxidised by the oxygen of the acid, and its 
 deposition upon the carbon plate is effectually prevented. 
 The nitric acid will of course, owing to the loss of oxygen, 
 become gradually changed in its composition, and useless 
 for the purpose. 
 
 Exercises. 
 
 1. Sketch and explain the electric action that causes the battery 
 current. 
 
 2. As far as energy is concerned, what is the current due to ? 
 
in VOLTAIC ELECTRICITY 137 
 
 3. "What is the use of amalgamating the zincs 1 
 
 4. Explain the part played by the porous cell. 
 
 44. Electromotive Force. We have here spoken of the 
 electric difference which is continuously kept up at the 
 junction of dissimilar metals; this may be termed (for 
 the present purpose) the Electromotive Force of the 
 arrangement, and is generally denoted by the letter E. 
 This electromotive force may be regarded as chiefly, at all 
 events, depending upon the electro-chemical difference be- 
 tween the two plates, so that zinc and copper would give 
 one value of E, zinc and carbon a second, zinc and plati- 
 num a third, and so on. Suppose we confine ourselves to 
 zinc and carbon, then, if we have a single cell, its electro- 
 motive force will be E. If, however, we have two cells in 
 series, that is to say, the zinc of the one cell being con- 
 nected with the carbon of the next, we shall have a total 
 electromotive force equal to 2E, if three cells in series, 
 3E, and so on. 
 
 45. Ohm's Law. It must not, however, be imagined 
 that if two circuits have the same electromotive force the 
 current will necessarily be the same in each. This leads 
 us to discuss the law which regulates the rate of 
 
 flow, intensity, or strength of the current produced, 
 known as Ohm's law, because it was discovered by 
 Ohm, a German physician. 
 
 In order to explain this law, imagine that we 
 have a thick cylindrical metallic rod (Fig. 58), of 
 which the upper cross-section A is kept at an 
 electric potential or level different from that of 
 the lower cross -section B. This difference of 
 electrical level we shall call E. In consequence of this 
 electrical difference between the top and bottom being 
 kept up at these places, there will be a continued flow 
 of electricity from the top to the bottom, the strength of 
 which will depend amongst other things upon the value of 
 
138 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 E ; double E and you double the flow, make E three times 
 as great and you increase the flow in the same proportion, 
 and so on. Thus the strength of the current or C is 
 proportional to the electromotive force or E. 
 
 In the next place, the flow of electricity will be propor- 
 tional to the cross-section of the rod at A, so that if we 
 double the cross -section we shall double the flow. The 
 double cross -section virtually makes the single rod into 
 two rods, and this law hardly requires further explanation. 
 The next point is that if we double the length of the rod 
 we halve the flow, other things being the same in other 
 words, the flow is inversely proportional to the length of the 
 rod. To prove this, let us suppose that the rod in the 
 above diagram is cut by an imaginary cross-section half- 
 way between the top and the bottom. The electrical dif- 
 ference between this section and the bottom will only be 
 one half of that between the top and the bottom, or it will 
 be j, and yet, since we have not altered the state of things, 
 we shall have the same current C as before in the lower 
 half of the rod. In other words, we may either regard 
 the current C as produced by an electrical difference E 
 between the top and bottom of the rod, or by an electrical 
 difference equal to -% between the middle and bottom of the 
 rod. Now had there been an electric difference = E be- 
 tween the middle and the bottom, we should obviously 
 have had a double current in other words, for the same 
 electrical difference the current is inversely proportional to 
 the length of the rod. 
 
 Finally, the amount of current will depend upon the 
 nature of the rod if it be of copper there will be a large 
 flow for a small electrical difference, if it be of wood the 
 flow will be much smaller, and if of ebonite there will be 
 scarcely any flow whatever. 
 
 All that we have now stated is conveniently expressed 
 by Ohm's law and the other laws associated with it. The 
 
in VOLTAIC ELECTRICITY 139 
 
 following is a statement of Ohm's law : Let represent the 
 strength of the current in a circuit, E the electromotive 
 force, and R the resistance this current experiences from 
 the materials of the circuit, then 
 
 r _E 
 -R- 
 
 To define the resistance, or that which impedes the flow 
 of electricity, we must bear in mind what we have already 
 indicated above : (1.) that the conductivity is directly, and 
 hence the resistance is inversely, proportional to the cross- 
 section of a rod or wire ; (2.) that the conductivity is in- 
 versely, and hence the resistance is directly, proportional to 
 the length ; (3.) that the conductivity depends on the sub- 
 stance of which the rod or wire is composed, each substance 
 having its own specific conductivity ; hence the resistance 
 also depends on a specific resistance, which will vary in- 
 versely with the specific conductivity. In fine, resistance 
 may be regarded as the reciprocal of conductivity, so 
 that we may either assert that the current is jointly and 
 directly proportional to the electromotive force and the 
 conductivity of the circuit, or directly proportional to 
 the electromotive force and inversely proportional to the 
 resistance. 
 
 The resistance of a circuit is usually divided into two 
 parts the internal or essential resistance of the battery, 
 consisting chiefly of that of the liquid into which the 
 plates are immersed, and the external resistance, which 
 may be varied according to circumstances. The laws now 
 given apply equally to the internal and to the external 
 resistance. If we denote the former by E. and the latter 
 by r, then Ohm's law will stand as follows : 
 
 C- 
 - 
 
 We may now apply Ohm's law to give an explanation 
 of the experiments of Lesson XXI. 
 
140 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 In the first place, for one cell, without any external re- 
 sistance except the copper strip, we shall have C = ^, while 
 for two such cells in series we shall have C = || = |. Thus 
 both theory and experiment agree in demonstrating 
 that the current is the same in these two cases as 
 a matter of fact the galvanoscope indications were 48 
 and 49. 
 
 Again, when the two cells are connected together in 
 multiple arc, we have virtually one large cell of a double 
 cross-section. Here the current will be, since the resist- 
 ance is halved owing to the cross-section being doubled, 
 = ^ = ^- Accordingly we ought to have a double 
 current, and, as a matter of fact, the galvanoscope indica- 
 tions increased from 48 to 62. We must not, however, 
 in the meantime attempt to use these numbers to give 
 us an accurate measurement of the comparative intensity 
 of the current in the two cases ; this will come afterwards, 
 when we describe the galvanometer. Suffice it, however, 
 that both by theory and experiment the current is much 
 larger when we have the two cells connected in multiple 
 arc than when we have a single cell or two cells in series. 
 Thirdly, when we interpose a considerable external resist- 
 ance, such as a piece of carbon rod, not only is the current 
 greatly reduced in strength (from 48 to 16), but the two 
 cells in series give us decidedly more than a single cell, 
 the numbers being 16 for a single cell, and 28 for the two 
 cells in series. This follows at once from Ohm's law, which 
 will give us for a single cell under these circumstances 
 Cj = j^p, and for two cells C 2 = g^,- Now if r is consider- 
 able, C 2 will be decidedly greater than C T , and if it be very 
 great compared to R, C 2 will be nearly double of Cj. 
 
 Finally, we see from Experiment IV. that a rise of 
 temperature increases the resistance of an iron wire, and 
 the same law will hold for other metals. 
 
 When the external part of a circuit is composed of 
 
in VOLTAIC ELECTRICITY 141 
 
 varying resistances, we must remember, in applying Ohm's 
 law to it, that the same quantity of electricity passes in 
 one second through every cross-section of the circuit. For 
 if this were not the case, more positive electricity might be 
 carried into some region than was carried out of it, so that 
 positive electricity would there accumulate, or less might be 
 carried in than was carried out, so that the region would 
 become more and more negative. But both of these sup- 
 positions are inadmissible, inasmuch as when a current is 
 established we have a constant state of things. We must 
 therefore suppose that the quantity of electricity passing 
 any cross-section in unit of time, or, in other words, the 
 current, is constant throughout the circuit. Now under 
 these circumstances, what we have already said will lead 
 the reader to infer that the difference of potential (which 
 we shall take to be the cause of the electromotive force) 
 between any two points in a circuit must so dispose itself as 
 to be proportional to the resistance between these points, 
 so that the greater the resistance, so much the greater 
 is the electromotive force. In other words, we have in the 
 whole circuit a given electromotive force E to dispose of, 
 and this must be distributed along the circuit, so that the 
 force between two points shall always be proportional to 
 the resistance between these points. 
 
 Exercises. 
 
 1. Define Ohm's law. 
 
 2. Explain your own experiments of Lesson XXI. in accordance 
 with Ohm's law. 
 
 46. The Units of Theory and Practice. Ohm's law may 
 be written in three ways : 
 
 = CR ..... (2) 
 = ..... (3) 
 
142 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 If in (1) E = 1 and R = 1, we define 
 
 Unit current as the current in a circuit with unit E. M. F. and 
 unit resistance (4) 
 
 If in (2) C = 1 and E = 1, then we define 
 
 Unit E. M. F. as the E. M. F. in a circuit with unit current and 
 unit resistance . . . (5) 
 
 If in (3) E = 1 and C = 1, we define 
 
 Unit resistance as the resistance in a circuit with unit E. M. F. 
 and unit current (6) 
 
 Having then fixed upon independent values for any 
 two of the units, the third will be determined by one of the 
 definitions (4), (5), or (6). We are at liberty to select 
 any units we please. Thus, for instance, the unit current 
 might be that produced by a Daniell's cell of a certain 
 construction and size when its poles were connected by a 
 specified wire ; and the unit of resistance might be that 
 between the ends of a cylinder of pure silver of specified 
 diameter and length. But every one is now agreed that it 
 is desirable that the units should be derived from the 
 fundamental units of length, mass, and time adopted in this 
 work, namely the centimetre, the gramme, and the second. 
 Accordingly methods have been devised of defining the 
 electrical units with reference to these three fundamental 
 units. 
 
 The units so obtained are of very inconvenient mag- 
 nitude for practical purposes, and hence practical units 
 have been chosen by taking a submultiple of the unit of 
 current and multiples of the units of E. M. F. and resist- 
 ance. Thus are obtained : 
 
 The ampere = KT 1 of the C. G. S. unit of current. 
 The volt =10 8 ,, ,, E. M. F. 
 
 The ohm = 10 9 ,, ,, resistance. 
 
 The units which we are here discussing are called Electro- 
 magnetic Units, to distinguish them from units of dif- 
 
in VOLTAIC ELECTRICITY 143 
 
 ferent nature called Electrostatic Units, which are 
 derived from the effects of electrostatic repulsion and 
 attraction. 
 
 It will be seen from the numerical values above given 
 that if we have a circuit in which the resistance is one 
 ohm and the E. M. F. one volt, then the strength of the 
 current will be one ampere ; for ^ = 10" 1 . 
 
 Ohm. A Committee of the British Association found 
 that the resistance of the ohm is represented nearly 
 by the resistance of a column of pure mercury 105 cm. 
 long and 1 sq. mm. in section at C. They caused 
 coils of an alloy of silver and platinum to be issued as 
 standards. Resistance coils based on these standards are 
 called B. A. ohms. Recent experiments of Lord Rayleigh 
 and others prove beyond doubt that the B. A. ohm is more 
 than one per cent too small. The B. A. ohm therefore 
 can only really be regarded as an empirical unit, just as is 
 the case with the standard metre. An attempt is, however, 
 being made to substitute for the old standards new ones of 
 correct value. These are called True Ohms, sometimes 
 Rayleigh Ohms. In accordance with the recommendations 
 of a Congress held at Paris in 1884 a legal ohm is denned 
 to be the resistance of a column of pure mercury about 
 one centimetre longer than that denning the B. A. ohm, or 
 106 cm. More exactly the relation between the units is 
 
 1 Congress oliin = l < 0112 B. A. ohm. 
 1 B. A. ohm = -9889 Congress ohm. 
 
 In Germany the Siemens unit or S. U. is largely used. 
 It is supposed to denote the resistance of a column of pure 
 mercury 1 sq. mm. in section and 1 metre long at C. 
 
 1 S. U. unit =-9540 B. A. ohm. 
 
 A megohm is one million ohms. A microhm is one 
 millionth of an ohm. 
 
144 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 Volt. 
 
 1 Congress volt=l'0112 B. A. volt. 
 
 A Darnell's cell has approximately an E. M. F. of one 
 volt. 
 
 Ampere. The ampere in common use being depend- 
 ent on the ratio of the volt to the ohm, is left unchanged, 
 and has the same value as the Congress ampere. 
 
 A milliampere is one thousandth of an ampere. 
 
 Exercises. 
 
 1. Define unit current. 
 
 2. "What is an amp&re, volt, and ohm ? 
 
 3. Distinguish between a "B. A. ohm" and a "legal ohm." 
 
 4. Find the number of microhms in a megohm. 
 
 5. Convert 5000 C. G. S. units of current into milliamperes. 
 
 47. The Mirror Galvanometer. To take advantage of 
 Ohm's law for electrical measurement the student must be 
 provided with a galvanometer. The best form of galvan- 
 ometer will be one in which currents are simply proportional 
 to the deflections. This is the case with the mirror galvan- 
 ometer, an instrument of extreme value to the electrician. 
 
 In the following lessons it will be necessary for the 
 student to have a mirror galvanometer of simple construc- 
 tion. The student may easily learn how to put together 
 such an instrument, and it is desirable that this should be 
 attempted by all students. 
 
 LESSON XXII. Construction of Mirror 
 Galvanometer. 
 
 48. Materials. A wooden base B (Figs. 59 and 60) 
 8 inches in diameter and 1 inch thick. A pillar P, 3 
 inches in diameter and 4 inches high, bored with a small 
 hole passing along its axis. A reel K, 3 inches in diameter 
 and 1J inch thick, with flanges of half an inch and a 
 
Ill 
 
 VOLTAIC ELECTRICITY 
 
 145 
 
 central hole 1J inch in diameter, with a small recess on 
 one face. A plug to fit the hole of the reel. The reel 
 with plug is seen in the two upper figures of Fig. 61. The 
 
 M 
 
 Fig. 59. SIMPLE MIRROR GALVANOMETER. 
 
 above may be prepared by any wood-turner. A round piece 
 of glass for window, to fit the recess in the reel. Bobbins 
 of No. 28 S.W.G. silk-covered, and No. 20 S.W.G. cotton- 
 covered, wire. Three binding screws (No. 3 telegraph 
 binding screws). A brass rod r to support the directing 
 magnet M, which may be of crinoline steel, and which is 
 VOL. I L 
 
146 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 en. 
 
 fixed to a cork C. The cork slides up or down the rod. 
 The magnetic needle for suspension requires to be attached 
 to the back of a small mirror. It has aluminium foil for 
 a damper and a cocoon fibre for suspension. The mag- 
 netic needle is made of watch spring. 
 
 Fig. 61. 
 PARTS OF MIRROR GALVANOMETER. 
 
 Fig. 60. 
 DIMENSIONS OF MIRROR GALVANOMETER. 
 
 Scale, Lamp, and Lens (Fig. 62). The scale requires three 
 pieces of wood. The base B 1 6 inches x 6 inches x 1 inch 
 thick. The front A 16 inches x 9 inches x \ inch thick. 
 The shade S 1 6 inches x 4 inches x J inch thick. The 
 front has a f-inch hole h 7-J- inches from the bottom. A 
 paper scale ab 16 inches long is divided into millimetres. 
 The lamp is a small paraffin lamp P that may be hooked 
 on to the scale, which is provided with two staples for the 
 purpose. A lens of 5 -inch focus is fitted on a cork sup- 
 ported by a bottle L laden with shot. The lens is used for 
 focusing (see Fig. 62). 
 
 Construction. /. Winding the Reel. This may be done 
 
Ill 
 
 VOLTAIC ELECTRICITY 
 
 147 
 
 by hand, but it is far more expeditious to employ the 
 simple machine of Fig. 63. The reel K is slipped upon 
 
 Fig. 62. SCALE, LAMP, AND LENS. 
 
 the somewhat conical axis, where it is wedged firmly. A 
 
 Fig. 63. WINDING THE REEL. 
 
 few turns of wire are then wound round the axis, and the 
 wire is then wound regularly on the reel with a moderate 
 
148 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 tension from the bobbin B, which may be mounted on a 
 metal axis supported by two uprights so as to revolve. 
 The winding machine and bobbin holder should be clamped 
 or screwed down to the table. First wind one layer of 
 No. 20 wire, then give it a coat of melted paraffin applied 
 with a brush, then wind a second and third layer, applying 
 paraffin to each. Leave about 12 inches of wire for 
 making connections ; this may be wound round the axis. 
 Secondly, replace on the winding machine the bobbin of 
 No. 20 wire by the bobbin of No. 28 silk-covered, and 
 wind on about 300 turns. Paraffin will not be required 
 with this wire, the insulation of the silk being sufficiently 
 good if the wire be not roughly handled. Should any bare 
 places appear they should be covered with tissue paper that 
 has been steeped in paraffin. 
 
 The free ends of the wires should be dipped in paraffin, 
 and they should be run together so as to leave the reel at 
 the same place. A piece of ribbon is wound round the 
 reel to keep the wire in its place and as a protection from 
 dust. 
 
 //. Fit together the woodwork, screw the pillar to 
 the base, fasten the reel on the top of the pillar by brackets 
 of zinc or brass, run the wires down through the hole in the 
 pillar and through that in the base, solder the end of the 
 No. 20 wire, and the beginning of the No. 28 to the same 
 binding screw, the other ends going to separate binding 
 screws placed one on each side of the common binding 
 screw ; thus the three screws will serve for the two coils, 
 and by using the extreme screws, the two coils may be 
 used in conjunction. It is best first to solder short lengths 
 of wire to the shanks of the binding screws before passing 
 them through the holes in the base, and then solder the 
 ends of these wires to the free ends of the coils, for it is 
 difficult to solder the latter directly to the short shanks of 
 the binding screws. The base may either be supported 
 by levelling screws (three window-fasteners do very well) 
 
in VOLTAIC ELECTRICITY 149 
 
 or raised until it is horizontal by means of three small 
 wooden feet. 
 
 ///. The next firing will be to make the needle. 
 Harden and magnetise J inch of watch spring, and fix 
 it to the back of a small mirror by wax. Cut out a 
 piece of aluminium foil in diamond shape, leaving a tag 
 to which the mirror must be fixed. The completed needle 
 is seen in Fig. 61, where the circular glass mirror, the 
 horizontal magnet, and the diamond -shaped aluminium 
 damper all these being in the same plane will be recog- 
 nised. A hole must be pierced in the end of the tag with 
 a small needle for the reception of the suspending fibre. 
 
 Notes. (1.) It is perhaps better to use a large disc of aluminium as 
 damper, in order that the air resistance may be as much as possible. 
 (2. ) The mirrors are best obtained from the opticians. They should 
 be ground concave of a metre focus. The mirrors made by silvering 
 microscopic glass by one of the chemical processes are generally not 
 satisfactory. 
 
 IF. Fix a small piece of wire to the inner portion of 
 the plug K (Fig. 61), and suspend the needle from it by 
 means of a single fibre of cocoon silk. This operation is 
 one requiring considerable skill and care; it does not, 
 however, require special description. 
 
 V. Next arrange the cork with the directing magnet 
 on the rod. Put in the window with a little putty. 
 
 VI. Fasten the scale together, stretch a wire across 
 the hole, and glue the paper scale upon the cross-piece. 
 
 Setting up of Galvanometer and Scale.- Place the instru- 
 ment in the magnetic meridian, and set the scale a 
 metre away, the centre of the scale being opposite to the 
 mirror and parallel to it. Eaise the galvanometer or scale, 
 and bend the aluminium support of the needle slightly, if 
 necessary, until the reflection from the mirror falls on the 
 scale. Focus by means of the lens until a distinct image 
 of the wire is obtained in the middle of the image of the 
 hole upon the scale. Bring this image to the middle of the 
 
150 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 scale by turning the directing magnet. The instrument 
 will now be ready for use. 
 
 49. Use of Box of Coils. It is necessary in many 
 experiments to have the means of varying by degrees the 
 amount of resistance in a galvanic circuit. A box of 
 coils arranged in series is generally used for this purpose 
 whenever the requisite variation is capable of being made 
 by steps, none of which are less than a unit of resistance. 
 Fig. 64 exhibits the interior of such a box of coils as usually 
 
 Fig. 64. INTERIOR OF Box OF COILS. 
 
 arranged, so as to serve the double purpose of a resistance 
 box and a Wheatstone's bridge. In the present lesson it 
 is only required for the former purpose. A plan of 
 the arrangement of the coils is seen in Fig. 65. On a 
 block of ebonite abed there are mounted a good many 
 thick brass connecting pieces distributed in three rows, 
 somewhat in the shape of the letter S. The parts AB, BC 
 are known as the Proportional Arms. These are con- 
 nected with the Rheostat Arms DEF by means of a 
 brass piece CD, movable at pleasure by unscrewing its 
 
VOLTAIC ELECTRICITY 
 
 151 
 
 clamp screws at C and D. At A, B, C, D, E and F are 
 binding screws. Between each of the brass pieces there is 
 a space into which a well-fitting brass plug or stopper may 
 be placed so as to make perfect metallic contact from the 
 one piece to the other. The plugs may be inserted or 
 removed at pleasure, being provided with an ebonite 
 handle for the purpose. The holes and plugs are all 
 exactly similar, so that any plug would fit any hole. On 
 
 Fig. 65, PLAN OF Box OF COILS. 
 
 the inside of the ebonite lid there are bobbins for holding 
 the wire. Each bobbin consists of a brass tube covered 
 with a layer of paper. It is provided at each end with 
 an ebonite disc. The bobbin is kept in position by two 
 screws which pass through the lower ebonite disc. These 
 screws are each in connection with the wire of the bobbin 
 below and with the corresponding brass segment on the 
 upper side of the ebonite lid ; but they may be separated 
 from the latter if necessary by unfastening two small 
 screws. Usually, however, the screw joints at these 
 points are soldered in order to render the contact more 
 secure. 
 
 The wire employed for these resistances is of German 
 silver, 1 selected both on account of its high resistance and 
 the small variation of this due to change of temperature. 
 The wire is covered with one or two layers of white silk. 
 
 1 German silver is an alloy of 50 to 60 parts of copper, 25 to 30 
 parts of zinc, and 15 to 20 parts of nickel. 
 
152 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 In winding the wire is doubled upon itself, and then 
 wound so doubled. This method is adopted in order to 
 avoid self-induction^ and also to avoid any electro-magnetic 
 effect which might vitiate the galvanometer readings. 
 For the lower resistances thick wires are employed, in 
 order that a great length of wire may be obtained, 
 and thus a more exact adjustment secured. Further- 
 more, the lower resistances may be subjected to greater 
 heat than the higher resistances. The actual sizes of the 
 wires used in the rheostat arm are exhibited in the follow- 
 ing table : 
 
 TABLE E. 
 
 SERIES OF WIRES SUITABLE FOR RESISTANCE COILS. 
 
 nh in Q Diameter of Wire 
 
 Ohms. in Inches> 
 
 1 '05 
 
 2 -05 
 5 '04 
 
 10 -031 
 
 20 -031 
 
 50 -022 
 
 Diameter of Wire 
 in Inches. 
 
 Ohms. 
 
 100 -020 
 
 200 '013 
 
 500 -013 
 
 1000 '008 
 
 2000 '008 
 
 5000 -005 
 
 The resistances of the various proportional arms are 1 0, 
 100, 1000, the sizes of wire as given above being used for 
 these resistances. 
 
 The student will understand that a set of standard 
 resistances plays in the measurements of resistance the 
 same part that a set of standard masses plays in the 
 measurements of mass. 
 
 50. Care and Use of the Box of Coils. The success of 
 some of the subsequent measurements will depend largely 
 upon the observance of the following precautions : (1.) The 
 ebonite should be free from dust, etc., especially in the 
 intervals between the brass pieces. A little paraffin oil 
 should be rubbed over the surface when it is cleaned. (2.) 
 The plugs should be bright and free from grease. They must 
 
in VOLTAIC ELECTRICITY 153 
 
 be made so as to fit well into their places, and they should be 
 tightened by means of a screw motion. Occasionally they may 
 be just touched with the finest emery paper, but this should 
 be done as seldom as possible, for otherwise the plugs may 
 become loose in their holes. (3.) The connecting pieces 
 and the surfaces of the connecting screws should be bright 
 and clean, and the screws should be firmly screwed in their 
 places. It is hardly necessary to remind the student that 
 when a plug is inserted into its hole between two brass 
 segments, the result is that the current virtually passes 
 through these segments and through the plug, which present 
 very small resistance, and not sensibly through the bobbin 
 which is underneath. When, however, the plug is with- 
 drawn, the current must all pass through the bobbin. 
 
 51. The Rheostat. It will be seen that the box of coils only 
 allows us to vary the resistance of a circuit by jumps or suc- 
 cessive steps, but often we wish to have a very gradual vari- 
 ation. This is accomplished by means of the rheostat, of 
 which Fig. 66 shows a simple and satisfactory form. Two 
 
 Fig. 66. STRAIGHT WIRE RHEOSTAT. 
 
 German-silver wires are laid side by side on a long graduated 
 board. The ends terminate in metal plates, to which they 
 are soldered. Two of the plates are seen at p and p', and 
 the other two are seen provided with binding screws. To 
 
154 PKACTICAL PHYSICS FOR SCHOOLS CH. 
 
 connect the two wires a movable metal contact piece c is 
 used. This has its lower edge (Pt) covered with a piece of 
 platinum foil. The contact piece is supported by two side 
 strips (one is seen at c'), and is made to press firmly on the 
 wires owing to the weight of a block of lead L that is held 
 by the side pieces. To prevent a lateral motion two guide 
 arms are provided, of which g is one. In use the instru- 
 ment is included in the circuit and the contact piece moved 
 until the desired resistance is obtained. 
 
 52. Figure of Merit. In order to express the sensibility 
 of a galvanometer in measurable terms, it is usual to deter- 
 mine the current in amperes which will be required to 
 produce a deflection on the scale of one division. 
 
 The current required is called the Figure of Merit. This 
 current, and therefore the figure of merit, will depend 
 upon the position of the directing magnet, and also upon 
 the distance of the scale from the galvanometer. It is 
 desirable that the scale should be kept at a fixed distance 
 from the galvanometer, so that it is the position of the 
 directing magnet that will have to be raised or lowered in 
 order to obtain the required sensibility. 
 
 LESSON XXIII. -Figure of Merit of Galvanometer. 
 
 53. Apparatus. A mirror galvanometer and its acces- 
 sories, a box of coils, a Dani ell's cell, a plug key (Fig. 67). 
 
 Method. For the purpose of this lesson it will be 
 necessary to obtain approximate values of the resistance of 
 the battery and of the galvanometer. 
 
 Resistance of the Galvanometer. Make connections as in 
 Fig. 68, where B is the battery, K a plug key, G the 
 galvanometer, E the box of coils, and S a shunt, or, in other 
 words, a short piece of wire placed so as to short-circuit the 
 battery at pleasure. When the shunt is of sufficiently small 
 resistance, the deflection of the galvanometer may be reduced 
 
Ill 
 
 VOLTAIC ELECTRICITY 
 
 155 
 
 to a readable amount. Furthermore, the combined resistance 
 of the battery and shunt will be so small, that in comparison 
 with that of the rest of the circuit it may be neglected. If 
 
 Fig. 67. PLUG KEY. 
 
 Fig. 08. 
 
 now resistance be introduced into the lower part of the 
 circuit by taking plugs out of the resistance box until the 
 original deflection is halved, we shall know that the total 
 resistance has been doubled, so that the added resistance 
 must be equal to that of the galvanometer. 
 
 Resistance of the Battery. To determine this the same 
 principle is applied, only the shunt is now transferred (Fig. 
 69) to the galvanometer. Here the resistance of the gal- 
 vanometer being very great compared to that of the shunt, 
 the great body of the current will go through the circuit 
 and shunt, and only a very small portion of it through the 
 galvanometer. The intensity of the current will therefore 
 be virtually regulated by the resistance of the main circuit, 
 and this intensity will of course be recorded by the gal- 
 vanometer. Thus by this arrangement the galvanometer 
 records the strength of the current, but does not sensibly 
 interfere with it. Now let us introduce, by means of the 
 box of coils, resistance until the deflection of the galvan- 
 ometer is halved; this means that the current is halved, 
 and that the resistance of the whole circuit is doubled. 
 Hence the additional resistance introduced must be equal 
 to that of the battery, as the joint resistance of shunt and 
 galvanometer is negligible. 
 
 In making these tests, if the battery should vary, the 
 
156 
 
 ' PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 results will be affected. It is therefore important to make 
 the tests quickly, and the battery circuit should only 
 remain closed while the tests are being made. More 
 especially is this true when the battery is short-circuited, 
 for it is a rule that the smaller the resistance of the circuit 
 the more liable is the battery to be inconstant. 
 
 Figure of Merit. Make connections as in Fig. 70. Em- 
 ploy resistances so as to give successively deflections of 
 about 150, 100, and 50 divisions. 
 
 JT 
 
 -HW- 
 
 B 
 
 Fig. 69. 
 
 Fig. 70. 
 
 Divide the electromotive power of the battery in volts 
 (a Daniell's cell with E. M. F. = 1*08 volt approximately) 
 by the total resistance in ohms of the circuit. This will 
 give the current in amperes, which, when divided by the 
 deflection, will give the figure of merit required. 
 
 Example Resistance of Galvanometer. To reduce deflec- 
 tion from 240 to 120 divisions, 9 ohms were required, 
 which is the resistance of the galvanometer. 
 
 Resistance of Battery, To reduce from 220 to 110, 3 
 ohms were required. 
 
 Figure of Merit. 
 
 R = Total Resistance. 
 2962 
 4342 
 8652 
 
 D = Deflection. 
 150 
 100 
 50 
 
 Figure of Merit = j^ 
 00000243 
 00000248 
 00000249 
 
 Mean '00000247 ampere, 
 or 2*47 microamperes. 
 
in VOLTAIC ELECTRICITY 157 
 
 The directing magnet had its north pole to north, and 
 was placed at the top of the support. 
 
 54. Determination of E. M. F. Unless we are provided 
 with standards of E. M. F., it will be difficult to determine 
 the E. M. F. of a cell in volts. No official standard has been 
 yet issued. The best available is a cell of Latimer Clark's 
 construction. 
 
 LESSON XXIV. Comparison of Electromotive 
 Forces by the High Resistance Method. 
 
 55. Exercise. To compare together the electromotive 
 force of various cells. 
 
 Apparatus. A coil of high resistance at least 5000 
 ohms, a mirror galvanometer and its accessories. 
 
 Method. This consists simply in observing the deflec- 
 tions produced when the high resistance is in circuit. 
 
 Theory of the Method. Let Ej be the electromotive force 
 of one of the cells (say a Daniell's cell), and E 2 that of 
 another cell (say one of Bunsen's). Also let B t and B 2 be 
 the respective resistances of these cells, while E is the 
 resistance of the external circuit, including the galvan- 
 ometer. When the Daniell's cell is in circuit we shall 
 have, by Ohm's law, 
 
 and when the Bunsen's cell is in circuit we shall have 
 hence 
 
 Now if R be very great compared to B, or B 2 , this propor- 
 tion will virtually become (since B! + E is sensibly the same 
 
 as B 2 + E) p 
 
 Ui :U, : : Jfij : 1C, (2) 
 
158 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 In other words, the electromotive forces are to one another 
 in the same proportion as the currents, that is to say, in 
 the same proportion as the deflections produced. 
 
 The higher the resistance E, the more accurate will be 
 this method. To obtain an idea of the error produced let 
 us imagine that the observed deflections are 100 and 200 
 divisions. This will, according to formula (2), also be the 
 ratios between the electromotive forces. But if the re- 
 sistance of the batteries be respectively 5 ohms and 0'5 
 ohm, and R be = 5000 ohms, we shall have by formula (1) 
 
 or almost exactly the same as before. 
 
 Example. Standard cell(E. M. F. = 1-46 volt) gave 190 
 divisions of deflection through 20,000 ohms. With the 
 same resistance the results with other cells were 
 
 Daniell, 148 divisions, hence E. M. F. = 1 ' 4 ^ 148 = 1-U volts 
 Bichromate, 260 = 1 ' 4 ^ x () 260 = 2-00 
 
 LESSON XXV. Proof of Ohm's Law. 
 
 56. Apparatus. A mirror galvanometer ; a coil of very 
 fine German-silver wire at least 5000 ohms in resistance ; 
 two small plates of copper having binding screws soldered 
 to them, and fixed to a board so that their inner edges 
 are just a metre apart ; a thin German-silver wire, which 
 is stretched tight along the board and soldered to the 
 copper plates ; a key or commutator ; a few cells of a 
 constant battery will likewise be required. 
 
 Method. Make connections as shown in Fig. 71, in 
 which B is the battery, K the key, G the galvanometer, 
 R the high resistance, PQ the German-silver wire. The 
 unconnected end of the wire leading from the high 
 
Ill 
 
 VOLTAIC ELECTRICITY 
 
 159 
 
 resistance should be filed into a wedge shape, and then 
 thrust through a cork, which is intended to serve as a 
 handle and prevent the temperature of the observer's 
 hand from affecting the wire. Observations are made 
 in the following order : place the free end at different 
 points along the wire, and read the deflection produced 
 at each point; reverse the poles of the battery, and 
 then repeat the observations in the opposite order. The 
 two results may be somewhat different, owing to possible 
 variation in the strength of the current. The mean should 
 therefore be taken. 
 
 ^-J 
 
 Fig. 71. PROOF OF OHM'S LAW. 
 
 Now if the differences of potential or electromotive force 
 along the wire are, as Ohm's law would indicate, proportional 
 to the resistances, that is to say, to the length of wire between 
 the two points at which the potential is taken or tapped, it 
 follows that the number expressing this resistance should have 
 a constant ratio to that expressing the difference of potential. 
 But the difference of potential will be expressed by the 
 current of the galvanometer which it produces, so that 
 ultimately this current will be proportional to the distance 
 between P and the free end of the galvanometer wire. 
 
 That this proportion holds fairly well will be seen from 
 the following series of experiments. But before exhibiting 
 
160 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 this series we would remark that the galvanometer circuit 
 is to be here regarded as one which taps the main circuit 
 above the wire and indicates the difference in potential by 
 means of the deflection produced, without sensibly inter- 
 fering with this main current. 
 Example. 
 
 Reading on PQ. 
 
 Deflection. 
 
 
 
 (1) 
 
 I. 
 
 II. 
 
 Mean (2). 
 
 (2) 
 
 (i) 
 
 10 
 
 11 
 
 12 
 
 11-5 
 
 1-150 
 
 20 
 
 24 
 
 24 
 
 24-0 
 
 1-200 
 
 30 
 
 37 
 
 35-5 
 
 36-3 
 
 1-210 
 
 40 
 
 48 
 
 47'5 
 
 47-8 
 
 1-195 
 
 50 
 
 60 
 
 59-5 
 
 59-8 
 
 1-196 
 
 60 
 
 70 
 
 70-5 
 
 70-3 
 
 1-171 
 
 70 
 
 82 
 
 82 
 
 82-0 
 
 1-171 
 
 80 
 
 94 
 
 94 
 
 94-0 
 
 1-174 
 
 90 
 
 106 
 
 106 
 
 106-0 
 
 1-178 
 
 100 
 
 118 
 
 118 
 
 118-0 
 
 1-180 
 
 The results of this lesson may best be represented 
 
 Fig. 72. 
 
 graphically. Let the line of abscissae or horizontal line 
 represent distances on the wire, and the line of ordinates 
 
Ill 
 
 VOLTAIC ELECTRICITY 
 
 161 
 
 the observed potentials at these points. On plotting the 
 observations we obtain a nearly straight line (Fig. 72). 
 This shows at once that the fall of potential between two 
 points is proportional to the resistance between these 
 points. This method of recording results will enable the 
 student to understand the principle of Wheatstone's Bridge. 
 
 57. Wheatstonds Bridge. Suppose that OAC and O'A'C' 
 (Fig. 73) are two wires whose resistances are represented by 
 
 Fig. 73. THEORY OP WHEATSTONE'S BRIDGE. 
 
 their lengths. Let their ends be connected by thick copper 
 pieces, 00' and CPC', of which the resistances may be 
 neglected. We shall suppose that a battery is connected 
 with 00' and CPC', whereby these parts are kept at a 
 constant difference of potential, represented by the equal 
 lines CD and CD' (the potential at 00' being supposed for 
 VOL. I M 
 
162 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 convenience equal to zero). The fall of potential along the 
 wires will be given by OBD and O'B'D'. Take any point A 
 in 00 and find the potential at this point by erecting an 
 ordinate AB. Now a corresponding point A' can be formed 
 along O'C', such that the potential A'B' at this point shall 
 be equal to AB. In this case a galvanometer connecting 
 A and A' would not indicate any current, since these points 
 being at equal potentials no current would pass from the one 
 to the other through the galvanometer. But under these 
 circumstances what must be the relation between the 
 resistances OA, AC, O'A', A'C' ? We have 
 
 OA AB A'B' O'A' 
 
 OA 
 
 O'A' 
 
 hence 
 
 OC~CD~C'D'~0'C" OA + AC~0'A' 
 
 OA O'A' 
 
 This is the principle of Wheatstone's Bridge, which is 
 usually arranged in the form shown in Fig. 74, where 
 
 P, Q, E, S are four resistances. If these be in the ratio 
 ? = *L then the galvanometer will not be affected. When 
 
in VOLTAIC ELECTRICITY 163 
 
 this adjustment is made any one of the four resistances 
 may be determined if the other three are known. 
 
 LESSON XXVI. The Wheats-tone's Bridge. 
 
 58. Apparatus. A mirror galvanometer with its acces- 
 sories. A slide half-metre Wheatstone's bridge, or the fol- 
 lowing materials for its manufacture : (1.) Board of var- 
 nished wood 2 feet long, 4 inches broad, f inch thick. (2.) 
 Some sheet copper T V inch thick. (3.) Seven telegraphic 
 binding screws. (4.) Uncovered German-silver wire, 2 feet 
 long, No. 28 S.W.G. (5.) A half-metre boxwood scale 
 \ inch broad and J inch thick. This should be divided 
 along one edge into half centimetres. (6.) Sixteen \ inch 
 brass screws. (7.) Two small pieces of copper, J inch 
 square, T X F inch thick. 
 
 Method of Manufacture. The completed bridge is shown 
 in Fig. 75. At CDE and FGH are L-shaped pieces of 
 
 Fig. 75. SIMPLE WHEATSTONE BRIDGE. 
 
 sheet copper, each provided with two binding screws. AB 
 is a straight piece of copper with three binding screws. 
 Between E and H is the boxwood scale, having a German- 
 silver wire stretched along its upper surface and soldered 
 to the copper at E and H. In making the bridge 
 (1.) The copper strips should be cut out. Fig. 76 shows 
 their shapes and dimensions. They will require to be 
 drilled with holes just large enough to receive the shank 
 of a binding screw at the places marked with large 
 circles ; also with smaller holes at the places shown, in 
 order to receive the screws for fastening the coppers to 
 
164 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 Fig. 76. 
 
 the board. (2.) The boxwood scale must be screwed down 
 in the position shown in Fig. 75, the heads of the screws 
 being screwed below the surface 
 
 o e . Q^g |0( of the gcale> (3^ r rhe bindillg 
 
 screws must be soldered to the 
 copper straps. This operation may 
 be performed without a soldering 
 iron, the strips being heated in 
 a Bunsen's flame. Also at the 
 shaded portion of the L-shaped pieces a square piece of 
 copper must be soldered, in order that the level of the 
 copper may be brought up to the level of the scale. (4.) 
 Bore holes in the wood to admit the shanks of the binding 
 screws, then fasten the copper strips down by means of 
 the screws. (5.) One end of about 2 feet of the German- 
 silver wire, which must not have an insulating covering, 1 
 is to be soldered to E, then, the other end being held by 
 an assistant, the wire must be stretched straight along 
 the scale and then soldered at H. The soldering should be 
 performed by means of a small iron, and care should be 
 taken that the wire is in metallic communication with the 
 coppers at the ends of the scale. 
 
 The Bridge Connections. Fig. 77 shows the necessary 
 
 Sli 
 
 Fig. 77. SCHEME OF BRIDGE CONNECTIONS. 
 
 1 To remove silk from a wire without injury to the wire, it should 
 be boiled in a strong solution of caustic soda. 
 
in VOLTAIC ELECTRICITY 165 
 
 arrangement for comparisons of resistance. Here the 
 letters correspond with those of Fig. 74, which should 
 be first drawn by the student, in order to help him in 
 making his connections. It will be noticed that in the 
 arrangement used in practice E and S are varied at will 
 by sliding the battery terminal along the German -silver 
 wire. To do this more conveniently the battery terminal 
 is thrust through a cork at C, and the end of the wire 
 is filed into a wedge-shaped form. A portion of the cork 
 may be cut away if necessary, so that it may be held 
 against the edge of the base board as it is moved along. 
 The galvanometer (G) should be provided with a simple 
 shunt (Sh) for lessening its sensibility at will. 
 
 Operations with the Bridge. (1.) Measure 8 feet (i.e. four 
 times the length of the base board) of No. 36 S.W.G. silk- 
 covered copper wire. Make it into a doubly wound spiral, 
 and connect its bared ends across the gap P of the bridge. 
 Make a second spiral in exactly the same manner, and 
 connect it across the gap Q. Shunt the galvanometer, and 
 touch the end F of the bridge with the free battery 
 terminal, the galvanometer will be deflected, say, to the 
 right ; now touch the end E and the deflection should be 
 to the left. This will show that the connections are 
 correct, that the contacts at P and Q are good, and that 
 neither of the spirals is broken. Find roughly the position 
 at which the galvanometer shows no deflection, then remove 
 the shunt and obtain the position of equilibrium more 
 accurately. Call the position of equilibrium a, then, since 
 the bridge may be considered to be divided into 1000 parts, 
 we shall have 
 
 a 
 
 Q 1000-a 
 
 Example. The bridge reading is 499, hence 
 P_ 499 _499_ 1 
 Q ~ 1000 - 499 ~ 501 ~ 1 '004' 
 
 or P is very nearly equal to Q. 
 
166 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 (2.) Make a third spiral of 8 feet of No. 36, place it 
 in the same screw holes as the spiral at P, so that the 
 two spirals are in multiple arc. Now compare the two 
 resistances. 
 Example. 
 
 a=331 1000-a=669 
 
 P_331_ 1 
 Q~669~2'02 
 
 or the wires in multiple arc have only half the resistance 
 of the single wire. 
 
 (3.) Place the two spirals at P in series by connecting 
 their ends by small clamps, and again compare the resist- 
 ances. 
 
 Example. 
 
 a=668 1000-a = 332 
 
 P_668 
 Q-3~32- 2 
 
 4_i 
 
 showing that the effect of doubling the length of the wire 
 is to double the resistance. 
 
 (4.) Take 8 feet of No. 28 S.W.G. copper wire for Q 
 and balance it against 8 feet of No. 36 for P. Find the 
 average diameter of both wires as exactly as possible by 
 the micrometer-calliper. 
 
 Example. 
 
 a = 819 1000-a = 181 
 
 p 819 A.M 
 Q = l8i = 452 
 
 Diameters No. 28= *015 inch ; No. 36= '007 inch. 
 Square of diameter, No. 28 _ '000225 _ 
 Square of diameter, No. 36 ~ '000049"' 
 
 from which we see that the resistance varies inversely as 
 the square of the diameter. 
 
 (5.) Compare the resistance of one spiral of No. 28 at 
 P and the other at Q in multiple arc with the spiral of No. 
 36. 
 
in VOLTAIC ELECTRICITY 167 
 
 Example. | = 1-221. 
 
 Now we have previously found that the spiral of No. 36 
 wire had a resistance of 4*52, calling that of the spiral of 
 No. 28 unity. What then will be the resistance of the 
 spirals in multiple arc 1 This is found by aid of the follow- 
 ing rule : The resistance of wires in multiple arc is equal to the 
 reciprocal of the sum of the reciprocals of the respective resist- 
 ances. Thus in the above case the resistance of Q will be 
 
 1 1 
 
 1 -1-221- 
 + 4-52 
 
 (6.) Calibrate a rheostat, such as that of Fig. 66. 
 
 LESSON XXVII. Manufacture of a One-Ohm CoiL 
 
 59. Apparatus. The same as before, with the addition 
 of some silk-covered German-silver wire, No. 28 S.W.G.; 
 materials for mounting the coil, and a standard ohm. 
 
 Method. Cut off one metre length of the wire and 
 measure its resistance, then calculate what should be the 
 length to give one ohm resistance. From the total length 
 cut off a piece rather greater than the calculated length, 
 and proceed to mount it with attached terminals for 
 future use. The methods of mounting that might be 
 adopted are very various. In Fig. 78 we have one of the 
 simplest of these. Here ab is a flat piece of hard wood, 
 notched along its two edges. The wire is wound between 
 the notches, and the ends are soldered to two copper strips c 
 and c'. Each copper strip must have a small hole h through 
 which the German-silver wire may be passed before it is 
 ultimately soldered to the copper ; also a hole for a screw s 
 for securing the copper to the wood, and a notch n which fits 
 the binding screw of the bridge. Ribbon or tape is wound 
 
168 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 outside the wire for protection, its ends being secured by 
 small tacks. The wire having been mounted must have 
 its resistance tested ; if this should be found to be rather 
 too great the wire should be unsoldered at one end, drawn 
 
 Zi 
 
 Fig. 78. THE ONE-OHM COIL. 
 
 through the small hole in the copper, and again soldered. 
 This adjustment must be repeated if necessary. It is not, 
 however, desirable to spend much time in making an exact 
 adjustment, but when this is sufficiently good the resistance 
 should be measured as exactly as possible, and its value 
 recorded on the wood. 
 
 Example. One metre of the wire gave against the 
 standard ohm a balance on the bridge at 52, hence its 
 resistance was 100 ^ 2 _ 520 = 1*083 ohm. Hence the length of 
 1 ohm in millimetres will be 1 -^ 1 = 923 millimetres. A 
 piece 925 mm. was cut off and mounted, as described; its 
 resistance was found rather too great. On reducing the 
 length about 1 '5 mm. it was found to be almost an ohm. 
 
 LESSON XXVIII. Calibration of Galvanoscope. 
 
 60. Apparatus. That of Lessons XXIII., XXIV., and 
 XXVI. ; also a Bunsen's or a Grove's cell. 
 
 Metlwd. (1.) Charge the cell and compare its E. M. F. 
 with that of a standard cell by Lesson XXIV. (2.) Measure 
 
Ill 
 
 VOLTAIC ELECTRICITY 
 
 169 
 
 the resistance of the galvanoscope by Lesson XXVI. (3.) 
 Measure the internal resistance of the cell by Lesson 
 XXIII. (4.) Connect the cell, box of coils, and galvan- 
 oscope in series, and take readings of the latter with dif- 
 ferent resistances in the circuit. (5.) Calculate the current 
 in amperes producing the different deflections. Draw a 
 table up for use with the instrument ; also plot a curve 
 showing the relation between the currents and deflec- 
 tions. 
 
 Example. A vertical galvanoscope was calibrated. 
 
 E. M. F. of cell = 1-87 volt. 
 
 Resistance of cell = '25 ohm, nearly. 
 
 Resistance of galvanoscope = 9*75 ohms. 
 
 If R be the resistance from box of coils, then the current 
 C in amperes will be C = R+ : i? 7 ft . B ' from which was cal- 
 culated the following table : 
 
 R. 
 
 C. 
 
 Deflection. 
 
 
 
 187 
 
 75 
 
 1 
 
 170 
 
 73 
 
 3 
 
 144 
 
 69 
 
 5 
 
 125 
 
 65 
 
 10 
 
 0935 
 
 58 
 
 15 
 
 0748 
 
 51 
 
 20 
 
 0623 
 
 45 
 
 30 
 
 0467 
 
 37 
 
 50 
 
 0311 
 
 25 
 
 100 
 
 0170 
 
 13 
 
 200 
 
 0089 
 
 7 
 
 The curve plotted from these numbers was regular. 
 
CHAPTER IV. 
 THE TANGENT GALVANOMETER. 
 
 61. WHEN the measurements that we require to obtain 
 do not need a sensitive galvanometer, it is often convenient 
 to use the tangent galvanometer. In order to under- 
 stand thoroughly the principle of the instrument it will be 
 desirable to make, by means of such an instrument, a 
 number of experiments. 
 
 LESSON XXIX. Proof of Law of Tangents. 
 
 62. Apparatus. (1.) A hoop provided with a single turn 
 of thick wire and a number of turns of fine wire. The 
 woodwork of the hoop should be cut away in one place to 
 allow of the number of turns to be counted and the mean 
 radius of the coil to be ascertained. 
 
 The hoop (Fig. 79) is mounted on a base provided with 
 two uprights, upon which the deflection magnetometer of 
 Lesson XIV. may be fixed so that it may slide to or from 
 the hoop. (2.) A box of coils, constant battery, a commu- 
 tator, and connecting wires. 
 
 Experiment I. To Verify the Law of Tangents. Arrange 
 the battery with the commutator, the box of coils and 
 the galvanometer being placed in series (see Fig. 80). The 
 battery used should be one of low resistance and of great 
 constancy, like a Bunsen's. We shall assume either that 
 its resistance is so low as to be negligible, or that it has 
 
CH. IV 
 
 THE TANGENT GALVANOMETER 
 
 171 
 
 been measured by the method of Lesson XXIII. It will 
 be taken for granted also that the resistance of the thin 
 
 Fig. 79. TANGENT GALVANOMETER WITH SLIDING COMPASS Box. 
 
 wire galvanometer coil has previously been ascertained by 
 means of the Wheatstone's bridge. 
 
 Place the coil of the instru- 
 ment in the magnetic meridian. 
 This should be the case when 
 the pointer is at zero. Change 
 the resistance in the circuit until 
 the deflection caused by putting 
 on the current is about 60. 
 Eead both ends of the needle, 
 reverse the current, and again 
 read the ends of he needle. 
 Take more plugs out of the re- 
 sistance box, so as to reduce the 
 deflection. Eepeat the readings. Again increase the resist- 
 ance, and proceed as before. Do this several times. Arrange 
 and calculate your results as in the following example : 
 
 Fig. 80. 
 
172 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 a 
 
 O Ol O> 
 
 (M CO <N 
 
 C^ CO I- 
 
 T* (M r-l 
 
 >p t~ GO 
 
 rH CO N 
 
 O> r- 1 OO 
 CD 1C W 
 
 01 01 00 rH 01 
 O (N O> O rH 
 t- 10 CO OS N 
 
 <M (M (M O O 
 
 g S g S 
 
 TH 01 00 N 
 
 t- O 1^- CO I-H 
 
 > O CO CO N 
 
 00 <M rH * 
 
 fe S ?? c^ S 
 
 Jt^, 
 
 rH CO 
 
 co g o> bO 
 
 ^ QTJ 03 ^ r T3 
 
 flfti 
 
 1*0 o -g 
 
 K 03 w t)0 "o 
 
 1 
 
 "S 
 
 5 
 
 ;-i 
 
 s i 
 
 , *i 
 
 ^ i j 
 
 - H 
 
 c3 ^** o> 
 
 i ^ 2J >* 
 
 "^ fM "-S 
 
 ^ ft'g 
 
 y ^ 
 
 23 rd S 
 
 ^cg 
 
 fi-s* 
 
 (=1 S G C 
 
 a -^ a a 
 
 ^ 'S ^_3 
 
iv THE TANGENT GALVANOMETER 173 
 
 Explanation. We wish to prove the following rela- 
 tion 
 
 Current = constant quantity, depending upon the size of hoop and 
 the number of the coils multiplied by the tangent of the angle of 
 deflection, 
 
 or using letters 
 
 C = Ktana (1) 
 
 where C is the current, K is the constant, and a the angle 
 of deflection. 
 
 Now, according to Ohm's law, 
 
 C =I < 2 > 
 
 where E is the E. M. F. of the battery used, which may 
 be supposed to remain constant, and II the total resistance 
 in the circuit. From (1) and (2) 
 
 -p 
 R tan a = ^r = constant. 
 
 Thus if (1) is correct, we ought to find that the resist- 
 ance of the circuit multiplied by the tangent of the angle 
 of deflection remains a constant quantity. In the previous 
 example this is seen to be the case within the limits of 
 error of the experiment. 
 
 Use of Graphical Method. We see from (1) and (2) 
 that tan a ought to vary inversely with E. If this is true, 
 by plotting tan a with reference to ^ a straight line should 
 be obtained, as in the analogous case of Lesson XXY. In 
 the previous example the values of tan a and of ^ have 
 been given to facilitate the use of the graphical method. 
 
 LESSON XXX. Proof of Law of Distance. 
 
 63. Exercise. To prove experimentally the law relating 
 to the action of the galvanometer coil on the magnetic 
 needle at different distances. 
 
174 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 Apparatus. As before. 
 
 Method. Take deflections with the compass box at 
 different distances from the coil, reading off the distances 
 by help of the pointers on the ends of the uprights and the 
 scales on the arms. Take readings on both sides of the 
 hoop, with the commutator in its two positions, in each 
 case reading both ends of the needle. Measure the mean 
 radius of the coil, and finally compare the tangents of the 
 mean deflections with values derived by calculation from 
 the formula 1 
 
 = tan a, 
 a' + rf 
 
 where a is the radius of the hoop and 
 hoop from centre of magnetic needle. 
 Example. a = 3*75 inches. 
 
 the distance of 
 
 (1.) 
 
 Distance from 
 
 (2.) 
 
 (3.) 
 
 (4.) 
 
 "(5.) 
 
 (6.) 
 Adopted 
 
 centre of com- 
 pass needle to 
 centre of coil 
 
 Mean de- 
 flection. 
 
 Tangent of 
 deflection. 
 
 Value of 
 
 3-3-4 
 
 value of 
 K a2 - 
 
 / .j i (>\2 
 
 
 or x. 
 
 
 
 
 
 
 inches. 
 
 J 
 
 
 
 
 
 o 
 
 40 
 
 8391 
 
 2667 
 
 3-147 
 
 8391 
 
 i-o 
 
 37 
 
 7536 
 
 2406 
 
 3-132 
 
 7570 
 
 1-5 
 
 34 
 
 6745 
 
 2135 
 
 3-160 
 
 6716 
 
 2-0 
 
 30-75 
 
 5949 
 
 1832 
 
 3-247 
 
 5766 
 
 2-5 
 
 26-75 
 
 5040 
 
 1536 
 
 3-281 
 
 4834 
 
 3-0 
 
 22-25 
 
 4091 
 
 1270 
 
 3-221 
 
 3995 
 
 3-5 
 
 18-5 
 
 3346 
 
 1042 
 
 3-210 
 
 3278 
 
 4-0 
 
 15-375 
 
 2750 
 
 08532 
 
 3-222 
 
 2685 
 
 4-5 
 
 12-75 
 
 2263 
 
 06996 
 
 3-234 
 
 2192 
 
 5'0 
 
 10-5 
 
 1853 
 
 05760 
 
 3-218 
 
 1812 
 
 5-5 
 
 8-875 
 
 1561 
 
 04767 
 
 3-275 
 
 1500 
 
 6-0 
 
 7-5 
 
 1317 
 
 03970 
 
 3-242 
 
 1249 
 
 On dividing the numbers 2 in the third column by the 
 
 1 For the proof of this see vol. ii. p. 319 of our larger work (file- 
 entary Practical Physics). 
 
 2 The columns with logarithms have been omitted. 
 
iv THE TANGENT GALVANOMETER 175 
 
 numbers in the fourth the quotient should be constant, 
 
 Fig. 81. GRAPHICAL PROOF OF LAW. 
 
 as we see it is from (5), at least within the errors of 
 observation. In experiments of this kind, where the degree 
 
176 PRACTICAL PHYSICS FOR SCHOOLS OH. 
 
 of accuracy is not high, the law is best tested by the use of 
 the graphical method that is, by plotting two curves and 
 comparing their form. The continuous line of Fig. 81 
 shows the result of taking the numbers in the first column 
 as abscissae and those in the third column as ordinates, 
 thereby giving a curve showing the relation obtained by 
 experiment. In order to make a curve showing the 
 theoretical relation comparable with that due to experi- 
 ment, some value must be given to K which will bring the 
 numbers in the fourth column near those in the third 
 column. If we wished the two curves to fall upon each 
 other, the best value to give to K would be the mean of 
 the constants in the fifth column. We have selected the 
 value 3 '147, which will enable us to distinguish without 
 confusion the two curves, the theoretical one being a dotted 
 line. On multiplying the numbers of the fourth column 
 by 3'147 the numbers of the sixth column are obtained, 
 which give the required ordinates of the theoretical curve. 
 It will be noticed that the two curves are very like 
 each other, thereby giving us reason to conclude that the 
 theoretical formula is risrht. 
 
 LESSON XXXI. Determination of Constants of 
 Tangent Galvanometer. 
 
 64. Exercise. To find the constant of the tangent 
 galvanometer by calculation and by experiment. 
 
 Apparatus. The depositing cell of Lesson XX., with 
 accompanying liquids, etc.; a Daniell's battery; box of 
 coils; commutator; chemical balance ; stop-watch; the gal- 
 vanometer whose constant is required. 
 
 Experimental Method. Adjust the number of cells in the 
 battery and the resistance until the deflection of the gal- 
 vanometer is not greater than 60, the connections being 
 as in Fig. 82, where D is the depositing cell. Next 
 thoroughly clean the anode and the working cathode dry 
 
IV 
 
 THE TANGENT GALVANOMETER 
 
 177 
 
 them in a current of hot air and weigh them to within half 
 a milligramme. Now fix them in their position in the de- 
 positing cell, the circuit being still incomplete. Set the stop- 
 watch to an exact hour, and then simultaneously start the 
 current and the watch. Eead the galvanometer, rapidly re- 
 verse the commutator so as not to lose time, and read again. 
 Take readings from time to time and adjust the resistance 
 
 Kathode Anode 
 
 Fig. 82. 
 
 in circuit if the deflection does not keep constant. The 
 deposition should be continued for some time, at least two 
 hours, and at the end of the time the current should be 
 discontinued, and the watch stopped. Remove the cathode, 
 wash it well first in common water and then in distilled 
 water, dry it in a current of hot air and weigh it. From 
 the gain in weight in the observed time calculate the aver- 
 age current that has been circulating. This having been 
 determined, deduce the constant of the galvanometer from 
 the formula 
 
 C 
 
 K = 
 
 tana' 
 
 where a is the average deflection. 
 
 VOL. I 
 
 N 
 
178 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 To find C we apply the rule : An ampere of current 
 will deposit '000326 grm. of copper per second. 
 
 Precautions. The battery chosen for this purpose should 
 be a constant one. When the constant to be determined 
 is small, Daniell's may be employed. The Daniell's battery 
 should be left short-circuited through a resistance some 
 time before use, so that it may be in a normal working 
 condition. 
 
 If it be necessary to have a strong current, a Grove's 
 or Bunsen's battery should be used, and it will then be 
 necessary to employ plates in the depositing cell of a large 
 size ; for when a certain density of current (that is to say, 
 number of units of current to unit area of electrode) is 
 exceeded the deposit is in the form of a powder and does 
 not adhere. It is ascertained that the loss of weight of the 
 anode cannot be used as an accurate measure of the current, 
 owing to secondary corrosive chemical action and disinteg- 
 ration producing loss of weight, which would vitiate the 
 determination of real electrolyte loss. 
 
 Example. 
 
 "Weight of cathode at commencement . . 10 '425 grms. 
 at end . . . 11-219 
 
 Gain in weight . . . 794 
 Mean deflection 47. Tan 47= 1 '0724. Time 125 minutes. 
 
 '794 
 Hence weight of copper in grammes per second = 6Qxl2 5' 
 
 '794 
 Strength of current in amperes = 6Q x 125 x . QQQ326 - 
 
 '794 
 Constant of galvanometer = 60x 125x . QQ 3 26irr0724 = ' 3 28 ' 
 
 Method by Calculation. The complete formula for the 
 tangent galvanometer is l 
 
 - 
 C= 
 
 See Elementary Practical Physics, vol. ii. p. 321. 
 
iv THE TANGENT GALVANOMETER 179 
 
 where C is the strength of current, H the horizontal com- 
 ponent of the earth's magnetism, n the number of turns in 
 the coil, and the other letters have their previous significa- 
 tion. 
 
 If x = 0, that is to say, when the compass needle lies in 
 the plane of the coil, then the formula becomes 
 
 To find H we proceed by the method of Lesson XVI. 
 The deflections are first taken with the compass box on 
 the instrument, and then the vibration box is substituted. 
 
 The value of K obtained by the above formulae should 
 agree with that obtained by copper deposition. It must, 
 however, be remembered that if the measurements have 
 been in C.G.S. units, it will be necessary to multiply the 
 result by 1 in order that it may compare with the con- 
 stant for amperes (see p. 142). 
 
 LESSON XXXII. Determination of Resistance 
 and B. M. P. 
 
 65. Apparatus. Tangent galvanometer^ commutator, 
 box of coils, a Daniell's and a Bunsen's cell, and connecting 
 wires. 
 
 Exercise. To find the resistances of the two cells. 
 Theory of the Method. Let the battery to be tested, along 
 with its commutator, the galvanometer, and the box of 
 resistance coils, be placed in series (see Fig. 80). 
 Let E = Electromotive force of the battery, 
 B = Resistance of battery, 
 G = Resistance of galvanometer and connecting 
 
 wires, 
 
 R = Resistance of the coils, 
 a = Angle of deflection, 
 
180 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 then, from Ohm's law, the current C passing through the 
 galvanometer will be 
 
 But 
 
 C = Ktana ..... (2) 
 
 by the theory of the tangent galvanometer. Hence 
 
 BTGTR =Ktana ' ' 
 
 Let now R be changed to K I} causing a to be changed 
 to Oj, then 
 
 Hence, dividing (3) by (4), we obtain 
 
 B + G + R 1= tana 
 B + G + R tan^ 
 
 Hence 
 
 B _R tan a - Rj tan i _ Q / 6 % 
 
 tan ttj - tan a 
 
 a general formula for the battery resistance. 
 
 The expression (6) may be simplified in approximate 
 measurements by making E = 0, a l = 45, then 
 
 or. still better, by making tan a x = | tan a, and then 
 
 B = R 1 -(2R + G) .... (8) 
 
 "When this last formula is used the method is called the 
 half-deflection method. 
 
 Practice of the Method (1 .) The lest values of a and <x r 
 Having completed the connection as figured above, and 
 placed the galvanometer in the magnetic meridian with the 
 pointer at 0, the first consideration will necessarily be 
 
iv THE TANGENT GALVANOMETER 181 
 
 which is the best coil of the galvanometer to use, and what 
 is the best value of deflection to obtain. On consulting 
 a table of tangents it will be found that the effect of 
 making an error in the reading will be greater at the 
 extremities of the scale than at the middle, thus 
 
 tan 10= -1763 tan 45 = 1'000 tan 8d = 5'671 
 
 11= -1944 46 = 1'0355 81 = 6'314 
 
 Difference '0181 Difference '0355 Difference 0'643 
 = 9 '8 per cent =3 - 5 per cent. =10 '7 per cent 
 
 of the whole mean effect. 
 
 We see from these examples that both small and large 
 deflections must be avoided. 
 
 If we consult our tables more minutely we shall find 
 that the effect of making an error is actually smallest 
 at 45, a result which is likewise in accordance with 
 theory. 
 
 In testing the resistance of a battery by the method of 
 this lesson we shall require to observe two deflections. It 
 follows as a corollary to the result just given that these 
 ought to be at equal distances on either side of 45, the 
 best part of the scale being between 30 and 60. Hence 
 the first deflection should not be greater than 60. Now 
 the less external resistance we place in the circuit, the 
 greater will be the effect of the battery resistance on the 
 whole current ; hence if a coil of the galvanometer can be 
 found which with R = gives a not greater than 60, that 
 will be the best coil to take, provided that the battery 
 continues constant. 
 
 Example. Single coil used. Six yards of connecting 
 wire = '07 ohm. The connecting wires were carefully 
 twisted together so that they had no direct effect upon the 
 galvanometer. This was tested by moving the wires and 
 ascertaining that this did not produce any movement of 
 the needle. 
 
 The following results were obtained : 
 
182 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 Expt. Resistance. Commutator up. Commutator down. Mean. 
 
 East end West end East end West end 
 of needle, of needle, of needle. of needle. 
 
 I. 53-8 54 56 56 64 '95 
 II. 1 30 30 31-2 311 30-57 
 III. 2 20 20 21 21 20'5 
 
 Here we have to make use of the formula 
 
 -r, R tan a - R, tan a, ~ 
 
 r> = - - f 1 - - U-, 
 
 tan 04 - tan a 
 
 also G + connecting wires = '07. 
 Now from the tables we find 
 
 tan 54 -95 = 1-4255 
 tan 30 -51= '5906 
 tan 20 '50- '3739. 
 
 Hence, from Experiments I. and II., 
 1 x '5906 
 
 From Experiments I. and III., 
 
 while from' Experiments II. and III., 
 
 which gives a mean result of '65. 
 
 Exercise. To compare the E. M. F. of the two cells by 
 the " Metliod of Sum and Difference" 
 
 Place the batteries to be compared in series, then 
 
 _ ^ ^ (1) 
 
 where e is the total resistance in the circuit. 
 
iv THE TANGENT GALVANOMETER 183 
 
 Now interchange the poles of one of the batteries so as 
 to cause E x and E 2 to oppose each other, and let the result 
 be as follows : 
 
 The resistance in circuit being the same as before. From 
 (1) and (2) we find 
 
 Ei + E 2 _tanai 
 
 (4) 
 
 and from (3) we obtain 
 
 EI _ tan cti + tan a 2 
 E 2 tan ai tan a 2 
 
 or the electromotive forces are to one another as the sum 
 and difference of the tangents of the angles of deflection 
 when the cells are in conjunction and opposition. 
 
 Example. Terminals 1-4. Total resistance in circuit, 220 ohms. 
 Cells in conjunction. 01 = 60 '4, tan cti = l'76. 
 ,, opposition. a.7 = 31'0, tan a 2 = '6. 
 El _176+-6_2'36_ 
 Es~176--6~l'16~' 
 
 66. Additional Exercises on the Use of the Tangent Galvanometer. 
 A tangent galvanometer, whose constants are known, is of great 
 value in the laboratory for ascertaining the current required for 
 telegraphic instruments, for ascertaining rapidly the condition of a 
 battery, and for the graduation of simple galvanometers. These uses 
 will furnish the student with additional exercises, such as we give 
 
 -, -, * 
 
 below. 
 
 (1.) Ascertain the current in amperes that will be sufficient to ring 
 an electric bell. 
 
 (2.) Ascertain the current that a bichromate cell will give from 
 time to time when working in short-circuit. 
 
 Example. A bichromate cell was placed in circuit with the copper 
 strap of a tangent galvanometer, the total external resistance being 
 15 ohm. The following readings were taken : 
 
184 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. IV 
 
 Time. 
 
 Deflection 
 a. 
 
 Ktan<*= 
 Amperes. 
 
 
 45 
 
 36 
 
 2-96 
 
 
 50 
 
 35-9 
 
 2-95 
 
 
 53 
 
 35-1 
 
 2-86 
 
 
 54 
 
 35 
 
 2-85 
 
 
 55 
 
 347 
 
 2-82 
 
 K = 4-074 
 
 56 
 
 34-4 
 
 279 
 
 
 57 
 
 34 
 
 275 
 
 
 58 
 
 33-5 
 
 270 
 
 
 59 
 
 33 
 
 2-65 
 
 
 On stirring the liquid of the cell the deflection rose to 52 '5 = 5 '31 
 amperes, but in ten minutes later the deflection was 257 = 1 "96 
 - ampere. The bichromate cell is thus seen to be under these conditions 
 extremely inconstant. By keeping the liquid continually stirred, or 
 by blowing air through the cell, it became very constant. 
 
 67. The Mirror Galvanometer a Tangent, Galvanometer. The stu- 
 dent may be reminded that in the case of the mirror galvanometer 
 the tangent law applies ; but as the angular deflections are small, 
 it may be shown that the readings of the scale are proportional to the 
 currents. 1 
 
 See Elementary Practical Physics, vol. ii. p. 88. 
 
CHAPTEK V. 
 
 MEASUREMENT OF RESISTANCE. 
 
 68. THIS chapter will be devoted to a description of a very 
 convenient method of measurement of resistance that is 
 extensively employed. It demands the use of a box of 
 coils, a cheap form of which has been designed for this 
 work (see Appendix B). 
 
 69. Theory and Use of Shunts. To reduce at will the sen- 
 sibility of the galvanometer, shunts, the use of which will 
 be already familiar to the student, are employed. Figs. 83 
 and 84 show two such arrangements in frequent use, the 
 
 Fig. 83. 
 PLAN OF CIRCULAR SHUNT Box. 
 
 Fig. 84. 
 PLAN OF SQUARE SHUNT Box. 
 
 corresponding parts in each being similarly lettered. Fig. 
 85 exhibits the general plan of the shunt connections. 
 
11 B 
 
 186 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 When a plug is inserted at d the galvanometer is short- 
 circuited through the thick metal portions between A and 
 B ; but when the plug is removed from d and inserted at 
 a, 5, or c, the galvanometer is shunted* through one or other 
 of the resistance coils of the shunt. The resistance that a 
 shunt must have in order to diminish the current in any 
 ratio may be readily ascertained. 
 Let G be the resistance of the 
 galvanometer and S the resist- 
 ance of any shunt, while 
 denotes the main current which 
 we wish to shunt. This current 
 will divide between the galvan- 
 ometer and shunt in the inverse 
 
 Fig. 85.-SCHEME OF SHUNTS. ^^ Qf ^ resistanceg in each . 
 
 that is to say, in the ratio of S to G, and hence the current 
 GJ going through the galvanometer will be 
 
 f~l ___ i ^ ft ( ~\ \ 
 
 Suppose now that we wish to allow only the th part of the 
 current to go through the galvanometer, or, in other words, 
 let Cjs? |. In this case we shall have from (1) 
 
 C_ S p _ G ,. 
 
 w-G+s ' *stj- 
 
 from which we find as follows for the values of n in com- 
 mon use : 
 
 Ifw=10 S= i ofG. 
 n = 10Q S = & of G. 
 
 The positions a, b, and c are marked either with the num- 
 bers yV, TITO-* T(5inr > implying the fractions of the whole 
 current which they pass through the galvanometer, or with 
 the numbers -J-, -g^, -gj-g, implying the ratio between their 
 resistances and that of the galvanometer. 
 
v MEASUREMENT OF RESISTANCE 187 
 
 LESSON XXXIII. The Box of Coils used as a Bridge. 
 
 70. Exercise. To learn the use of a box of coils for 
 measuring resistance by Wheatstone's method. 
 
 Apparatus. (1.) The Box of Coils. One of the best- 
 known arrangements is the Post Office Resistance Box. A plan 
 of this box will be seen in Fig. 86, in which AC and AB are 
 
 Fig. 86. THE POST OFFICE RESISTANCE Box. 
 
 the proportional arms, and EFGD the rheostat arm. The 
 bridge will best be understood by comparing it with the 
 typical diagram (Fig. 87), in which the parts are lettered in 
 the same way as in the figure of the box. At A (Fig. 86) 
 no binding screw is provided, but a wire passes under 
 the ebonite top of the box to a stud at a, so that on 
 pressing the key aAf the binding screw at A' is in con- 
 nection with A. In like manner the terminal at B' may 
 be put in contact with the point B by pressing the key 
 
188 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 CH. 
 
 B'6. The rheostat arm is connected with the proportional 
 arms by a brass connecting piece (not shown), which ought 
 to be strongly clamped by the binding screws at B and 
 E. At C and D are double bind- 
 ing screws one for the wire of 
 the unknown resistance, or line 
 wire, besides which there will be 
 the galvanometer wire at C and 
 the battery wire at D. The 
 order in which the various resist- 
 ances occur will be seen in the 
 diagram. At the place marked 
 INF is the plug called the "in- 
 finity plug." Should this plug be 
 removed the connection between 
 the parts of the rheostat arm on 
 either side of it will be com- 
 pletely broken. 
 
 (2.) The Ledancht Battery. This form of battery is chosen 
 for measurements of resistance, since it deteriorates but 
 little on standing, so that it is always ready for use. On 
 the other hand, it runs down very rapidly when short-cir- 
 cuited. But when the circuit resistance is small, as is the 
 case when our object is rather to find the direction of deflec- 
 tion than to measure its amount, the current is only required 
 for a few seconds at a time, and in this case any variation 
 in the strength of the current is of little consequence. 
 Again, when the current is required for a longer period, as 
 it is when accurate determinations are being made, the re- 
 sistance in the circuit will necessarily be so high that the 
 constancy of the battery will be unaffected, inasmuch as 
 it is doing little work. It is convenient to have four 
 cells of this battery fitted with a switch, so that 1, 2, 
 3, or 4 cells may be thrown into circuit as required (see 
 Appendix). 
 
 (3.) The Connecting Wires. These should be of gutta- 
 
MEASUREMENT OF RESISTANCE 
 
 189 
 
 perclia covered copper wire. The wires leading to the 
 galvanometer and battery may be No. 20 B.W.G. Those 
 leading to the unknown resistance should, however, be 
 thicker, and be provided with copper strips soldered at the 
 ends, as we have shown in Fig. 40. The use of these strips 
 ensures a greater surface of contact. 
 
 Method of making the Connections. In Fig. 88 we have 
 a plan of the connections where G is the galvanometer, S 
 
 Fig. 88. CONNECTIONS FOB MEASUKING RESISTANCES. 
 
 the shunt, X the unknown resistance, L the Leclanche' 
 battery, and CBB'A' the Post Office bridge. The wires 
 going to the same parts should be brought together as 
 much as possible. When a and 6 are pressed down, the 
 contacts indicated in the figure are made. The gal- 
 vanometer should be at least a metre away from the 
 
190 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 measuring apparatus, and if the resistance to be measured 
 consists of many turns of wire, it is necessary that it 
 should be so far distant that it cannot directly affect the 
 galvanometer. 
 
 Method of Measuring Resistances. The resistance of the 
 connecting wires that go to the unknown resistance should 
 first be measured. (We shall suppose that these wires 
 are each about two yards long : for the purpose of dis- 
 tinction they will be spoken of as the resistance con- 
 nectors.} In order to do this, take the wires out of the 
 binding screws at m and n, and clamp their extremities 
 together. 
 
 Place the -9-^-9- shunt in the galvanometer, and put on 
 one cell of the battery. Make P = 10, Q = 10, and 
 K = 0, that is to say, keep all the plugs of the rheostat 
 arm in. Press the battery key first, in order that the 
 momentary current due to self-induction may have ceased 
 before bringing the galvanometer into circuit. Then, whilst 
 it is down, press the galvanometer key for a few seconds. 
 The galvanometer will now be deflected, say to the right. 
 If no deflection is obtained there must be a faulty connec- 
 tion at some place. In this case examine the battery and 
 galvanometer connections, and especially ascertain whether 
 any of the leading wires are broken. With gutta-percha 
 covered wires such an accident may easily be overlooked, 
 for the wire frequently becomes broken while the covering 
 remains complete. 
 
 Next, P and Q remaining the same as before, make 
 E, = oo . On pressing the keys momentarily as before, the 
 deflection should now be to the left, i.e. in the opposite 
 direction, for the leading wires should have a resistance 
 between that of E, = and E, = oo . If the deflections 
 are not in opposite directions the connections are probably 
 wrong, and should be examined. Various resistances 
 must now be tried, until a balance is obtained. The 
 order of procedure will best be seen by studying the 
 
MEASUREMENT OF RESISTANCE 
 
 191 
 
 following table, which gives the result of an actual 
 measurement. The student is advised to arrange his 
 results in this form until he is quite familiar with the 
 use of the bridge. 
 
 
 
 
 
 
 Value of X 
 
 
 
 
 
 
 
 which would 
 
 
 No. of 
 Cells. 
 
 Shunt. 
 
 P. 
 
 Q. 
 
 R. 
 
 balance = 
 /QR\ 
 
 Deflection. 
 
 1 
 1 
 1 
 
 riv 
 
 T97 
 
 10 
 100 
 1000 
 
 10 
 10 
 10 
 
 1 
 
 1 
 1 
 
 1 
 1 
 01 
 
 To right. 
 To right. 
 To left. 
 
 4 
 4 
 
 No shunt 
 No shunt 
 
 1000 
 1000 
 
 10 
 10 
 
 6 
 5 
 
 06 
 
 05 
 
 To right. 
 To left. 
 
 From this we see that the resistance of the leading 
 wires is between '05 and "06 ohm. To obtain this 
 resistance more accurately the extent of the deflections 
 must be noted in the last two cases, and the true value 
 of X found by interpolation, as shown below : 
 
 Value of . 
 
 06 ohm 
 
 05 , 
 
 Deflection. 
 
 36 divisions to right. 
 
 37 left. 
 
 Hence '01 causes a difference of seventy-three divisions, 
 and hence the value of ~, which would correspond to no 
 deflection of the galvanometer, will be ^ = X = -05 
 + '^jf = '05507 ohm approximately. 
 
 The resistance of the leading wires being known, the 
 measurement of the resistance of several coils should be 
 proceeded with, as exhibited in the following examples : 
 
 Examples. I. Galvanometer coil of copper 
 
 P = 100, Q = 10, R = 
 
 No deflection. 
 
 ,, ,,9897, 9897. Slight deflection. 
 X = 989 -6 - -055 = 989'545 ohms. Temp. 15 C. 
 
192 PRACTICAL PHYSICS FOR SCHOOLS CH. v 
 
 II. Galvanometer coil of copper^ 
 
 P=1000, Q = 10, R=1020, ^ = 10-20. Deflection of - 4. 
 1019, 10-19. +21. 
 
 X = 10-19+' 01x21 - '055 = 10-143. 
 
CHAPTER VI. 
 THE QUADRANT ELECTROMETER. 
 
 71. THE quadrant electrometer bears the same relation to 
 electrostatic measurements that the mirror galvanometer 
 bears to electro-magnetic measurements. The indications 
 of the scale of the latter may be considered as directly 
 proportional to the currents passing through its coil, and 
 those of the former to the differences of potential at the 
 terminals of the electrometer. The chief use of an electro- 
 meter in the laboratory is in comparing the electromotive 
 forces of cells in open circuit. It is also of great value in 
 studying the production of a difference of potential by 
 other than chemical means. In the cable factory and at 
 cable stations it is employed for testing the insulation of 
 submarine cables after the manner of the method of Lesson 
 VIIc. In many tests it may replace the galvanometer 
 with much advantage, such, for instance, as that of Lesson 
 XXV. 
 
 LESSON XXXIV. Use of Quadrant Electrometer. 
 
 72. Exercise. To compare the electromotive forces of a 
 Darnell's cell, taken as a standard, with two other Darnell's 
 cells, (1) separately, and then (2) placed in series, arid 
 (3) in multiple arc. 
 
 Apparatus. (1.) The quadrant electrometer of Figs, 
 VOL. I o 
 
194 
 
 PRACTICAL PHYSICS FOR SCHOOLS 
 
 89 and 90 is of a simple and workable form. It consists 
 of a wooden box, mounted on three levelling screws, with 
 a wooden door at the back and a glass one in front. The 
 woodwork is almost entirely, and the glass front is partly, 
 coated with strips of tinfoil. To prevent confusion, 
 
 neither the front nor 
 the back is shown in the 
 figure. There are three 
 holes in the top of the 
 box. The central one 
 is for the reception of 
 a long glass tube, fitted 
 in its place by means 
 of a cork. At the top 
 of the tube is the charging 
 electrode C, which is pro- 
 vided with a small bind- 
 ing screw, supported on 
 the top of a rod of 
 ebonite, fitted by a cork 
 into the top of the tube. 
 The binding screw is in 
 connection with an ex- 
 tremely fine silver wire 
 that supports the mirror 
 M and the aluminium 
 paddle-shape needle seen 
 in Fig. 90. Through the 
 other holes in the top 
 of the case pass the 
 charging electrodes A and 
 B. These consist of ebonite rods, terminating in binding 
 screws in connection with wires leading to the quadrants. 
 The quadrants consist of four brass boxes, open along the 
 inner edges. They are seen in elevation in Fig. 89 and 
 in plan in Fig. 90, at A lt B p A 2 and B 2 . They rest on a 
 
VI 
 
 THE QUADRANT ELECTROMETER 
 
 195 
 
 sheet of ebonite, to which three of them are permanently 
 screwed. It is better that the fourth should be adjustable. 
 The alternate quadrants are connected together, as shown 
 in Fig. 90 ; thus A x is connected with A 2 and B x with 
 B 2 . Within the quadrants is suspended the needle. 
 From the lower surface of the needle hangs a small 
 weight, which may also act as a damper, and which is 
 useful in levelling the instrument. A piece of looking 
 glass below this weight may be used to assist in the 
 operation. (2.) A water battery consisting of small cells 
 containing zinc and copper strips, and charged with water, 
 
 Fig. 90. 
 
 will be required. Fig. 91 shows a convenient form of the 
 battery. (3.) Lamp and scale. 
 
 Principle of the Instrument. One pole of the water 
 battery is connected with C, and the other pole is put to 
 earth. The needle is thereby raised to a certain potential V, 
 which may be regarded as constant. If the needle lies 
 symmetrically with regard to the quadrants in the position 
 shown in the "figure it will remain undeflected, providing 
 that all the quadrants are at one potential. Should, how- 
 ever, Aj and consequently A 2 be at a potential V 1 , and Bj 
 with B 2 at a potential V 2 , then the needle will turn through 
 a certain angle, depending upon the torsional rigidity of 
 
196 PRACTICAL PHYSICS FOR SCHOOLS CH. 
 
 the wire which opposes the motion. If V is high com- 
 pared with V 1 and V 2 , then the amount of deflection will 
 be proportional to V x - V 2 . 1 
 
 Method of Use. (1.) Set the instrument about one 
 metre from the lamp and scale. (2.) Level until the 
 needle is central. (3.) Put the electrodes A, B and C to 
 earth. (4.) Make the spot of light central by turning C. 
 
 Fig. 91. A WATER BATTERY. 
 
 (5.) Connect C with one pole of the water battery, the other 
 pole being earthed. (6.) If the light does not remain 
 central, shift the movable quadrant. (This adjustment in 
 some instruments is done once for all by the maker.) (7.) 
 Leave A earthed, but insulate B and connect it with one 
 pole of the cell to be tested, the other pole of which is 
 1 For proof see Elementary Practical Physics, v*ol. ii. p. 431. 
 
vi THE QUADRANT ELECTROMETER 197 
 
 earthed. (8.) Kead the deflection. (9.) Disconnect the 
 pole connected to B and earth B a short time in order to 
 discharge the quadrants. (10.) The poles of the cell that 
 were connected respectively to B and to earth must now 
 be reversed. (H.) Again read the deflection. The num- 
 ber of divisions that the spot of light has passed over in 
 the two positions is proportional to the E. M. F. of the 
 cell. (12.) Repeat the operations several times and take 
 the mean of the deflections. 
 
 Note. These operations may be performed more readily with a 
 specially designed electrometer key. 
 
 (13.) Eeplace the cell by a second one and proceed as 
 before. 
 
 Example. Cell a. 
 
 Experiment. - pole to earth, + pole to earth, Total Deflection 
 
 + pole to B. - pole to B. Division. 
 
 1 +51 -53 104 
 
 2 +50 -55 105 
 
 3 +52 -50 102 
 
 Mean . 1037 nearly. 
 
 Cell ft gave 108-1 divisions. Cell y gave 102-8 
 divisions. Cell ft and y in series gave 212*0 divisions, and 
 in multiple arc 106 -2 divisions. 
 
 Taking a as Tl volt, ft is 
 
 l-lxlQ8-l_ 
 103-7 
 
 Similarly the other values can be expressed in volts. 
 
APPENDIX 
 
 A. 
 
 ADDITIONAL PRACTICAL DETAILS. 
 
 1. Switch for Battery. Fig. 1 shows the general arrangement 
 of a switch for one or two cells. A metal bar SS 1} provided 
 with a handle at S x and pivoted at S, may be placed in contact 
 with any one of three metal segments, 0, 1, and 2, that are fixed 
 
 B 
 
 Fig. 1. BATTERY SWITCH. 
 
 to a wooden or ebonite block. When the switch is at both 
 cells are out of the circuit that connects A and B, and according 
 as the switch is at 1 or 2 one or two cells are in circuit. In- 
 stead of a pivoted switch a plug switch is often used. 
 
200 APPENDIX A 
 
 2. Silk for Suspension of Galvanometer Needles. The best silk 
 is obtained from the middle of a good cocoon. The cocoon 
 should be steeped in tepid water, and the silk wound off it on 
 to a simple reeling machine. Fig. 2 shows such a machine, in 
 which the reel R is made of a number of glass rods that connect 
 
 Fig. 2. REEL FOR SILK. 
 
 the two wooden ends of the reel. When the silk has been 
 wound, the handle h should be removed, and the whole covered 
 by a glass shade to protect the silk from dust. See also Ele- 
 mentary Practical Physics, vol. i. Appendix C. 
 
 3. Clamp and Binding Screws. The various patterns of these 
 are shown in Fig. 3. 
 
 1 is of the ordinary French pattern. 
 
 la is a special pattern of the same, with a second binding 
 screw at the end of its shank. 
 
 2 is an ordinary telegraphic binding screw. 
 2 a is the same with a lock nut. 
 
 26 is the same with a double-screw for use with two separate 
 wires. 
 
 3 and 3a are common clamp screws for connecting two 
 wires. 
 
APPENDIX 
 
 201 
 
 36 is the telegraphic pattern that is also useful for connecting 
 
 plates. 
 4 is a battery clamp. 
 
 la 
 
 Fig. 3. CLAMP AND BINDING SCREWS. 
 
 4. Soldering. Perhaps no operation in the electrical labor- 
 atory is so important or requires to be performed so often as 
 soldering ; hence a few details relating to it will be useful. The 
 materials requisite are a small soldering iron, soft solder, and a 
 means of heating the iron. We find the soldering-iron heater 
 of Fletcher very useful for the purpose. There will further be 
 necessary either powdered resin or chloride of zinc for enabling 
 the solder to make good contact. The former material is much 
 to be preferred for electrical apparatus, but it is more difficult 
 to solder by its means than by the chloride of zinc. When the 
 latter is used the soldered place should afterwards be washed, 
 otherwise galvanic corrosion will take place at the joint. 
 
 5. Substitutes for the Mirror Galvanometer. As it is not 
 always convenient to use this instrument, it may be useful to 
 describe some substitutes. (1.) Simple Current Detector. Take a 
 piece of glass tubing 5 inches long and 1 inch in diameter. Wind 
 
202 APPENDIX B 
 
 a coil round one end, giving each layer a coating of hot paraffin 
 wax, which will bind the strands together. The tube must be 
 used with its long axis horizontal. Suspend by a silk fibre from 
 a cork (which closes one end of the tube) a magnetic needle so as 
 to be in the centre of the coil. The needle must be provided 
 with a long pointer, reaching to the distant end of the tube, 
 which likewise must be closed with a cork. Mount on a base- 
 board with binding screws. (2.) The Astatic Current Detector. 
 A more delicate instrument may be made on the principle of 
 the ordinary astatic galvanometer, 1 constructed in a simple 
 manner by using a postal box fitted like the comparison magnet- 
 ometer of page 101, but without the arms. (3.) Proportional 
 Galvanometer. An instrument, whose scale divisions are nearly 
 proportional to current strength, may be made after the manner 
 of either of the above instruments, but it will be necessary to 
 have the pointer at least 1 2 inches long and capable of moving 
 over a linear scale of 200 divisions. The pointer, which must 
 be very light and yet rigid, may be either of glass fibre, alumi- 
 nium, or straw. 
 
 B. 
 PRICE LIST OF APPARATUS AND MATERIALS. 2 
 
 The apparatus and materials may be obtained from Mr. W. 
 Groves, 89 Bolsover Street, Portland Place, London. The 
 apparatus marked * is of a specially designed pattern, approved 
 by the authors, and of which Mr. Groves is the only authorised 
 maker. Mr. Groves supplies the apparatus of two classes. That 
 of class B is made of varnished pine, and has paper scales. 
 That of class A is of hard wood polished, has boxwood scales, 
 and is of altogether superior workmanship. 
 
 1 See Elementary Lessons in Physics, by Balfour Stewart. 
 
 2 Many of the prices must be regarded as only a guide ; definite 
 prices cannot be given, owing to the great variation in the dealers' lists 
 and current market prices. 
 
Till 
 
 i0 
 
 
 
 
 
 
 1 
 
 3 3 
 3 
 
 
 
 1 
 2 
 2 
 2 
 10 
 8 
 10 
 3 
 15 
 7 
 
 6 
 6 
 
 6 
 
 
 
 
 
 6 
 
 . 1 
 
 
 5 
 5 
 
 6 
 
 
 
 APPEN 
 
 I. General. 
 
 Bunsen burners . . . ... 
 
 Drawing-board ....... 
 
 T square and set square 
 
 Callipers, inside and outside .... 
 
 Slide callipers, reading to '1 mm. ; length, 15 cm. 
 Imperial standard sheet-metal gauge 
 Micrometer wire-gauge ..... 
 
 Balance (Becker's) . . ... . from 1 : 5s. to 
 
 Box of weights, 100 to '01 grm. 
 
 Fletcher's blowpipe . 
 
 Foot-bellows for same .... 
 
 * Model of Vernier in wood .... 
 
 * Circular protractor, with radial arm (Fig. q) y Class A, brass 
 
 scale, 15s. ; Class B, paper scale 
 
 Glass rod and tubing ..... per Ib. 
 
 Test tubes per dozen, 3d. to 
 
 *Box containing silk fibre, cocoon silk, silk thread, and 
 
 ribbon 016 
 
 Copper wire, cotton covered, per Ib., No. 18, Is. 6d. ; No. 
 
 28, 3s. ; No. 36 5 
 ,, Gutta-percha covered, per dozen yards, No. 
 
 16, 3s. ; No. 20 
 
 Retort stands from Is. 6d. to 
 
 Tripod stands from 9d. to 
 
 India-rubber tubing for gas connections . per foot 
 Wooden blocks for supports (various) . . .0 
 
 Iron clamps for fixing apparatus to bench . . each 
 
 Glass cutter ... 
 
 Evaporating basins .... from 6d. to 
 
 Beakers . . . . . .in nests, from 2s. to 
 
 Cork borers ..... . set of best 
 
 Corks ..... per dozen, from 2d. to 
 
 Telegraph binding screws . . per dozen, from 2s. to 
 
 Clamp screws for connecting wires . . . per dozen 
 
 German-silver wire, covered with silk, per Ib., from 10s. 6d. to 1 
 
 50 
 1 
 1 
 
 1 6 
 3 6 
 
 2 
 
 4 
 2 
 
 1 6 
 
 1 6 
 
 2 
 
 5 
 
 6 
 
 9 
 6 
 
 3 
 
 1 
 
 II. Electrostatics. 
 
 Two pieces of glass tubing (Fig. 1) 
 
 Supporting hook for same (Fig. 1) 
 
 Two polished ebonite rods ..... 
 
 Pad of silk containing three thicknesses of flannel 
 
 Catskin or other fur ...... 
 
 Two gold-leaf electroscopes (Fig. 2) . 
 "Tin can with insulated bottom . 
 
 1 6 
 
 1 
 1 6 
 1 6 
 
 050 
 010 
 
204 APPENDIX B 
 
 Block of paraffin wax . . . . . . .010 
 
 Stand for supporting glass rod, etc., when testing insulation 
 
 (Fig. 3a Note) 026 
 
 *Two Brass knobs, mounted (Fig. 4) 036 
 
 *Electrophorus (Fig. 5) 026 
 
 *Tin can with insulating handle (Fig. 6) . . .010 
 
 * Apparatus showing + and - electricity produced in equal 
 
 amounts (Fig. 8) 036 
 
 * Perforated zinc cover for Fig. 9 010 
 
 * Drying oven of tin, with Fletcher's burner (Fig. 2a) . .070 
 Gold-leaf electrometer (Figs. 10 and 10a) Class A, 15s. ; 
 
 Class B 076 
 
 *Tin can, with inner insulated can forming an air condenser 020 
 ,, with paraffin between the tins . . . .026 
 
 * Ebonite cup for oils (page 55) . . . . . .026 
 
 *Insulated condenser like Fig. 11, but improved, so that 
 
 lid is separately supported and adjustable, Class 
 
 A, 1 ; Class B 10 
 
 Electrical amalgam in box, 2 oz., mixed with tallow . .010 
 ^Collection of insulators of different kinds, in box, for ex- 
 periments of page 33 026 
 
 Goldbeater's pad, knife, and tip . . . . .029 
 
 Gold leaf per book 013 
 
 Dutch leaf per book 003 
 
 *Simple quadrant electrometer (Fig. 89) Class A, 2; 
 
 Class B 1 10 
 
 * Water battery of 100 cells (Fig. 91) Class A, 2 ; Class B 1 10 
 
 III. Magnetism. 
 
 Pair bar magnets and keepers in box . . . .030 
 Horse -shoe magnet in box . . . . . .036 
 
 * Knitting-needles, sewing-needles, watch-spring, soft iron 
 
 nails, pieces of soft iron, crinoline steel, ferrotype 
 iron, sheet of steel, strip of tinned iron, two brass 
 clamps . . . . . . . . .040 
 
 Iron filings in bottle, with muslin 006 
 
 Steel filings in bottle 006 
 
 Long thin bar magnet . . . . . . .020 
 
 Small pocket compass 010 
 
 * Azimuth compass (Fig. 18) . Class A, 9s. ; Class B 6 
 *Dip circle (Fig. 26) . . . Class A, 1 : 15s.; Class B 16 6 
 
 * Deflection magnetometer (Fig. 33) Class A, 1 : 12s. ; Class B 17 
 
 * Magnets for same each 010 
 
 Comparison magnetometer (Fig. 36) Class A, 2 ; Class B 16 6 
 *Four magnets for same . . . . . . .026 
 
 "Spring balance (Fig. 87) . . Class A, 1 : 5s. ; Class B 15 
 
APPENDIX 
 
 205 
 
 "Vibration box with stirrups (Fig. 35) Class A, 15s. ; Class B 
 
 *Two magnets, and two brass bars for same . . .0 
 
 Paraffin wax ....... per Ib. 
 
 Paraffin bath of sheet-iron, with iron stand . . .0 
 Sealing-wax varnish ...... per bottle 
 
 Coaguline cement ...... per bottle 
 
 *Magnctoscope (Fig. 13) . . . Class A, 4s. ; Class B 
 
 IV. Voltaic Electricity. 
 
 *Two pint Bimsen cells in box (Fig. 38) . . . 
 
 *Two pint Bichromates in box, with lifting arrangement 
 
 (Fig. 39) 
 
 *Pohl's commutator (Fig. 42) ... 
 '"Magnet suspended for telescopic stand (Fig. 43) 
 *Wire one metre long (Fig. 43) . . . 
 *Daniell's cell (Fig. 46) 
 *Plating bath (Fig. 47) 
 
 Scratch brush (Fig. 48) 
 *Galvanoscope and sliding stage (Fig. 52) Class A., l:10s. 
 
 Class B 
 
 *Mirror galvanometer (Fig. 59) Class A, 1 : 10s. ; Class B 
 *Scale and lamp for same (Fig. 62, but improved) . . 
 
 Set of shunts for same ....... 
 
 *Box of coils, with proportional arms (Fig. 86) 1 . . . 
 
 Plug key (Fig. 67) ........ 
 
 *Coil of high resistance, 5000 ohms in coil . . . . 
 
 *Wheatstone's bridge . Class A, 1 : 10s. ; Class B 
 
 ^Current detector (see Appendix A) Class A, 14s. ; Class B 
 *0ne-ohm coil .... Class A, 10s. ; Class B 
 
 *Tangent galvanometer, hoop and stand (Fig. 79) 
 
 Class A, 1 : 5s. ; Class B 
 Straight Rheostat (Fig. 66) Class A, 14s.; Class B 
 
 Measuring vessels . . 
 
 Four-inch glass funnel . 
 
 Stoneware jug ... 
 
 File for battery and wires . 
 
 Stiff nail brush . 
 
 Sulphuric acid (commercial) . . per Ib. 
 
 Nitric acid (commercial) . . *. per Ib. 
 
 Copper sulphate (commercial) . . per Ib. 
 
 Zinc sulphate (commercial) . . per Ib. 
 
 Mercury .... . . per Ib. 
 
 Platinum foil ... . . per square inch 
 
 Platinum wire ... ... per inch 
 
 
 
 
 
 10 
 066 
 040 
 036 
 036 
 060 
 010 
 
 10 
 16 6 
 10 
 0100 
 600 
 
 026 
 
 060 
 15 
 10 
 5 
 
 15 
 10 
 016 
 006 
 016 
 009 
 006 
 2 
 006 
 5 
 3 
 026 
 006 
 001 
 
 1 These are sufficiently accurate for all school work. 
 
206 APPENDIX 
 
 Caustic soda ....... per Ib. 
 
 Emery paper ....... per sheet 
 
 V. Parts of Apparatus. 
 
 Boxwood scales divided into millimetres . . 2s. to 10 
 Paper scales divided into millimetres . . .010 
 
 Paper circles divided into degrees . . .Is. and 006 
 
 Postal boxes Id. to 1 
 
 Mirror glass 010 
 
 Cardboard .006 
 
 C. 
 THE PHYSICAL LABOEATORY WORKSHOP. 
 
 No physical department of a school can be considered com- 
 plete without being provided with a workshop. This room need 
 not be large ; it should, if possible, be on the basement and near 
 the laboratory. 
 
 The following list will serve as a guide for the kind of 
 fittings, tools, and materials requisite. 
 
 I. Fittings. 
 
 Joiner's bench, 10' long, 2' 6" broad, 32" high, with deal top and frame 
 fitted with a bench-vice and dog and tool rack at the back. 
 
 Mechanic's bench, 10' long, 2' 6" broad, 34" high ; pine top 3" thick, 
 fitted with vice and tool rack at the back. 
 
 Soldering bench, 3' long and 2' broad, with blowpipe and jet for Bun- 
 sen burner. On the pine top should be a sheet of g" iron. 
 
 Grindstone to work by foot' power stone 2' diameter, with trough for 
 water . . . .150 
 
 II. Lathe and Lathe Tools. 
 
 A well-finished lathe, with machine - planed iron gap-bed, 
 back-geared headstock, steel mandril and tee rests, face 
 plate, fitted together on iron stand . . . .700 
 
APPENDIX 207 
 
 Three-jawed steel chuck 
 
 1 
 
 
 
 Set of turinng tools for wood ...... 
 
 3 
 
 6 
 
 ,, for metal ...... 
 
 3 
 
 6 
 
 Half set of twist and plain drills on stand T V to " 
 
 1 
 
 
 
 Milling wheel with handle . . 
 
 2 
 
 
 
 III. Joiner's Tools. 
 
 
 
 Set of bench planes trying, 6s. 6d. ; jack, 4s. 9d. ; smooth- 
 
 
 
 ing, 3s. 9d 
 
 15 
 
 
 
 Cross-cut saw ......... 
 
 5 
 
 
 
 Tenon saw .......... 
 
 5 
 
 6 
 
 Lock saw, 12" 
 
 1 
 
 4 
 
 Plough and bits . . . 
 
 1 
 
 
 
 Two hammers . . . . . 
 
 3 
 
 4 
 
 Mallet 
 
 2 
 
 
 
 Spoke-shave 
 
 
 
 10 
 
 Brace and bits .......... 
 
 15 
 
 
 
 Two screwdrivers, 9d. and Is. 2d 
 
 1 
 
 11 
 
 Four chisels, ", %", 1", and 1J" ...... 
 
 3 
 
 6 
 
 Gouge, J" .......... 
 
 
 
 9 
 
 Bevel, 2s. 3d. 6" square, Is. lOd. .... 
 
 4 
 
 1 
 
 2' rale 
 
 1 
 
 6 
 
 Six sprigbits, lOd. ; four gimlets, Is. 6d. . . . . 
 
 2 
 
 4 
 
 Compasses, 8", 2s. ; pincers, 8", 2s 
 
 4 
 
 
 
 Two marking gauges . , . . . 
 
 1 
 
 6 
 
 One oilstone, Is. 6d. ; slip, 5d. ; oil-can," 5d. . . . 
 
 2 
 
 4 
 
 One scraper, 5d. ; cork rubber, 4d. ; two punches, 4d. . 
 
 1 
 
 1 
 
 IV. Mechanic's Tools. 
 
 
 
 One pair outside callipers, 6" ..... 
 
 1 
 
 6 
 
 One pair inside ,, 6" . . . . . 
 
 1 
 
 6 
 
 One steel square, 5" . 
 
 2 
 
 6 
 
 One pair spring dividers, 7" ...... 
 
 3 
 
 
 
 12" steel rule 
 
 1 
 
 6 
 
 Centre punch ......... 
 
 
 
 6 
 
 Hand-vice . 
 
 2 
 
 3 
 
 One pair each of round-nose, ilat-iiose, and cutting pliers 
 One 10" half-round file, and one 10" hand file . 
 
 5 
 2 
 
 6 
 
 
 
 One 8" square file, and one 8" round file .... 
 
 1 
 
 4 
 
 Cutting shears . 
 
 2 
 
 6 
 
 Cold chisels, |*, ", and f" . 
 
 3 
 
 
 
 Notched screw-plate and taps 
 
 10 
 
 6 
 
 Bench vice . 
 
 15 
 
 o 
 
 Tinsmith's anvil . . . . . . 
 
 10 
 
 V 
 
 
 
 Wrench 
 
 6 
 
 
 
208 APPENDIX r> 
 
 Soldering iron . . . . . . . . .014 
 
 Metal saw . . .'"'. 046 
 
 V. Materials. 
 
 Boards of pine, 1", ", and " thick, 3^d. , 2d., 2d. per foot 
 
 respectively. 
 Boards of baywood, 1", f", and " thick, 7d., 6d., 5^d. per 
 
 foot respectively. 
 
 Sheet tin per sheet 005 
 
 Sheet copper per Ib. 7 
 
 Sheet zinc 3 
 
 Sheet brass ,, 6~ 
 
 Solder 11 
 
 Glass paper ..... per dozen sheets 009 
 
 Emery paper . . . . . . ,, ,, 009 
 
 D. 
 
 THE RECORDING AND CALCULATING RESULTS 
 OF EXPERIMENTS. 
 
 A great part of the value of Physical Laboratory work will 
 be lost if the student is not taught to systematically record the 
 results of his experiments in a suitable note-book. The use of 
 loose sheets of paper is very objectionable. The notes may be 
 taken in pencil in the laboratory, and copied out into a larger 
 note-book in ink at home. Calculations and sketches should be 
 shown on the left-hand page, and observations, descriptions, 
 formulae, and theory on the right-hand side. We would advise 
 the use of note-books ruled into squares, as they are convenient 
 for plotting curves, and a help in drawing to scale. The 
 calculations should be made by the aid of four-figure logarithms, 
 which give sufficient accuracy. We cannot sufficiently urge the 
 importance of young students being taught to use such tables, 
 and we see no reason why the use of logarithms should not be 
 included in the arithmetical courses of schools. Unfortunately, 
 as the school mathematical work is at present arranged, students 
 
APPENDIX 
 
 209 
 
 are not introduced to logarithms until they are fairly well 
 advanced with trigonometry. Every student should have a 
 copy of one of the cheap editions of mathematical tables that 
 are now published, which for the purpose of this work must at 
 least contain 
 
 (1) A table of four-place logarithms. 
 
 (2) A table of four-place anti-logarithms. 
 
 (3) A table of natural tangents to tenths of a degree. 
 
 (4) A table of logarithmic tangents to tenths of a degree. 
 
 With the aid of such tables, the teacher is advised to work 
 through with the student the following example of the method 
 of recording and calculating results : 
 
 Example. 
 
 M 
 
 Calculation of == 
 
 M_(25-15+5-15)2(25-15-5-15)2 
 
 H~~ 2(25-15) ten28 30 ' 
 
 ^(30-3)2(20)2 
 50-3 
 
 tan 28 30'. 
 
 log 30-3 = 1-4814 
 2 
 
 2-9628 
 
 2 log 20 = 2 -6020 
 Log tan 28 30' =9 -7348 
 
 5-2996 
 log 50-3 = 1-7016 
 
 log = 3-5980 
 
 log 20 =1-3010 
 2 
 
 2-6020 
 
 Determination of M and H by the method 
 of Lesson XVI. 
 
 Deflection Observations 
 
 Mean. 
 28-6 
 
 d = 25 -15 cm. I = 5 -15 cm. 
 
 End of Needle 
 
 Position. East. West. 
 
 1 28-5 28-7 
 
 la 28-2 28-6 28'4 
 
 2 28-3 28-1 28-2 
 2a 28-6 29-0 28'8 
 
 Mean of means 28-5=28 30' 
 
 1 = 3963 
 
 Vibration Observations 
 
 h. m. s. 
 
 Time of starting 11 
 
 Time of 100th oscillation 11 10 50 
 
 Time of 100 oscillations 
 
 t= 6-5 sec. 
 
 VOL. I 
 
210 
 
 Calculation of I 
 
 10-3 
 10-3 
 
 1030 
 
 APPENDIX 
 
 106-09 
 1-96 
 
 12)108-05 
 9-004 
 
 Calculation of MH 
 
 1-4 
 
 5-6 
 14 
 
 1-96 
 
 9-004 
 
 2744 
 617400 
 
 617-7 
 
 MH: 
 
 (3-142)2(617-7) 
 
 (6-5)2 
 log 3-142= -4972 log 6-5 = -8129 
 
 2 log 3-142= -9944 
 log 617 -7 = 2 -7908 
 
 3-7852 
 2 log 6-5 =1-6258 
 
 1-6258 
 
 log MH = 2-1594 
 
 Calculation of M and H 
 
 logMH = 2-1594 
 log g= 3-5980 
 
 2)5-7574 
 log M = 2-8787 
 
 2 ) 2-5614 
 log H =1-2807 
 
 Determination of Moment of Inertia 
 W=68'6 grvns. a = 10"3 cm. &=l'4cm. 
 
 i=w a 12 
 
 1 = 617-7. 
 
 Determination of MH 
 
 MTT *** 
 MH = . 
 
 MH = 144-3 
 
 Determination of M and H 
 
 = 756-3. 
 
 H=^M-^ ='1906. 
 \H/ 
 
APPENDIX 211 
 
 E 
 
 THE REQUIREMENTS OF A PHYSICAL LABORATORY 
 FOR SCHOOLS. 
 
 1. The Laboratory Fittings. We can give the best idea of the 
 requirements of a physical laboratory by describing the chief 
 arrangements of three recently-fitted laboratories. 
 
 (1.) The Manchester Grammar School (see Plan, Fig. 4). The old 
 English room on the basement has recently been converted into a 
 physical laboratory. It has the following fittings : 
 
 AA and AA. These are two long tables specially designed for 
 juniors. Each table has accommodation for twenty boys, who are 
 supposed to work in pairs. The general arrangement of these tables 
 will presently be described. 
 
 B and B. Two strong working tables. In the centre of each is a 
 four-way gas tap for Bunsen burners, and a luminous burner mounted 
 on an arm with universal movements. 
 
 C. A strong working table, with gas arrangements like B. 
 
 D and F are square-topped slate slabs supported on stone piers. 
 
 E is a stone pier with a slab of stone on the top. Height only 15 
 inches. 
 
 G and H are slate slabs supported on piers of white brick. 
 
 K and L are wooden benches supported from the wall and by front 
 
 M with N constitutes a working bench, fixed firmly between the 
 pillar P! and the buttress. By drawing down two blinds between M 
 and N the space having F as a centre becomes a dark room, for the 
 remainder of the space is enclosed by a roofed partition 10 feet high. 
 The roof of the dark room is used for storage. 
 
 P 2 and P 4 are pillars to which black-boards are fixed. 
 
 P 3 . Around this pillar a table is fixed. 
 
 Q is an extensive series of cupboards and drawers for the storage of 
 apparatus. 
 
 R consists of ten cupboards placed 18 inches above the heating 
 apparatus. 
 
 ^n Sfc ^3' an( l ^4 are sink 8 - 
 
 Hj, H 2 , Ho, and H 4 are shelves. 
 
 T! is a mechanic's bench with lathe, T 2 a joiner's bench, T 3 a chemi- 
 cal bench, T 4 a blowpipe bench. These, together with the fume cup- 
 board U, are separated from the main laboratory by a partition 5 feet 
 high. Above T 3 and T 4 are fume hoods f, and f 2 . 
 
 At V is the demonstrator's table mounted on a platform. 
 
212 APPENDIX E 
 
 At X is a fireplace. Above W is a strong hook, fastened into the 
 
 ceiling, for supporting a Foucault's pendulum. There are also hooks 
 
APPENDIX 
 
 213 
 
 above D and in the pillars Pj and P 3 for the support of wires and 
 pendulums. 
 
 The regulation height of the benches and slabs is 2 feet 10 
 inches. 
 
214 
 
 APPENDIX 
 
 BLAIRLODGE SCHOOL. POLMONT. 
 PLAN OF PHYSICAL LABORATORY. 
 
 SCALE 
 
 Fig. 6. 
 
 IS IS 17 18 19 
 
E APPENDIX 215 
 
 (2.) The Hulme Grammar School, Manchester (see Plan, Fig. 5). 
 The physical laboratory is on the first floor. It is intended to accom- 
 modate thirty boys. C are the working tables with cupboards beneath 
 at the shaded portions. D, Slate slabs supported on corbels let into 
 the walls. E, Platform with demonstration table. F, Workshop. G, 
 Darkroom with sliding curtains. H, Sink, above which is a Fletcher's 
 hot- water apparatus. The height of the room is 14 feet. It is crossed 
 by two iron girders, which are bared for suspensions. To the left of 
 the outer door and at the left of the window on the extreme right are 
 oak beams 9 feet high that project 2 feet from the wall that are also 
 used for suspensions. At heights of 6 feet and 4 feet respectively 
 wooden belts run round the walls, to which fittings may be secured. 
 Above each table, against the wall, are two iron brackets folding back 
 against the wall. Operations requiring the use of a fume cupboard are 
 carried on in the chemical laboratory. In the basement accommoda- 
 tion has been provided for a larger workshop with lathes. 
 
 (3.) Blairlodge School, Polmont, N.B. (see Plan, Fig. 6). This is 
 divided into an elementary and advanced laboratory. The latter (a) 
 forms also a dark room, the top of which is used for storage. It is 
 fitted with a slate slab c, a sink d, a square slate slab p, and an apparatus 
 cupboard b. The demonstrator's seat is at e in the elementary labora- 
 tory, and his desk at f. Behind him are two windows, provided with 
 curtains, through which he can overlook the advanced laboratory. The 
 other fittings of the elementary laboratory are three benches for twenty- 
 four juniors, g, h, and h, arranged like those to be presently described. 
 A square-topped slate slab j, a longer slab i for balances, a hinged win- 
 dow shelf k, a long chemical bench m provided with a sink and having 
 cupboards and drawers beneath and shelves above. At n is a stink 
 cupboard, and at 1 a blowpipe table. Apparatus cupboards are shown 
 at b and b. The laboratory is lit both by gas and electricity. There 
 are dynamo leads to the dark room and the stink cupboard. Below 
 the latter secondary batteries are placed. Arrangements are made for 
 electrically connecting the stink cupboard with the benches and the 
 benches with each other. The school is provided with a well-fitted 
 workshop. 
 
 2. Working Benches for Juniors. We shall now give further 
 details of a working bench for juniors, similar to the design 
 adopted at two of the before-mentioned schools. 
 
 Fig. 7 shows the front and end elevations of the bench, and also 
 the plan of its top with the overhead rail removed. It is intended to 
 accommodate eight juniors working in four pairs at the positions a, 
 !, b, &i, c, Cj, and d, d^ It is 10 feet long by 4 feet wide. The height 
 is 2 feet 10 inches. Down the middle of the top of the table is a 
 4-inch plinth, underneath which is a gas-pipe supplying two standards 
 g and g, each with two two-way gas nozzles for Bunsen's burners 
 (fixed just above the level of the table), and two luminous burners 
 
216 
 
 APPENDIX 
 
 above the overhead rail. The last mentioned is 4 inches square, and 
 is supported by a central and two end posts r, r, r. The central 
 plinth has two boxwood scales divided into millimetres, let into 
 it flush with the top of the table. These scales are numbered along 
 two edges in such a way that the scales can be used by boys work- 
 ing on both sides of the table. Fixed to the overhead rail are four 
 hinged brackets b, b, which may be clamped at any position by 
 thumb screws. They serve to support pendulums, etc. A number 
 of hooks are also provided for similar purposes. These are also screwed 
 into the rail, which also is provided with name-plates bearing the 
 names of the boys. It is intended that the gas standards shall take 
 
 ' y ^ ' 
 
 TT 
 
 r 
 
 : o 11 o 
 
 o ii o : 
 
 
 Li ELEVATION U 
 
 END VIEW 
 
 Fig. 7. 
 
 the place of retort stands, and that clamps for fixing apparatus shall 
 be screwed to the wooden uprights. The top of the table should pro- 
 ject beyond the frame 2 inches all round, so that apparatus can be 
 clamped down. There are eight drawers each 6 inches deep, divided 
 into partitions along the dotted lines shown. No cupboards are shown, 
 but these may be added if storage room should be required. They 
 should, however, be only at the ends of the benches, as it is important 
 not to interfere with comfortable sitting. The spaces under the tables 
 are useful also for placing stools and supports. In the figure a shelf is 
 shown useful for the reception of batteries, etc. For the purpose of 
 connecting batteries binding screws are fixed in the central plinth, 
 and are in connection with wires beneath the table. Binding screws 
 are also connected with the gas-pipes to serve as "earths" 
 
APPENDIX 217 
 
 F. 
 
 NOTES ON THE ORGANISATION OF 
 LABORATORY WORK. 
 
 1. Mechanical Assistant Every large school requires a 
 mechanical assistant to make and repair apparatus for the labora- 
 tory and lecture -room. He should also have charge of the 
 workshop. It is important for him to have a good knowledge 
 of working in wood, and to be able in addition to do light 
 metal-work. A knowledge of glass working should be acquired 
 by practice. 
 
 2. Constructive Work We have described in this volume 
 how certain pieces of apparatus may be made by the student. 
 The knowledge of the use of tools and the properties of materials 
 so gained is of great value. It cannot, however, be expected 
 that any portion of the limited school time devoted to practical 
 physics should be employed in constructive work. The students 
 should rather be encouraged to make use of the workshop 
 in their own time for this purpose. At residential schools 
 this need not present much difficulty of arrangement. 
 
 3. The Collective and Separate Systems. In the collective 
 system all the students work at the same lesson at the same 
 time. This enables the, teacher to give collective instruction, 
 and has other advantages from a didactic point of view. But 
 one objection to the system is that it involves the multipli- 
 cation of pieces of apparatus of the same kind, and hence with- 
 out great expense it is impossible to have anything but the 
 cheapest and simplest apparatus. It might be applicable to the 
 earlier lessons on electrostatics, but could not be much used 
 afterwards. It is a good method to commence with, but the 
 separate system will soon be found necessary. In other words, 
 all will not be working at the same lesson. It will not be 
 found difficult to arrange the order of the lessons in such a way 
 that no confusion shall result. 
 
218 APPENDIX F 
 
 4. The Indicator Board. The use of the separate system will 
 be facilitated by adopting a device employed by Pickering, and 
 since used at Cambridge and elsewhere. This consists of a 
 board to show what "work each student is doing. It may be 
 made in various forms. " A convenient plan is to drive pins 
 obliquely into a drawing-board in rows, so that they shall be 
 separated about 3 inches horizontally and 2 inches vertically. 
 The heads of the pins are then cut off and cards hung on them, 
 those in the first vertical row bearing the names of the experi- 
 ments, those in the other rows giving the names of the students." 
 
 5. Companionships. It will be found advisable, as a rule, for 
 students to work in couples. If a little discretion.be exercised 
 in selecting the companions, far more satisfactory work will be 
 done than if they worked separately. 
 
INDEX 
 
 AMALGAM, electrical, 19 
 Amalgamation mixture, 110 
 
 of zinc, 109 
 Ampere, defined, 144 
 
 experiment of, 116 
 Angular measurement, units of, 15 
 Anode, definition of, 124 
 Apparatus, list of, 202 
 Areas, mensuration of, 2 
 
 standards of, 2 
 
 BALANCE, the, 10 
 
 rider of, 12, 13 
 Battery, sulphuric acid for, 110 
 
 bichromate, 112 
 
 mixture for, 113 
 
 Bunsen's, 108 
 
 Daniell, 123 
 
 charging, 124 
 
 discharging Bunsen's, 122 
 
 in multiple arc, 132 
 
 in series, 132 
 
 Leclanche, 188 
 
 precautions with Bunsen's, 112 
 
 primary and secondary, 112 . 
 
 switch for, 199 
 
 theory of, 133 
 
 water, 196 
 Bound and- unbound electricity, 26, 
 
 27 
 Boxes for making apparatus, 64 
 
 CALCULATIONS, method of making, 
 208 
 
 Calibration of galvanoscope, 168 
 Callipers, outside and inside, 5 
 
 the slide, 5 
 Capacity, unit of, 42 
 Cathode defined, 125 
 Cavendish's method for comparing 
 
 specific inductive capacities, 52 
 Circles, dividing of, 15 
 Circular divisions, copying of, 16 
 Coercive force, 62 
 Coils, box of, 150, 187 
 
 care of, 152 
 
 Commutator, Pohl's, 115, 116 
 Compass card, 65 
 Condensers, 44 
 
 comparison of, 52 
 
 discharge of, 45 
 
 energy of charging, 43 
 
 experiments with, 49 
 Conducting power of glass, 21 
 oils, 55 
 
 Conduction, electrification by, 21 
 Consequent points or poles, 64 
 Copper plating, 123 
 
 determination of cur- 
 rent by, 178 
 
 cleaning liquids for, 126 
 
 depositing liquids for, 127 
 Cosine defined, 76. 
 Coulomb, 37, 105 
 
 DANIELL'S cell, 123 
 Density, estimation of, 15 
 electrostatic unit of, 42 
 
220 
 
 INDEX 
 
 Detector, 128 
 Diagonal scale, 3 
 Dip circle, to make a, 77 
 theory of, 79 
 observations, 82, 83 
 
 errors of, 83 
 
 theory of errors, 
 
 84 
 
 Dip, magnetic, defined, 80 
 Dividing of circles, 15 
 Drying oven, 19 
 Dyne, the, 38, 39 
 
 EBONITE, 19 
 
 Electrical laws, 36 
 
 Electricity produced in equal and 
 
 opposite amounts, 33 
 Electrification by friction and con- 
 duction, 17, 32 
 of metal, 28 
 by induction, 23 
 Electrolysis of dilute sulphuric acid, 
 
 119, 122 
 Electrometer, gold-leaf, 137 
 
 quadrant, 193 
 Electromotive force comparisons. 
 
 157, 179, 197 
 force defined, 137 
 Electrophorus of Volta, 27 
 Electroscope, gold-leaf, 17 
 
 experiments on potential with, 
 
 46 
 
 improved, 47, 48 
 E. M. F.'s, comparison of, 179 
 Enclosure, effect of a conducting, 
 
 34, 48 
 
 no electrification in an, 34 
 protection afforded by, 35 
 Equipotential surfaces, 41 
 Erg, the, 39 
 Estimation of tenths, 4 
 Exercises, additional, 2, 15, 20, 33 
 64, 71, 77, 82, 84, 85, 117, 136, 
 141, 183 
 
 FARADAY'S ice-pail experiments, 29 
 Figure of merit, 154 
 
 Foot-pound, 38, 39 
 
 Friction, electrification by, 20 
 
 GALVANOMETER, tangent, 170, 173, 
 176, 178, 183 
 
 lamp and scale for, 146 
 
 mirror, 144, 184 
 
 substitutes for, 201 
 Galvanoscope, 127 
 
 calibration of, 168 
 Gauge, the micrometer wire, 7 
 
 the sheet-metal, 7 
 
 English standard, 8 
 Gauss, tangent position of, 89, 90 
 Glass, conducting power of, 21 
 Gold leaf, manipulation of, 18 
 Gravity and electricity compared, 39 
 
 H, COMPARISON of, 96, 98 
 Haldat's figures, 64 
 Helix, polarity of, 118 
 
 INDUCTION apparatus, 28 
 
 charging by, 25 
 
 electrification by, 28 
 
 study of, 25 
 Inductive specific capacity, 45 
 
 KILOGRAMME DES ARCHIVES, 9 
 
 LABORATORIES for schools, 211 
 organising work in, 217 
 working bench for, 215 
 
 Law of inverse squares, 68 
 
 Laws of electricity, 36, 37 
 
 magnetism, fundamental, 69 
 vibrating magnet, 93 
 
 Lengths, standards of, 1 
 
 Lifting hook, 125 
 
 Lines of force, 72 
 
 Litre, definition of, 2 
 
 M, DETERMINATION of, 98 
 
 Magnetic axis defined, 57 
 couple, 74 
 curves, 62 
 distribution, 105 
 field, 62, 63 
 fields, strength of, compared, 98 
 
INDEX 
 
 221 
 
 Magnetic horizontal component, 74 
 meridian, 57 
 
 to mark down, 66 
 moment defined, 77, 89 
 
 compared, 96, 97, 103, 
 
 104 
 
 moments compared under dif- 
 ferent circumstances, 104, 
 105 
 
 Magnetisation by induction, 60 
 Magnetism, coefficient of induced, 
 
 106 
 
 Magnetometer for deflections, 90 
 for comparisons, 100 
 for vibrations, 93 
 Magnetoscope, 58 
 Magnets, interaction of, 87 
 Mariner's compass, 64 
 Memoria technica, 117 
 Metre defined, 1 
 MH, determination of, 95 
 Mirror and scale, 16 
 Moment of inertia, 94, 95 
 determination of, 96, 98 
 
 OHM coil, to make, 167 
 
 defined, 143 
 Ohm's law, 139 
 
 proof of, 158 
 
 PARAFFIN wax, 19 
 Plating bath, 124 
 
 Porous pots, examination and pre- 
 paration of, 110 
 Potential, 38, 41, 46 
 
 experiments on, 46 
 Pound, the standard, 9 
 
 RESISTANCES in multiple arc, 167 
 measurement of, 155, 162, 163, 
 
 179, 190 
 Rheostat, 153 
 Rider of balance, 12, 13 
 
 SCALE, diagonal, 3 
 Scratch brush, 125 
 Screw clamps, 109, 200 
 Shunts, 185 
 Silk fibre, 208 
 
 Sine defined, 75 
 Soldering, 201 
 
 Specific inductive capacity, 45 
 Spring bows, 2 
 Standard pound, 9 
 kilogramme, 9 
 
 TANGENT defined, 76 
 
 galvanometer with sliding com- 
 pass box, 170 
 constants of, 176 
 exercises with, 
 
 183 
 
 formulae of, 178 
 to determine con- 
 stants of, 176 
 use of, to prove 
 law of distance, 
 173 
 
 proof of law of, 170 
 Time, estimation of, 15 
 Tools, list of, 208 
 
 UNITS of angular measurement, 15 
 of capacity, 42 
 of density, 42 
 
 of electrostatic quantity, 37 
 of force, 39 
 of work, 39 
 
 VERNIER, PIERRE, 4 
 
 the straight, 4 
 Volt defined, 144 
 Voltameter, to fit up, 120 
 
 electrode, to make, 120 
 Volume, standards of, 2 
 Vulcanite, 19 
 
 WEIGHING, method and precautions, 
 
 13, 14 
 Weights, 13 
 
 Wheatstone's bridges, theory of, 161 
 half metre, 
 
 163 
 connections, 
 
 164, 189 
 Wires for connecting, 188 
 
 YARD defined, 
 
 0? 
 
Printed by R. & R. CLARK, Edinburgh. 
 
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 ELEMENTARY PRACTICAL PHYSICS. 
 
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