UNIVERSITY OF CALIFORNIA LIBRARY OF THE DEPARTMENT OF - Received... Accessions No...^.. Book No..../.. UflfER DIVISION LABOBATOBY WOBK PRINTED BY SPOTTISWOODE AND CO., NEW-STREET SQUARE LONDON "WITH THE PUBLISHER THE LABOEATOEY WOEK A COURSE OF NATURAL SCIENCE BY A. G. EAEL, M.A., F.O.S. LATE SCHOLAR OP CHRIST'S COLLEGE, CAMBRIDGE SCIENCE MASTER AT TONBRIDGE SCHOOL UNIVERSITY OF CALIFORNIA ^' * * * • i-f'OG •"• LONDON LONGMANS, GEEEN, AND CO, AND NEW YORK : 15 EAST 16th STREET 1890 All rights reserved £3 .44J.TT TI T r * T>f*vf PREFACE THE course of work described in the following pages forms an introduction to all branches of Natural Science. The ele- mentary nature of the book has caused me to pay more atten- tion to method than to detail. Every student will need to follow closely and thoughtfully the performance of each ex- periment, in nearly all cases making his own observations and measurements, in order that the capacity for independent judgment, as well as an interest in original research, may be awakened at the outset. When a fact or law, discovered by means of a student's own personal observation and intelligence, turns out to be very familiar to others more advanced, the value of the research to the student himself is but slightly impaired. Each section conveys a definite lesson, and care has been taken that they may follow in inductive sequence. It is im- portant that each experiment and each stage of the course be described and reviewed at length in the student's note- book, which should contain many practical details omitted from the text-book, not only lest they should obscure the more important outlines of work, but also because it is in- tended that some freedom and originality in manipulation should be encouraged. The trials and practical difficulties of the laboratory are too valuable educationally to be set aside by . over-help, though it is essential that they should not be too 673285 VI ELEMENTS OF LABOKATORY WORK severe. It may be noticed that while tables are added to show the results of accurate observers, and to give information as to relative magnitudes, the numerical values resulting from the selected experiments have been generally left to be worked out by the students themselves from their own observations. The word speed has been used to denote the rate of motion of a particle along its path, in preference to the term velocity, which is now generally reserved to designate a quantity having both magnitude and direction, i.e. a vector. The sections numbered 3, 7, 12, 13, 14, 15, 24, 25, and 26, together with many of the additional exercises, may be omitted by be- ginners. Rooms devoted to practical science, and well equipped, are nowadays considered a necessary part of all public schools and colleges, and this book is simply intended to be used as a hand- book in such laboratories. An effort has been made to arrange a practical and progressive course which shall touch upon the chief problems, and point out the main lines of investigation in Natural Science, in preference to an attempt at explaining any one branch in detail. It is also hoped that the course may give some training in that habit of directly appealing to nature, rather than to theories, which is the root of all scientific progress, although unfortunately it is not always made the basis of scientific education, partly from want of time and partly from want of appliances. A. G. EARL. TONBBIDQE: 1890. CONTENTS CHAPTER I MEASUREMENT OF QUANTITY OF MATTER PJIGB 1. To find equal quantities of matter 1 2. To compare two quantities of matter ...... 2 3. To test the accuracy of a set of weights by the balance . . 3 4. To investigate the construction of an accurate balance . . 3 Additional exercises and questions . . . . .4 5. Measurement of length and volume 5 Additional exercises and questions ...... 6 6. Relative quantities of matter in equal volumes of different substances .7 Additional exercises and questions 8 7. Principles of systematic measurement ..... 8 8. Table showing relation of areas to linear dimensions . . .12 9. Table showing relation of areas to one another . . . .13 10. Table showing relation of volumes to linear dimensions . .13 11. Table showing relation of volumes to one another . . .13 12. Method of measuring very small quantities of matter . . 14 13. Methods of measuring very small distances. The vernier . .14 14. The micrometer screw, and spherometer 15 15. Other methods of measuring density and table of densities . 16 Additional exercises and questions 18 CHAPTER II OBSERVATIONS OF CHANGE OF POSITION 16. Relative position 19 17. Means of defining position with regard to a fixed point . . 20 18. Observation of change of position 21 19. Further observations of position and displacement . . .22 Vlll ELEMENTS OF LABORATORY WORK PAGE 20. Practical measurement of the paths of moving bodies . . .23 21. Observation of rotation .24 Additional exercises and questions 26 22. Rate of change of position .26 23. Change of speed or acceleration 27 24. Measurement of time . .27 25. Resultant of two simultaneous displacements . . . .28 26. Further consideration of simultaneous displacements . . .29 Additional exercises and questions 30 27. Examples of mechanical constraint of motion . . . .31 28. Conversion of circular into rectilinear motion . . . .32 Additional exercises and questions 34 CHAPTER III OBSERVATIONS OP CHANGES OF TEMPERATURE 29. Change of temperature causes change of density . . .35 30. Standard temperatures ........ 36 31. Relation of temperature-changes Lto quality and quantity of matter 38 32. Equal quantities of ice melted during equal temperature-changes in equal quantities of the same kind of matter . . .39 33. To measure the corresponding temperature-changes in water and copper 40 Tables of numbers expressing the relative quantities of various kinds of matter which are equivalent in thermal change . 43 34. To measure the numerical value of the temperature-change occur- ring in surrounding bodies when one gram of ice liquefies . 43 35. To measure the numerical value of the temperature-change in- volved in changing 1 gram of water at 100° into steam at 100° 45 Table showing the number of grams of water which would be changed from 1° C. to 0° C. by the fusion and also by the vaporisation of 1 gram of various kinds of matter . . .46 Table of melting-points of various solids 47 Table of boiling-points of various liquids . . . . .47 Table showing the density and volume of mercury at various temperatures . . .' 47 Table showing the density and volume of water at various temperatures 48 Table of mean coefficients of cubical expansion . . 48 Additional exercises and questions 49 CONTENTS CHAPTER IV OBSERVATIONS OF CERTAIN MUTUAL CHANGES, COMMON TO ALL KINDS OF MATTER PAGE 36. Bodies displaced equally from the earth, reach it again simul- taneously, if allowed to fall 52 37. Time of fall . 53 38. A body returns to the earth with a uniformly accelerated speed in a straight line 53 39. Meaning of term ' force ' 54 40. The moveable pulley 55 41. The lever 56 42. The pressure of liquids . . 58 43. The equilibrium of two liquid columns in communication . 59 44. The internal stress of liquids 61 45. The relation between mutual displacements . . . .64 46. New test for equal quantities of matter ..... 66 Additional exercises and questions 68 CHAPTER V OBSERVATIONS OF CERTAIN MUTUAL CHANGES EXHIBITED BY CERTAIN KINDS OF MATTER 47. Changes observable when certain bodies are rubbed together and separated 70 48. Communication of the property to other bodies . . .71 49. Investigation of the electric field ...... 71 Additional exercises and questions 73 50. Existence of electric stress indicated by the electroscope . 73 51. The quadrant electrometer . 74 52. Exploration of the electric field by two discs . . . .77 Additional exercises and questions 78 53. Electric phenomena produced by another method . . .79 54. Processes by which electric equilibrium is effected . . .80 55. An eiectric circuit, conditions necessary for . . . .81 56. The existence of magnetic stress indicated . . . .82 57. Deflection of a magnet by a substance forming part of an electric circuit 84 58. Construction of a galvanometer 85 59. Meaning of conductivity 86 X ELEMENTS OF LABORATORY WORK (50. Change of temperature in an electric circuit . . . .87 Table of approximate relative conductivities with mercury as unity 88 Kesistance of copper wire of various sizes . . . .89 61. Formation of a current by change of temperature . . .90 Additional exercises and questions ...... 91 CHAPTER VI OBSERVATIONS WHICH LEAD TO THE THEORY THAT ALL MATTER IS MADE UP OF VERY SMALL SEPARATE PARTICLES 62. The gradual re-arrangement of matter when some liquids are placed in contact 93 63. The gradual re-arrangement of matter when some solids are placed in contact with some liquids . . . . 94 64. The temperature-change attending solution, and the variation of rate of diffusion with temperature . . . . .96 65. The quantity of a solid dissolved varies with the temperature of the solvent 96 66. The gradual re-arrangement of matter when different gases are placed in contact 98 Table of solubility of air in water, and table of solubility of other gases in water and alcohol 99 67. Atmospheric pressure and its variations . . . ? . 99 68. Use of the cistern barometer . 101 69. The volume of a given mass of air varies inversely as the pressure ... . . . . . . . . 103 70. Graphic representation of correlative changes by diagram .104 71. The variation in volume of a given mass of air for a given change of temperature 106 72. The temperature-changes resulting from volume-changes in gases . . 107 73. The pressure of aqueous vapour at different temperatures, the measurement of 109 Table of pressure of aqueous vapour at different temperatures 110 Table of boiling-points of some saturated solutions . .110 74. Enunciation of Avogadro's theory Ill Additional exercises and questions 113 CONTENTS xi CHAPTER VII INVESTIGATION OF THE COMPOSITION OF VARIOUS KINDS OF MATTER PAGE 75. The separation of a complex body into different kinds of matter by a difference in degree of solubility in water . 116 76. The separation of a complex body into two different kinds of matter by a difference of boiling-point . . . .117 77 Chemical changes : changes observable when silver nitrate is maintained at a high temperature 118 78. Changes observable when silver iodate is maintained at a high temperature 119 79. Modification produced when silver nitrate is heated within a closed tube 120 80. Decomposition takes place when silver nitrate or similar bodies, either liquefied or in solution, form part of an elec- tric circuit 122 81. The quantity of a given kind of matter, liberated under the same electric conditions, is independent of the kind of matter associated with it, while the quantities of different kinds of matter liberated under the same electric conditions have a fixed invariable ratio to one another . . . 123 82. Decomposition of a body by close contact with another. Forma- tion of new kinds of matter when two bodies re-act chemi- cally 124 83. Chemical combination always takes place between definite quantities 126 84. The relative quantities of chemically re-acting matter. The action of magnesium and aluminium upon hydrogen sulphate and hydrogen chloride 127 85. The relative quantities of chemically re-acting matter. The re-action of silver nitrate with sodium chloride . . .129 86. Some conditions of chemical change. Two kinds of complexity of matter 130 Table of commoner elements 132 87. Measurement of the mass of a litre of air .... 133 88. Measurement of oxygen evolved when silver iodate is heated, and of the density of oxygen ...... 134 89. Analysis of air by means of phosphorus 135 90. Some effects of the atmosphere 136 91. Changes observable when the temperature of copper oxide is raised in a current of hydrogen or coal-gas . . . .138 ELEMENTS OF LABORATORY WORK 92. The synthesis of water by means of copper oxide . . .139 93. Different relative quantities of the same kinds of matter may combine chemically ........ 141 Table of homologous paraffins, bodies containing carbon and hydrogen in different relative quantities . . . .142 94. The rise in temperature during chemical combination . . 142 95. Dalton's atomic hypothesis and its later development . . 145 Additional exercises and questions ...... 148 CHAPTER VIII OBSERVATIONS WHICH LEAD TO THE THEORY THAT SPACE IS FILLED WITH A MEDIUM, THE ETHER, BY MEANS OF WHICH CERTAIN MODES OF MOTION ARE CONVEYED FROM ONE PORTION OF MATTER TO ANOTHER 96. On radiation or rectilinear propagation of light and tem- perature . . . . . . . . 150 97. Reflexion . . .151 98. The focal length of a concave mirror and of a convex lens . 152 99. The formation of a spectrum . . . . . . .155 100. The interference of light - •* . . 156 101. The explanation of interference . . .... 158 102. The explanation of rectilinear propagation . » . . 160 103. The interference grating . .162 104. The explanation of reflexion and refraction . . . .164 Table of refractive indices . . . . . . . 167 105. The explanation of spectra, with observations .... 167 Additional exercises and questions 170 APPENDIX 1. Observations of quantity of matter. Balances . . .173 2. Observations of dimensions and densities .... 174 3. Observations of temperature-changes. Thermometers . .174 4. Observations of fall of bodies to the earth . . . .175 5. Observations of electrification 176 6. Cells . , 176 7. Observations of solution, &c 177 8. Purity of substances . 177 9. Observations of radiation . 178 THE ELEMENTS OP LABOBATOBY WOEK CHAPTER I MEASUREMENT OF QUANTITY OF MATTER 1. To Find Equal Quantities of Matter.— 1. Use a balance, and counterpoise two pieces of wood, cutting away one or the other with a knife until exact balance is obtained. 2. Counterpoise a piece of wood and a piece of lead. 3. Counterpoise another piece of wood with the lead, and then observe that the two pieces of wood counterpoised by the lead counterpoise one another. The above exercises show : — 1. That with the same kind of matter, wood, the pieces which counterpoise each other are the same size, or there- abouts ; but different kinds of matter which counterpoise each other are not of the same size. 2. That two bodies counterpoise each other if they each counterpoise a third body ; for these two bodies have been found to act alike under the same conditions — that is, when placed in the same position, and with all the surroundings the same. Two such pieces of matter are said to be equal quantities B 2 t ELEMENTS OF LABORATORY WORK of matter /however unequal in size or different in appearance " 06\mterf)6isin£ brie quantity of matter by another will indicate equal quantities of matter only when the instrument used is correct. But by performing two operations as in (2) and (3) we find two quantities of matter which are counter- poised under precisely similar circumstances with a third un- changed quantity of matter (the piece of lead kept in the same pan). There is nothing changed in these two operations except the pieces of wood. Although the balance used may be inaccurate, the same inaccuracy holds for each case, and thus we can make sure that two bodies are equal quantities of matter even with an inaccurate balance. 2. To Compare Two Quantities of Matter. — 1. Take several equal quantities of matter, and find how many of th«m counter- poise with a given piece of wood, cutting away the wood if necessary. It is convenient to use a set of weights — that is, a number of bodies so arranged and measured that we can readily make up from them a quantity of matter which shall contain the smallest quantity any required number of times. The need of a large number of equal quantities is thus avoided. Use grams. One gram will be the standard. 2. See how many of the same standard quantities of matter are equal to a larger piece of wood, cutting away as before if necessary. 3. Compare similarly two other pieces of wood, but use much smaller standards. Notice that less cutting away, if any, is needed. Use centigrams. A centigram is one-hun- dredth of a gram. With milligrams or thousandths of a gram the comparison becomes still more accurate. The above exercises show : — 1. That two quantities of matter can be compared, by seeing how many times each contains a standard quantity. 2. That the standard quantity, if large, does not enable us to measure exactly ; but the smaller the standard, the more exactly can we measure and compare. 3. That the limit of exactness can never be attained, as inequalities will be shown by more delicate balances. The MEASUREMENT OF QUANTITY OF MATTER 3 degree of accuracy should depend upon the object of the com- parison. We see that two operations take place in weighing any substance. The first consists in finding out a quantity of matter which will counterpoise the substance, or which will take its place on the pan and counterpoise equally a third body on the other pan. The second operation needed is to find out how many times this quantity of matter contains the standard quantity. When a set of weights is used the second operation consists in reading the marks or numbers on the several weights required for counterpoise. When a spring-balance is used the pointer indicates how many times the standard quantity of matter would be required to produce the same elongation of the spring. In this case the counterpoise, or what corresponds, has been made once for all by the maker, and the results marked on the scale. Com- pare a spring-balance with an ordinary one. 3. To Test the Accuracy of a Set of Weights by the Balance. — Counterpoise a 2-gram weight with shot and paper, then replace it by another. If they contain equal quantities of matter the counterpoise will be maintained. Test the two 10-gram weights similarly, and other equivalents, such as the two 10-gram weights with the 20-gram. Any excess or deficit may be marked, if the comparison has been made with an exact standard, and the balance is reliable. 4. To Investigate the Construction of an Accurate Balance. It is advisable at this stage to learn the necessity of great care in the use of such balances as are used in a laboratory. This may be done by taking to pieces very carefully such a balance s the one illustrated (fig. 1). 1. Note the rest or catch which prevents the knife-edges being worn, by saving them from unnecessary jarring. 2. Compare the balancing of the beam upon its knife-edge, when the pans have been removed, with that of a strip of wood upon a blunt point. 3. Note that the knife-edges supporting the pans enable the matter wherever it may happen to be placed in the pan to B2 4 ELEMENTS OF LABORATORY WORK act at the same point on the beam (namely, at the knife-edge itself). 4. Observe the use of the pointer and scale. Hi- . 1. Additional Exercises and Questions. 1. Construct a set of fractions of a gram from platinum foil and aluminium foil, ttse a pair of scissors for cutting away, and impress the value on each when correct. 2. How may equal quantities of matter be determined on a balance which has unequal arms ? What arguments may be used in support of your method ? 3. Describe exactly what is meant by saying that a given body weighs 3'3 grams, and give the operations by which this knowledge of the body is obtained. 4. How many milligrams are contained in 103*725 grams ? What fraction, vulgar and decimal, of a gram is the quantity 7 centigrams together with 11 milligrams? 5. Why is it best to stop the balance from swinging when the pointer is at the centre of the scale, and why should the weights never be altered when the balance is swinging, or the pans breathed upon when an observation is being made ? 6. Which is the best method of judging when there is exact counter- poise— O) by seeing whether the pointer comes to rest at the centre MEASUREMENT OF QUANTITY OF MATTER D of the scale, or (#) by seeing if it swings an even distance on each side of the centre ? Make an observation and explain the result. 7. What kinds of matter should be used for standards in weighing accurately ? What is the advantage of aluminium over platinum for small standards ? Should weights be cleansed ? 5. Measurement of Length and Volume.— 1. Find out the length of a given object by seeing how many times a given standard length is contained in it. Use 1 centimetre as a standard. (1 centimetre is one-hundredth of a metre.) 2. Measure the dimensions of a regular- shaped body. Use 1 centimetre as a standard. 3. Measure a given plane area by means of a body of standard area, and also by calculation. Use a square centi- metre as standard. A square centimetre is a square of which the side is 1 centimetre. 4. Find out by calculation how many times a given cube is larger than a standard cube. Use as standard a cube of which the side is 1 centimetre. 5. Find out by displacement of water, which readily adapts itself to any shape, how many times a standard cube is contained in an irregular-shaped body. Use a graduated vessel, marking cubic centimetres. 6. Verify the graduation of a burette by weighing the quan- tities of mercury or water delivered into a weighed vessel. Each division need not be tested. Care is needed in finding when the middle point of the liquid surface is level with the proper mark on the vessel. The above exercises show that the same methods are used in comparing the lengths and volumes of various bodies as in composing quantities of matter, and that there is the same necessity for a standard length and a standard volume for purposes of comparison. Precautions in Measuring. — The distance between any two points is found by measuring the number of units of length in the imaginary straight line joining them. In measuring any given distance we have to depend on our eye- sight or touch for ascertaining the coincidence of two points or marks.- Care must be taken that this coincidence is real. 6 ELEMENTS OF LABORATORY WORK For determining coincidence of liquid level with a mark on a graduated vessel a reading telescope [or that of the catheto- meter] is used when accuracy is needed. The surface of a liquid in a tube is not horizontal. In this case the centre of the surface is observed at each operation. Sometimes it is not possible to apply a scale directly to a distance, as in measuring the diameter of a sphere. The measurement then takes place indirectly. Another distance, capable of being measured, is adjusted so as to be equal to it, and then measured in its place. The use of callipers and compass will illustrate this method, and show how the sense of touch is used. Compare the results obtained with each of these instruments for a given dimension, such as the diameter of a sphere. The alteration of the dimensions of bodies by change of temperature makes it necessary that measurement should take place under the same conditions of temperature. The length of a metal rod should be taken at different tem- peratures to illustrate this need. Additional Exercises and Questions. 1. What are the requisites of a good standard of length ? 2. By what processes may lengths be measured ? 3. How would you find out if a given standard is correct ? 4. What are the advantages generally of the Metric system of measurement ? 5. Describe exactly the assumptions made in measuring any dimen- sion of a body, and compare the reasoning used with that used in weighing a body. 6. Measure the distance between two given points which are not connected by matter. State the precautions needed. 7. Measure as accurately as possible by a good scale the value of an inch in centimetres. Suggest methods by which greater accuracy may be obtained. 8. Use a steel scale and show that the graduations vary with the temperature : measure when cold and after heating. 9. Test the graduation of a eudiometer tube by fixing it upright and reading the successive levels caused by the addition of equal quantities of water. The water may be delivered from a burette or a pipette. Mention the precautions which are necessary. MEASUREMENT OF QUANTITY OF MATTER 7 6. Relative Quantities of Matter in Equal Volumes of Different Substances. — 1. Compare the quantities of matter in equal volumes of mercury and water, and turpentine. Use a marked beaker or flask, and a balance. 2. Compare the volumes of the above substances when equal quantities of matter are taken in each case. Use a beaker for weighing, and ascertain the volumes by pouring into a graduated vessel. Commence with the turpentine. , 3. Compare the volumes contained in equal quantities of brass and water. The volume of a piece of brass is equal to that of the water it displaces, and, by the displacement of water in a graduated vessel, the volume of the brass is easily measured. 4. Taking as unit the quantity of matter contained in a given volume of water, calculate the numbers to be given to equal volumes of other liquids and solids. Refer to the table of densities. The above exercises show that the appearance and size of a body give no exact information as to the quantity of matter it contains. Bodies vary in density. In order to ascertain the density of a body the volume and quantity of matter are each measured. The volume of a liquid is easily measured as it adapts itself to any required shape, but the volume of an irregular- shaped solid is less easy. It may be measured by displacement of a suitable liquid in a graduated vessel. It is a great convenience to compare all substances by reference to a common standard, and water of a fixed density is selected. Then the numbers, called specific gravities, which tell how much denser various substances are than water, show their densities relatively to one another. But it is more systematic to express the density of a body by the number of units of mass in unit of volume. A body which has four units of mass in unit of volume is twice as dense as one containing two units of mass in unit of volume, and so on. It must be remembered, when we speak of equal quantities of different kinds of matter, that we do not refer to equal volumes, but to such volumes as contain what we have agreed to call equal quantities of matter. Later on we shall add to our knowledge of equal quantities of matter. 8 ELEMENTS OF LABORATORY WORK Additional Exercises and Qicestions. 1. Assuming that the density of brass is 8 — that is, that 1 cubic centimetre contains 8 grams of matter — find the volume of a given piece of brass by weighing and calculating. Compare the result with that obtained by measuring the volume of water displaced by the brass. 2. Compare the densities of lead and tin by weighing, and determin- ing volumes by displacement of water. 3. Suggest methods of finding both the apparent and real density of porous bodies. 4. How would you find the density of copper sulphate— a substance which dissolves in water ? 5. Mention the various precautions which must be taken during observations of density. 6. What hypothesis can you suggest in explanation of the difference in density observable among various kinds of matter ? 7. Principles of Systematic Measurement,— We have dis- cussed in the preceding sections concrete quantities of dif- ferent kinds — quantity of matter, quantity of length, quantity of area, quantity of volume, and quantity of density. By direct observation we have been able to decide when two given quantities of the same kind are equal. -We have then seen how many times a given standard quantity is to be taken to make up a quantity equal to the quantity being measured — that is, we obtain numerical values, or numbers expressing the magnitude of any concrete quantity. All that we can say of any quantity is that it is equal to so many times a quantity of the same kind selected as a standard, and all that we can directly observe is equality, or inequality, in quantity. The standard quantity of matter, or the unit of mass, now used in all physical measurements is called a gram. The standard quantity of length, or unit of length, now used is called a centimetre. For convenience in exact weighing, sets of weights are used — i.e. various pieces of brass and aluminium, carefully ad- justed by the maker, so as to contain certain multiples and fractions of the quantity of matter in a gram, and arranged as follows : — MEASUREMENT OF QUANTITY OF MATTER 100 grams 5 grams 0'5 grams O'Oo grams O'OOo grams 50 „ 2 0-2 „ 0-02 0-002 „ 20 „ 2 „ 0-1 0-01 „ 0-002 „ 10 „ 1 o-i „ o-oi „ 0-001 „ Investigation of these masses will show that all quantities of matter not exceeding 201 grams, and not less than *001 gram, are represented to within -001 gram. It may happen that a quantity of matter to be weighed differs in quantity from any possible collection of the above weights ; but it will differ by a quantity less than *001 gram, and this may be negligible, or the balance may be unable to mark it. Some balances, however, measure within smaller quantities. Larger quantities are measured by larger standards ; and names are given to multiples and fractions of a gram as seen in the table below, which represents a portion of the metric system of measurement. A mass of 1,000 grams is called 1 kilogram (equivalent to 2*2054 Ibs. avoirdupois). A mass of '1 gram is called 1 decigram. •01 „ „ 1 centigram. „ -001 „ „ 1 milligram. For convenience in measuring quantity of length, or distance between two fixed points, a scale is used. This may be looked upon as corresponding with a set of weights. It is a body of suitable material and form, marked so that the dis- tance from any mark to the next is equal to a centimetre, or, if greater accuracy is required, to '1 centimetre. Numbers are written at intervals for readiness in reading the total number of centimetres. If large distances have to be measured, a centimetre is too small a standard ; while for very small distances the centimetre has to be subdivided, in the same manner as the gram is subdivided for accurate weighing. The following table gives the names of lengths, derived from the centimetre, according to the metric system: — 10 ELEMENTS OF LABORATORY WORK A length of 10 centimetres is called a decimetre. A length of 10 decimetres or 100 centimetres is called a metre (equals 39*37 inches). A length of 1,000 metres or 100,000 centimetres is called a kilometre. A length of -1 centimetre or '01 decimetre or -001 metre is called a millimetre. The numerical value — i.e. the number expressing the mag- nitude of any quantity of matter or of any distance— shows its relation to a magnitude of the same kind selected as unit. Thus if M denotes a definite quantity of matter, and L a definite distance, and m and I the respective units, then — and j give the numerical values of these quantities. It is seen that numerical values vary directly as the quan- tities, and inversely as the units with which the quantities are compared. In other words, as the quantity increases the numerical value increases, but as the unit increases the numerical value diminishes. In practice the magnitudes of most quantities are expressed by a number, followed by the name of the units used — e.g. 20 centimetres, 3 grams. The necessity for the names arises from the use of various systems of measurement. For example, distances are, for other purposes, measured by inches, feet, yards, miles, &c., and quantities of matter by ounces, pounds, tons, &c. If one system were universal, numbers alone would denote the magnitudes of physical quantities. We shall after- wards see that all physical quantities, however complex in their nature, may be measured by the use of three fundamental units of length, mass, and time. This system is called the centimetre-gram-second, or C.G.S. system. It will be seen that all quantities are brought to a common scale by use of this system. Having selected the centimetre as the unit of length, it is necessary, in order to secure uniformity, to take as the unit of area the quantity contained by a square, each side of which is a centimetre ; and for unit of volume that quantity con- tained by a cube, each side of which is a centimetre. A MEASUREMENT OF QUANTITY OF MATTER 11 volume equal to that of 1,000 cubic centimetres [written 1,000 c.c.] is called a litre. The final authority for the unit quantity of matter in the C.G.S. system, and the standard by which it must be deter- mined, directly or indirectly, is the Kilogramme des Archives, a piece of platinum adjusted by Borda. The gram is '001 of this piece of platinum. All distances must be compared, directly or indirectly, with the distance between the ends of a rod of platinum when it is at the temperature of melting ice. This is the standard metre made by Borda in 1795. The centimetre is equal to •01 of this distance. The metre was selected as being the ten-millionth part of a quarter of the earth's circumference, so that all lengths might be compared with the circumference of the earth, a length looked upon as permanent, and hence always capable of being redetermiiied. That the earth's circumference should be commonly referred to as the standard is, however, impossible, and the alternate authority is now the length of the platinum rod made by Borda. Having fixed on a distance and called it a metre, a piece of platinum was prepared containing the same quantity of matter as a cubic decimetre of pure water at 4° C. This was called a 'kilogramme.' Hence a cubic centimetre of such pure water would have a mass of 1 gram. This process was adopted with the intention of being able to re-establish the unit of mass, if necessary, from the unit of length, but this is practically very difficult, and moreover the supposed relation is only approximate. Hence both the metre and kilogramme are arbitrary standards. It is part of the same uniform system to take a density of 1 gram per cubic centimetre as unit of density. It was intended to make the density of water unit, and it is very nearly so, for it contains approximately the unit quantity of matter in the unit volume. A body which contains 2 grams per c.c. would have a density denoted by 2, and so on. The number expressing the magnitude of a given den- sity is determined by finding the number of units of mass it 12 ELEMENTS OF LABORATORY WORK contains, and also the number of units of volume. Then the first number, divided by the second, gives the number expressing the density, or — D = M when D equals numerical value of density ,, M „ ,, „ ,, mass „ Y „ „ „ „ volume The unit of volume, however, is derived from the unit of length ; for if I denote the unit of length, I- denotes the unit of area, and I3 that of volume. Hence we may write d — — and perceive that d, the unit of density, is derived from the fundamental units of length and mass. If a different system of units is used in measuring density, then the numerical values will be found from the following equation : — M D _ m or D _ " " ~ Here D, M, and L stand for the respective concrete quan- tities, and d, m, I for the units adopted. 8. Relation of Areas to Linear Dimensions. A square, the side of which has a units of length, contains a2 units of area. A rectangle, the sides of which have respectively a and b units of length, contains ab units of area. A circle, the radius of which has r units of length, contains 77 r2 units of area. A cube, the edge of which has a units of length, contains 6«2 units of area. A sphere, the radius of which has r units of length, contains 47rr2 units of area. TT stands for 3' 141 5 9 nearly. MEASUREMENT OF QUANTITY OF MATTER 13 9. Relation of Areas to one another. English Measures. 1 acre contains 4,840 square yards — i.e. a square the side of which is a yard. 1 square yard contains 9 square feet. 1 square foot contains 144 square inches. Metric Measures. 1 hectare contains 10,000 square metres. 1 square metre contains 100 square decimetres. 1 square decimetre contains 100 square centimetres. 1 square centimetre contains 100 square millimetres. 1 metre = 39*37 inches nearly. 10. Relation of Volumes to Linear Dimensions, A cube, the edge of which has a units of length, contains d6 units of volume. A rectangular parallelepiped, of which the respective edges have a, b, and c units of length, contains abc units of volume. . A sphere, the radius of which has r units of length, con- tains f Trr3 units of volume. A circular cylinder, of height h and radius r, contains •nr^h units of volume. 11. Relation of Volumes to one another. English Measures. 1 cubic yard contains 27 cubic feet. 1 cubic foot contains 1,728 cubic inches. 1 gallon contains 8 pints or 4 quarts. 1 pint contains 34'659 cubic inches. Metric Measures. 1 cubic metre contains 1,000 cubic decimetres. 1 cubic decimetre contains 1,000 cubic centimetres (c.c.). 1 cubic centimetre contains 1,000 cubic millimetres. 14 ELEMENTS OF LABORATORY WORK 1 cubic decimetre is called a litre. 1 litre contains 1,000 cubic centimetres or 1,000,000 cubic millimetres. 1 litre contains 1'76 pints nearly. 12. Method of Measuring very small Quantities of Matter. Although a carefully constructed balance will readily indicate a difference of 1 milligram (or '001 gram) between the quan- tities in the two pans, and although the milligram * weight ' is the smallest quantity of matter which is placed in the pan for the purpose of comparing quantities of matter, yet we have to deal, in chemical measurements, with quantities far more minute than milligrams. In order to obtain this great ac- curacy of comparison, the operation of weighing is combined with that of solution. When a solid is dissolved in a liquid — for example, salt in water — there are numerous proofs that the solid is evenly distributed through the liquid. A small quantity of the solid is taken and dissolved in a large quantity of the liquid. For example, *1 gram of common salt may be dissolved in some water in a litre flask, and then more water added until it is full up to the litre mark. A portion of this may be trans- ferred to a burette graduated into cubic centimetres, or even into fifths of cubic centimetres. We may thus be certain how much of the salt is contained in our carefully measured portions of this solution j and we may be certain, by using the more accurately graduated burette, to within the 5 o^ro- (or "00002) of a gram. 13. Methods of Measuring very small Distances. — The Vernier. — Greater accuracy in the measurement of distances between two points is obtained when the ordinary scale is accompanied by a sliding scale, or vernier, which is divided so that n divisions correspond with n — l divisions of the scale. Then each vernier division is -th smaller than a scale division. n If the vernier has 10 divisions, for example, which are equal to 9 of the scale, a vernier division is yL smaller than a scale division. In use, the vernier is moved until the marked point, or end, is in the proper position for calculating the required dimension. In the diagram (fig. 2) the distance to be measured MEASUREMENT OF QUANTITY OF MATTER 15 is from a to b, the vernier standing at b, between 5 and 6 of the scale. Looking along the scale, it is found that division line 7 of the vernier and 1 2 of the scale more closely coincide 3 10 , 1 , , , , i . , , 20 30 . , 1 , . ^^^ W%%M\ III!!! a 612 i » * 5 6 7 8 9 10 Fig. 2. than any others. Since each vernier division is T^ less than a scale division, the distance between 5 and b is -^ of a scale division — that is, the whole distance is 5 plus T% or 5*7. With smaller divisions greater accuracy is obtained. Samples of verniers, for practice in reading, will be found on the barometer, cathetometer, and spectroscope. On the last it is used for reading very small angles. 14. The Micrometer Screw and Spherometer.— A small distance may be very accurately measured by means of screws carefully constructed, so that a given length of the stem con- tains a suitable number of threads. This micrometer screw works within a corresponding hollow screw. If the screw has 10 threads in a centimetre, and the hollow screw is fixed, one complete turn of the screw will cause it to advance •! centimetre. If the head of the screw takes the shape of a large graduated circle, containing, for example, 200 divisions, then a turn through one of these divisions will cause the screw to advance ^^ of '1 centimetre, or -0005 centimetre. In the Whitworth measuring machine a distance may be read to one-millionth of an inch, by a modification of this process. This method of measurement is illustrated in the use of the spherometer (fig. 3). A three-branched piece of metal stands on three fixed equidistant legs, and a micrometer screw with a large divided circular head moves through the centre, and is read by the aid of a fixed upright scale. The points of the legs and moveable screw are of hard steel, and they are adjusted on a true plane, so that all four are in the same plane 16 ELEMENTS OF LABORATORY WORK when the divided circle is at zero. Small vertical distances and curvatures are measured by finding the new position of Fig. 4. contact for all four legs by the sense of touch. The screw- gauge (fig. 4) also illustrates this method of measuring linear distances by the movement of a screw. Measurements should be taken with each instrument. 15. Other Methods of Measuring Density. — When a body is weighed while suspended in water or other liquid, it may be counterpoised by a smaller quantity of matter than when weighed in the air. Experiments show that this apparent loss is exactly equal to the quantity of water or other liquid dis- placed by the body — i.e. to the mass of the volume of the liquid equal to its own volume. In order to determine the density of a body, suspend it by a fibre of silk or by a thin wire to the hook at the end of a balance-beam. Weigh it in this position, and then support a vessel containing water over the pan of the balance, so that the body may now be weighed when immersed in water. Care must be taken that no air adheres to the body when in the water, and that the density of the water at the temperature of observation is used in the calculation, not that of water at the standard tempera- ture (0° C.). T. ., True mass Mass Density =- : — -n = ==-. r Apparent loss of mass V olume. in water. MEASUREMENT OF QUANTITY OF MATTER 17 By reference to a table of the densities of water at different temperatures, we find the volume of water corresponding to the quantity of matter apparently lost, and this is the same as the volume of the body measured. If the substance to be measured dissolves in water, a liquid which does not dissolve it is used. If the body does not sink in water, its density must be ob- tained simultaneously with that of a heavy body, of known density, which will cause it to sink. And a third method is to make such a mixture of two liquids, say alcohol and water, that the body will float in it at any depth. Then find the density of the mixture by direct weighing. This will be the same as that of the body. Table of Densities. J/ = 7 or units of mass in unit volume at 0° C. Air . Alcohol Aluminium Brass . Copper Ether Gold . Glass Glycerin . Iron . . . Hydrogen . . Ice . Lead . Nitrogen . Mercury Oxygen Platinum . Hydrogen sulphate Turpentine . Sea water . Pure water at 4° C. Wood. 0-00129 0-795 2-50 to 2-67 7'80 to 8-54 8-30 to 8-89 0-716 19-20 to 19-60 2-50 to 3-50 1-26 7-50 to 7-90 0-0000896 0-918 to 0-92 11-07 to 11-40 0-001256 13-596 0-00143 21-16 to 21-53 1-854 0-870 1-026 1-000013 0-4 to 0-9 18 ELEMENTS OF LABORATORY WORK Additional Exercises and Questions. 1. Calculate the number of cubic millimetres in a cubic inch. 2. If 2 litres of air weigh 2-5854 grams, what is the density of air ? 3. If the pitch of a screw is 1 millimetre and its circular head is divided into 100 equal divisions, calculate the linear distance corre- sponding with a turn of the circle through 73 divisions. 4. Determine the pitch of a screw by direct comparison with a scale, and also by ascertaining its linear movement when turned within a fitted hollow screw. 5. Measure the circumference of a penny by marking it and rolling it along a scale. Then measure its diameter and calculate from it the circumference. 6. Read the height of the barometer by using the vernier. 7. Take several readings of angles by using the vernier on a spectro- scope. 8. Ascertain the diameter of a wire by using the screw-gauge. 9. Find the thickness of a microscopic cover-glass by using the spherometer. Also measure several cover-glasses and compare the re- sult with the last observation. 10. How may microscopes be utilised for measuring very small distances ? 11. How is a long distance best measured ? What difficulties have to be overcome and what precautions are needed ? 12. Suggest methods for measuring irregular areas. 13. Compare the densities of several liquids by weighing the same body in each. 14. Observe the alteration of density, when the temperature of water is raised, by showing that the counterpoise obtained when a body is weighed in cold water is not maintained if warm water is sub- stituted for the cold. 15. Suggest a method of determining the density of a body lighter than water. Test your method. 16. How could the density of a gas be found out ? 1 7. What precautions are necessary in determinations of density, and what conditions have to be attended to ? Give the observations, in order, which are needed in an exact determination of density in the case of («) a gas, (&) a liquid, and (c) a solid. 19 CHAPTER II OBSERVATIONS OF CHANGE OF POSITION 16. Relative Position. — The simplest kind of change observ- able in nature is change of position, and the simplest observ- able instance of this occurs when two material particles change their position with regard to each other. A simpler case cannot be observed. We are unable to perceive a change of position in space except as occurring between two bodies at least, or be- tween two parts of the same body. Two bodies are always needed for the perception of movement, rough or exact measurements being made from one to the other. For this cause we are not conscious of the rapid movement of the earth, except by reference to some other body in space. One or more material bodies, coming under any kind of observation for investigation or measurement, will be called a material system. In investi- gation of any change, it is important to exclude from the system all unnecessary members, while including all that are essential. All research proceeds by gradually eliminating the non-essential elements of a change, or by including more and more members within the region of measurable change. The relative positions of two material particles may be represented by a diagram (fig. 5), where the length of the straight line A B drawn from A to B represents the distance of B from A. By agreeing to represent a distance in space of one metre by a length of line of one centimetre, or by any similar agreement, the diagram becomes a plan drawn to scale. The relative positions of any number of material particles, that is, the configuration of any system, may similarly be represented by ascertaining in this manner the distance of c 2 20 ELEMENTS OF LABORATORY WORK each from a given origin, and drawing corresponding lines on paper. We shall now proceed to show that such a representation is only partially true. It describes relative distances only. Fig. 5. 17. Means of Defining the Position of a Small Body with regard to a Fixed Point. — It is clear that we know nothing of position except by reference to some point taken as fixed ; and, since our description is always relative, it is of no import- ance to determine the real condition of this point, whether fixed or moving. Our statements and measurements are made on the assumption that the point of reference is fixed, although further investigation might show that the point of -reference is far from fixed. It must not be supposed, however, that the measurement of the linear distance of a body from a point, considered as fixed, completely describes position. It is necessary to state the direction in which the distance has been measured. For example, the circumference of a circle consists of an infinite number of points equidistant from the centre of the circle. And all positions on the surface of a sphere are the same linear distance from the centre of the sphere. Something more than linear dis- tance is needed. We require to know the direction in which the operation of linear measurement has been, or is to be, made. An inspection of the diagram (fig. 6) will show that if it be merely a question of the position of the particle A with regard to the point o, each of them being upon this flat sheet of paper, we may understand what is M Fig. 6. OBSERVATIONS OF CHANGE OF POSITION 21 meant by direction if we draw two straight lines which shall pass at right angles through the point o. Lines A M, A N drawn perpendicularly from A to these lines of reference show by their relative magnitude in what direction A lies with regard to o. It is important to note that our observations do not extend beyond particles, that is, bodies or portions of bodies so small that their dimensions may be neglected. How small such a body need be will depend upon the purpose of the measurements and the accuracy attainable. 18. Observation of Change of Position. — If the position of a particle be observed or measured at different times, and the necessary measurements be not found unchanged, then the particle has undergone a displacement or change of position. The simplest change of this kind which can be observed is the alteration in the linear distance between two particles A and B. If we consider these two bodies entirely by themselves, without reference to any other body, we may represent fully by diagram the amount of displace- ment during any given interval. All that is necessary is to draw a straight line, A B, representing the linear distance between them at the one instant of time, and another line, a b, representing in the same direction the linear distance at the other instant. The difference of the two lines in length taken on the same scale represents the displacement, but only when the straight lines A B and a b remain strictly parallel. As to the exact mode of displacement or condition of the par- ticles during the change, such a plan tells us absolutely nothing ; and as to whether one alone or both together have undergone an absolute displacement, we are unable to decide. We are unable to say in the simplest case of displacement whether A or B has moved. In other words, we are only aware of displacement as a change in a relation of two bodies at least, that is, we can observe relative displacement alone. If we refer to a third body, and make the necessary measure- ments, it is true we gain additional knowledge, but an exten- sion of our measurements to a fourth body might disclose further displacements. A little consideration will make clear the connection between our inability to know any- 22 ELEMENTS OF LABORATORY WORK thing of absolute position and our ignorance of absolute dis- placement. 19. Further Observations of Position and Displacement. — We have now to consider less simple modes of displacement. We have learnt that position, and consequently change of posi- tion, must be measured by reference to something considered as fixed, and further that reference to a single point is not suffi- cient even when we are limited to a given plane. If we consider the surface of the floor, one side and one end of a rectangular room as fixed, while a body within the room is in motion, a simple experiment will illustrate that the position of that body is completely defined at any moment by measur- ing its shortest distance from each of these three surfaces. Instead of these surfaces, the roof, other end, and other side might be used with the same completeness of definition, although the actual measurements might differ. But the same result would not follow if two of the surfaces were parallel. The three surfaces are best at right angles to each other. The body under consideration may now be caused to move in three directions, and in three directions only. It may be displaced with regard to one surface only, its distance from the other two remaining unaltered. It may also be displaced with regard to two surfaces at the same time, and, lastly, it may be displaced with regard to three surfaces simultaneously. These three methods include all the possible kinds of displacement, that is, if measurements be taken at two distinct times of the distances from the three surfaces, either one, two, or three may be found to have altered. By taking a number of con- secutive observations of these distances and marking the positions in some way, we may construct the path of the body. In common occurrences of displacement a series of rough measurements are made from sight, and, by the aid of memory, the path along which the body has moved may be described. But in every possible case of displacement, the limit of knowledge attainable is that given by three linear measure- ments from three plane surfaces at right angles to one another. These measurements may be taken at as short intervals of time as possible, and the more frequently they are made the OBSERVATIONS OF CHANGE OF POSITION 23 more completely is the path of the moving body known. Having made such measurements at sufficiently frequent intervals, we shall find that a particle may move : — 1. In a straight line with alteration of distance from one plane. 2. In a straight line with alteration of distance from two planes. 3. In a straight line with alteration of distance from three planes. 4. In a curved line with alteration of distance from two planes. 5. In a curved line with alteration of distance from three planes. 20. Practical Measurement of the Paths of Moving Bodies, The three necessary planes from which measurements of position have to be taken, may be illustrated by three plane pieces of wood, screwed together at right angles, as shown below. For readiness in calculation and measurement these pieces of wood should be covered with paper containing lines ruled at right angles to each other vertically and horizontally on each surface. By this means, the three inner faces are covered with equal squares of, for example, a centimetre in the side ; and if each of the lines so drawn is numbered, the position of a body with regard to any plane is readily per- ceived. The numbers may be written along the three lines of junction as shown in the figure. A small body fixed upon a wire, which is curved at the bottom so as to stand, will serve as the body of which the position requires to be defined. Different values result from the measurement as its position is changed. Several observa- tions should be made and recorded. It will be noticed, how- ever, that the distance from one plane, which is the one on which it stands, does not vary from the nature of the support. This may be varied by bending the wire. A little considera- tion of the model will show that we may get sufficiently accurate results by shutting one eye and looking with the other at the position marked by the body on each surface in succession. 24 ELEMENTS OF LABORATORY WORK Instead of varying the position of a body we may support a wire, a 6, as shown in the diagram, in such manner as to represent the path through which an imaginary body has been, or is being, dis- placed. The position of the wire may be varied in any manner, and it may be made to assume any shape. A number of measurements should be taken of various possible paths. If we now introduce an irregular-shaped body of considerable dimen- sions, it will at once be seen that three linear measurements are not sufficient to define its position. They would in fact define nothing more than the position of that portion of the body from whicli they were made, and no information would be supplied as to the rest of the body. In order to obtain this information accurately each portion of the body would require to be defined by its distance from the three planes ; but if the body is a rigid body, it is generally sufficient to make measurements from various portions of its surface. The more numerous the por- tions measured, the more accurate will be the description given by them of the position and shape of the body. It will be readily noticed that by shape we mean relative position of parts. 21. Observation of Rotation. — It must not be supposed that a knowledge of the exact position of any given portion of a body at two different times is sufficient for the purpose of describing the movement which the body has undergone in the interval, however small this interval may be. "We might find that in the interval the separate portions of the body have moved Fig. 7. OBSERVATIONS OF CHANGE OF POSITION 25 along paths which do not resemble that of the body as a whole. In other words, a rotation of the body may have taken place in addition to a translation, and it is at once recognisable that the essential of rotation is the possession of parts. That is rotation cannot exist unless a body possesses parts, and it cannot be observed unless we distinguish parts. If a sphere of perfectly even and similarly coloured surface were rotating we should be unaware except by touch. To become aware, marks upon the surface would be needed, from which rough measurements could be made by eyesight. In the case of an irregular-shaped body, rotation is easily observed. By making a hole in a body and placing it on the various wires representing paths, illus- trations of rotation may be given and its meaning made clear. Combinations of rotation with the various kinds of translation may also be shown. With this arrangement we find that a given body is capable of ten modes of motion with regard to three given planes, viz., the five which we have shown a point to be capable of exhibiting, together with five others derived from a combination of these with rotary movement. If we are not limited to special planes for purposes of measurement, we are able to arrange all kinds of motion into six classes, namely : — 1. Displacement in a straight line. 2. Displacement in a plane curve. 3. Displacement in a non-planar curve. 4. Displacement in a straight line with rotation, or rotation alone. 5. Displacement in a plane curve with rotation. 6. Displacement in a non-planar curve with rotation. All these classes should be illustrated not only with single bodies, but with systems of separate bodies, joined together by wires, and so forming a rigid system, that is, a system which does not undergo any internal displacements. In reality the parts of any rigid solid form such a system. If a system undergoes change of shape, if, for example, the wires connect- ing the various parts of the system used as a model were to shorten or lengthen while other displacements are taking place, it is easy to see how very complicated the path of any member of the system may be. 26 ELEMENTS OF LABORATORY WORK . Additional Exercises and Questions. 1. Why are two lines at least needed in order to define the position of a particle in a given plane ? 2. Compare the above method of defining position with that of using angles. Give diagrams. 3. Show by diagrams that the position of one point in a given plane with regard to another requires either two lines at right angles, or two lines drawn from these points to a third, before any description of that position can be given. 4. There are four points in the circumference of a circle which are similarly situated with regard to any two diameters drawn at right angles. How may their position with regard to one another be described ? 5. How may the position of a given area be defined ? 6. Draw a diagram defining the position of four particles in the same plane with regard to each other, that is, describe the configuration of such a system of particles. 7. Represent, by three sheets of paper or three books, three planes at right angles to one another. 8. Measure on the model planes the distance from each of a small body supported on a wire. Use a piece of string and a scale for measurement. Also measure from the squares by eye. 9. Place several bodies on the model to represent the different posi- tions at different moments of a given body, and bend a wire to show the probable path of the body. Wrhat conditions must be assumed before this path can be taken as the true one ? 10. Fix wires to show the various paths in which a particle may move with regard to the model. 11. Fix wires which shall represent the possible paths of a portion of a large body. How would they be altered if the shape of the body were changed during the displacement ? 12. Show that every portion of a rotating body moves in the second or third mode stated as possible for any particle, that is, either in a plane or non-planar curve. 22. Rate of Change of Position.— When both the extent and duration of a given displacement are observed we become conscious of motion. The unit of time is the second. If a displacement of a metre along the straight line joining two particles occurs in a second, or of two metres in two seconds, and so on, then if one of the particles be considered as fixed, the other is said to be in motion OBSERVATIONS OF CHANGE OF POSITION 27 at the rate of one metre per second, or to have, if the displace- ment is uniform, a speed of one metre per second. It is im- material which body is considered as fixed in position. The numerical value of the speed of a body so moving is the same as the number of units of length which are added in the unit of time to its distance from a selected origin. 23. Change of Speed, or Acceleration. — Motion is not always constant. It may be variable. If it be constant, the speed of a material particle, measured at two different times, is found to be unchanged. If it be variable, the speed is said to accelerate. The acceleration may be positive or negative, that is, there may be an increase or a decrease of speed. The change in speed occurring in a given interval gives the conception of rate of acceleration, just as speed is derived from combining the magnitude of the distance traversed with the time occupied. It is also obvious that the rate of acceleration may similarly be either constant or variable. It will be seen that the numerical value of rate of rectilinear and uniform acceleration is measured by the number of units of speed which are gained or lost in a unit of time. 24. Measurement of Time. — We are directly conscious of an order or sequence of events. The experience of all generations has led men to regard certain events as recurring with suffi- cient regularity to be constituted into fixed points, from which the more variable events may be dated, and by which they may be compared with one another. These regular events are the alternation of day and night, the changes of the moon, and the apparent maximum height of the sun. From these crude reckonings our more exact conceptions have grown ; but we still have to depend upon the rotation of the earth for our measure of time. A chronometer or clock is an instrument constructed so that the index moves over one division of the second-dial in •s"gcorr °^ *ne mean solar day. The number of seconds, elapsed since the beginning of the day, is calculated by means of the minute and hour fingers. A chronometer is compared with the revolution of the earth in the following manner : — 28 ELEMENTS OF LABORATORY WORK A telescope with a vertical cross-wire is mounted so that it swings in the plane of the meridian. The first apparent contact of the sun with the cross-wire is compared with the chronometer, and the contact again noted the next day. This observation gives the length of a solar day. These, however, vary throughout the year. The year is the period in which the earth completes its orbit round the sun. The mean length of all the days throughout the year is found, and it is called the mean solar day. Time-keepers are constructed so that the seconds, marked by them, are -g-^ J^ of this calculated mean solar day. This second is the unit in all physical measurements. The interval between successive transits of the same fixed star is called a sidereal day. A star being practically at an infinite distance, a sidereal day is the accurate period of the earth's rotation. The sidereal day is slightly longer than the mean solar day. 25. The Resultant of Two Simultaneous Displacements. — It is clear that a given displacement may have resulted from a movement along any number and any variety of paths. Ob- servations alone can decide the manner in. which the displace- ment proceeded. A particle may move in a straight line A B, or it may have taken any other path, such as A c, c B (fig. &). If the particle reach the position B at the same time by either path, a certain relation must hold between the speed along Fig 8 AB and the speeds along the paths AC, c B. The numerical value of the one must be the equivalent of the other two speeds, since the same result is obtained in each case, although the equivalence may not be very clear. If the cause, whatever it may be, which produces the displacement along A c co-exists with the cause which would, if it acted upon the body when it is in the position c, produce the displacement along c B, it will be perceived that the displacement will take place along the path A B, but only in those cases where the directions and amounts of displacement during a given time OBSERVATIONS OF CHANGE OF POSITION 29 could be represented, as in this case, by the three sides of a triangle. In other words, we may have one side of any tri- angle representing in direction and magnitude the displace- ment which takes place in a given interval of time, when a body is simultaneously acted upon by two causes which would, if they acted at different but equal intervals, produce dis- placements represented respectively in magnitude and direc- tion by the other two sides of the triangle. This generalisation may be expressed in still another form. We may say that if a body is subjected to conditions which would bring about a certain speed in a certain direction, and also to further con- ditions which would bring about, if the previous conditions had not existed, another speed in another direction, then the direction and magnitude of the resultant speed, which the body really acquires under the joint conditions, may be calcu- lated from the rectilinear distance to which the body would have been moved if the component displacements had suc- ceeded one another instead of being simultaneous. In case of two causes, or two combinations of causes, which would be capable in succession of giving to the body the speeds re- presented by A c and c B happening to coincide in time, then the line A B represents, in magnitude and direction, the resultant speed, or the direction and rate of the resultant displacement. We have therefore to remember, in connection with changes of this kind, not only direction but speed, or rate of displacement. 26. Further Consideration of Simultaneous Displacements, In the last section we have learnt how to find the resultant of two displacements. The method given is applicable to any number of displacements. It is merely necessary to note that our diagrams may be polygons instead of triangles, and that our method only applies to displacements which take place in the same plane. For displacements in different planes diagrams on paper would not suffice, but wire models may be constructed to exhibit both direction and magnitude. It is easy to see that if a body is acted upon by a cause which is capable of giving a displacement equal and opposite in direction to the resultant of displacements which would be produced by the action of other causes, then the body is at rest 30 ELEMENTS OF LABORATORY WORK in spite of the several causes tending to move it. It is frequently needed to find the causes which will be effective in keeping the equilibrium of a body in opposition to causes which may tend to displace it in various directions and at various rates. Those conditions will be effective under which the body would acquire a displacement equal and opposite to that which would be the resultant of the other displacements. It will afterwards be found that these considerations will sometimes be brought to bear upon important problems which require the above processes to be reversed. We frequently require to resolve a given displacement into its components — that is, to ascertain what other displacements would find in this given displacement their own resultant. And most commonly these displacements require to have directions which are at right angles. The construction of a few diagrams will show that a given displacement may result from an infinite variety of component displacements, and consequently a given displacement may be resolved into an infinite variety of components. Additional Exercises and Questions. 1. How is it determined whether the velocity of a body is uniform or variable ? 2. What is the unit of velocity in the C.G.S. system ? What would be the displacement in three minutes of a body moving uniformly with a velocity of seven ? 3. Show by a diagram that a single act of displacement may produce the same result as two or more successive displacements. 4. What will be the joint effect of several causes, each of which sepa- rately would produce the same displacement in the same direction ? What would be the condition of a body acted upon by causes which tend to move it in exactly opposite directions ? 5. By what processes would you trace the real path with regard to the earth of a person walking on the deck of a ship in motion (1) for- ward, (2) aft, (3) from side to side ? Draw diagrams and state the data required for calculating his velocity with regard to the earth in each case. 6. What will be the condition of a body which is acted upon at the same moment by causes which would,, if they acted in succession, pro- duce in it during equal intervals the displacement represented in direc- tion and magnitude by the three sides of a triangle taken in order ? OBSERVATIONS OF CHANGE OF POSITION 31 7. Show that if two adjacent sides of a parallelogram represent in direction and magnitude the displacements produced in equal intervals of time by two given causes, then the diagonal line between them must represent the direction and magnitude of the displacement produced in the same interval of time when these causes act simultaneously. 8. Show that the statements which have been made about displace- ments which take place in equal intervals of time must necessarily apply to speeds. 9. Show by diagram how to find resultant of any number of dis- placements occurring simultaneously in the same plane. 10. Construct a wire model to exhibit the resultant of several dis- placements in different planes. 27. Examples of Mechanical Constraint of Motion.— The ordinary methods of constraining motion or rendering- it determinate, and those which may be seen illustrated very frequently in machinery, are three in number, viz., the use of (1) guiding grooves or slots to allow sliding only, (2) pin and eye to allow turning only, (3) helix or screw guides, to allow screwing only. It will be seen that grooves and slots only allow translation in the direction of the groove. The pin and eye allow only rotation about an axis, while the helix allows rotation to proceed simultaneously with translation. It will be seen that the rigidity of solid matter is here utilised to prevent movement except in the desired directions. These modes of constraint really form the basis of machinery. We may obtain from them examples of all the kinds of dis- placement of which a body has been shown to be capable. But inasmuch as a body near the surface of the earth has always a tendency to move towards the earth, we always find the other movements of a body modified by this tendency, which also largely influences the structure of machines themselves. The most common as well as the most effective mode of con- straint is that in which a body moves along a straight groove ; examples of this may be seen in a piston working in a cylinder, and guide-blocks working in their guides. A lathe-bed or optical bench will also serve as examples. In these cases it will be seen that all particles of the guided and constrained body have parallel rectilinear paths. In cases of the second mode of constraint, such as the 32 ELEMENTS OF LABORATORY WORK movement of a wheel-axle, shafting, or pin on its bearing, all the particles of the constrained body move in concentric paths. In the third mode of constraint each particle of the body has a helical path, that is, each particle rotates about the same centre, but this centre is itself being displaced in a straight line. That is, the displacement of the whole body is composed of a translation and a rotation. Any hollow screw forms a helical guide. It is important to note that it makes no difference in any of the above examples which is at rest, the constraining or the constrained body. This follows from what has been pre- viously said about the relativity of motion. A little consideration will make clear the following state- ments : — 1. That if one point in a body be fixed, there can only be rotation taking place in that system, but the rotation may take place in any direction. 2. That if two points in a body be fixed, then the given system is still capable of undergoing rotation, but the rotation in question can only take place about the straight line in which these points are found. This straight line is called the axis of rotation. 3. If three points which are not in the same straight line be fixed, then there can be no movement of the body. 4. If one point in a body be constrained to move parallel to a line, the body may undergo rotation or translation or both. 5. If two points in a body be constrained to move parallel to a line, the body may be translated or rotated in one plane. 6. If three points in a body be similarly constrained, the body may only be translated. 28. The Conversion of Circular into Rectilinear Motion, We may readily show that a body may be constrained in two directions at right angles to one another, so as to take a circular path. The rectilinear motion of the bar (fig. 9) be- tween the guides at c and D causes the block E, moving in the groove A B, to have a circular path. The circular motion is produced by two sliding constraints at right angles. The conversion of circular into rectilinear motion (or, as it is called, reciprocating motion, on account of the to-and-fro OBSERVATIONS OF CHANGE OF POSITION 33 movement in a straight line), and inversely of rectilinear into circular motion, is also seen in fig. 10. A common requirement in mechanism is that rectilinear movement along a given line shall produce circular motion. This is seen in the rectilinear movement of a piston being used to drive a wheel by means of a crank-rod. The model shown may readily be cut out of cardboard and pinned together. The groove c D corresponds with the cylinder, and the part A B acts as a crank -rod, while the circular portion answers to the driving-wheel. By insert- Fig. 9. Fig. 10. ing the point of a pencil through A and B the two paths may be marked on paper. Methods of mere transference of motion may be seen in the leather bands by means of which motion is handed on from one wheel or pulley to another where needed. In this case we have the rotation of the rim of the pulley causing ordinary rectilinear motion in the band, and this, when it is needed, is again converted by contact with another pulley into rotary motion. In a locomotive the reciprocating motion of D 34 ELEMENTS OF LABORATORY WORK the piston-rod is converted into circular motion in the driving- wheel, and this into the rectilinear movement of the loco- motive by the friction of the rails. Every piece of mechanism affords some illustration of change or constraint of motion. Additional Exercises and Questions. 1. Bend a piece of wire so as to exhibit the path of any particle in a nut moving upon a screw. How would you proceed to make your model exactly represent the path of a certain particle upon a given nut moving on a given screw ? Describe also the path of any particle in a screw moving through a stationary nut. 2. Ascertain by direct observation the paths of a particle in a wheel, or round disc, rolling in a straight line. Draw it upon paper, and explain its shape. 3. What would be the path of every portion of a wheel which is spinning and being moved in the direction of its axis ? 4. Give examples of each kind of mechanical constraint of motion, stating the mechanisms which exhibit them. 5. How would you fix a given body so that it can move in a circle which may lie in any plane ? 6. Suggest a mechanism for converting one rotation into another rotation at right angles. 7. Show by means of a diagram— (1) that when a rigid body is trans- lated, every particle in it moves through an equal distance in the same direction, and (2) that when a rigid body rotates, each particle does not move through the same distance nor in the same direction. 8. Make clear by diagrams and observations that any displacement of a rigid system may be produced by a translation together with a rotation of that system about any point in it. 35 CHAPTER III OBSERVATIONS OF CHANGE OP TEMPERATURE 29, Change of Temperature Causes Change of Density. — 1. A hot body is placed in contact with a cold one. The cold body becomes warmer and the hot one colder. Generally, when bodies of different temperatures are placed together they will be found to assume the same temperature gradually. 2. Observe the increase in size of a piece of iron, or better, of platinum, when in contact with a hotter body, for example, a gas flame. Counterpoise when cold, and after it has been in contact with the hot body, replace it on the balance. Observe that the balance does not indicate any change in the quantity of matter. Generally, a rise in temperature is accompanied by a decrease in density, i.e., the same quantity of matter fills a larger volume. 3. Fill a small flask with water, mark on the flask the level of the water, and fill a similar flask with the same volume of mercury, and mark its level likewise. Place the flasks in contact with a warmer body, e.g., place them within a vessel containing hot water heated by a gas flame. Observe that the level of each liquid changes, but to a different extent ; while the quantity of matter in each case may be shown, by the balance, to be unchanged. Both the mercury and the water are raised to the same temperature ; but their densities are not equally diminished. The glass of the flasks will also change in density, but to the same extent for each, so that the apparent expansions give the actual relative expansions. The thermal condition or temperature of a body changes by thermal conduction or radiation. Conduction is dependent on material contact, that is, it only takes place when bodies D 2 36 ELEMENTS OF LABORATORY WORK touch one another, but radiation takes place between bodies when separated even by great distances. In any system of material bodies, whatever may be their natures, relative posi- tions, and temperatures, the final condition of the system is one in which they are all at the same temperature. The change may proceed by conduction or radiation, or by both. It is to be noted that we are directly conscious of variety of temperature, just as we are directly conscious of variety of motion. 30. Standard Temperatures. — 1. Observe that a thermo- meter shows the temperature of ice to remain constant while melting. Several observations are to be made. The density of the mercury in a thermometer does not alter until all the ice is melted. 2. Observe similarly that the temperature of water, when it boils under unaltered conditions, remains constant. 3. Note that these two statements cease to be true if the thermometer is very large compared with the quantity of ice or water used. In each case the introduction of the thermo- meter, a body of a different temperature, affects the thermal condition of the system ; but after a time the thermal condition becomes constant again, and is unaltered so long as the water boils or the ice is melting. Two standard temperatures are thus found, and other temperatures may be compared with them. The ordinary thermometer is constructed of a thin closed glass tube with a bulb at one end. This bulb, and a portion of the narrow even bore of the tube, contains pure mercury. The rest of the tube is empty, so as to allow free movement of the mercury. We perceive that an alteration of temperature causes the mercury to expand more than the glass containing it. The use of the instrument is founded on this inequality of expansion. The variations in the level of the mercury column, due to changes of density, are observed by the help of a scale. This scale is constructed by marking as zero the position of the column when the thermometer is placed in melting ice ; and, when the thermometer is in boiling water, marking the posi- tion of the column 100°. Between these points the scale is OBSERVATIONS OF CHANGE OF TEMPERATURE 37 subdivided into 100 equal lengths. A thermometer with a scale of this kind is said to be centigrade. When a portion of matter is at such a temperature that the mercury in a thermometer, placed so as to be in thermal equilibrium with it, stands opposite a certain number on the scale, that portion of matter is said to have a temperature of that number of degrees. For example, if the level of the mercury is at 15 the body is said to have a temperature of 15 degrees centigrade (or 15° C.). There is no difficulty in perceiving that we add nothing, so far, to our knowledge, when we say that a body is at 15° C. temperature. The thermometer is an instrument which enables us to say when two bodies are in the same thermal condition, on the assump- tion that similar causes produce similar effects. This assump- tion will afterwards be found to be reasonable. We cannot, however, yet consider that these numbers or degrees afford anything more than a rough comparison of different thermal conditions, nor is it likely that they give any correct informa- tion about the real basis of temperature. By the use of the balance we are able to decide when two quantities of matter are equal, and by the use of the ther- mometer we can judge when two bodies are at the same temperature. But by the use of the balance we can com- pare two quantities of matter, by collecting together a sufficient number of sufficiently small standard quantities to produce in each case the same effect. The numbers then indicate the rela- tion in quantity. In the case of temperature, on the other hand, we have at present no means of estimating quantity, and we are face to face with a different order of phenomena. Equality of temperature, just like sameness of colour, has no apparent connection with quantity. We begin now to deal with a condition or quality which cannot be isolated from matter, and which cannot be divided into parts or added together. We can, however, observe that changes of tempera- ture are determined both by the quantity and the kind of matter in which they take place. By combining the concep- tion of temperature with that of matter we may regard a change of temperature as a measurable quantity. 38 ELEMENTS OF LABORATORY WORK 31. Relation of Temperature-changes to duality and Quantity of Matter. — 1. Observe that when two quantities of water at different temperatures are mixed, the resultant tem- perature of the mixture is intermediate and varies with the quantity and temperature of each. 2. Observe that when equal quantities of turpentine and water at the same temperature are mixed respectively with equal quantities of water at a different temperature, the mixtures do not agree in temperature. 3. Observe that if two quantities of water at the same temperature, one of which is double the other, be mixed respectively with two other quantities of water, also in the ratio of 2 to 1, but at a different temperature, then the same temperature results in each case. Observe also that this holds true for other liquids, e.g. turpentine, and for other relative quantities, e.g. 3 to 1, or 2 to 3, and so on. The above exercises show that, when bodies of different temperatures are brought together, the resultant temperature varies with the quantity and nature of the matter contained by these bodies. The same temperature, however, is obtained if two quantities of matter, one at a high and one at a low temperature, be mixed, as is obtained when we mix two different quantities, at the same respective temperatures, either of the same or a different kind of matter, provided only the same relation in quantity be maintained. It is almost unnecessary to state that this experiment, and all others too, will be accurate only when our observation includes everything that is changed during the operation. Any change of tem- perature in one body proceeds simultaneously with changes of some kind in one or more other bodies. We are now con- cerned, however, with co-existent thermal changes only, and these may be observed to be reciprocal, i.e. a certain quantity of matter rises in temperature while another quantity falls. If a hot body be exposed in a room, the temperature of the sur- rounding bodies, including that of the air and the walls of the room, will rise, whilst its own temperature falls, until there is the same temperature everywhere. Hence arises the necessity in these preliminary observations of using liquids OBSERVATIONS OF CHANGE OF TEMPERATURE 39 which mix together so completely that they readily come to the same temperature throughout. The errors, due to changes in other bodies, must, however, always be taken into account. Various methods of raising different kinds of matter to the same temperature are possible. It is convenient to place them in thin glass vessels inside a larger vessel of hot or boiling water until a thermometer indicates the same tempera- ture. 32. Equal Quantities of Ice Melted during Equal Tem- perature-changes in Equal Quantities of the same Kind of Matter. — 1. Place equal quantities of ice in equal quantities of water at the same temperature, and observe in each case that the water is at the same, though lower, temperature, after the ice is melted. 2. Observe that the quantity of ice melted in an ice calori- meter varies directly with the quantity of matter used, pro- vided the bodies inserted are of the same temperature and of the same kind of matter. 3. Observe that equal quantities of different kinds of matter at the same temperature melt different quantities of ice, although they have meanwhile undergone the same changes of temperature. Use mercury and water. The above exercises show that the same physical change — that is, the change of a given quantity of ice to water — is Accompanied by an external change of temperature, which varies in different kinds of matter, but bears a simple relation to the quantity of matter undergoing it. The same change, of temperature in equal quantities of the same kind of matter is accompanied by equal changes, whether of temperature or of another class, in equal quantities of other bodies, but the same temperature -changes in equal quantities of different kinds of matter are not equivalent. They are not reciprocal with equal changes in other bodies. The change from ice to water is not a change of tempera- ture. The temperature remains the same, although neigh- bouring bodies simultaneously undergo a considerable thermal change which may be shown to be, for the same quantity of ice, constant in magnitude, 40 ELEMENTS OF LABORATORY WORK One form of an ice- calorimeter consists of several vessels with ice arranged so that a hot body placed inside may cause some of the ice to be melted and allow it to be measured. With the construction shown in fig. 11, the quantity of water which runs out into A measures the amount of ice melted by the body placed in B. The ice-jacket c c prevents the ice in D being melted by an external change of temperature. A calorimeter yielding more accurate results is one in which the quantity of ice melted is measured by the diminution of Fig. 11. Fig. 12. volume then taking place. Water in B (fig. 12) is caused to freeze around the tube A by a cold body placed within it. The tube c is connected with a mercury gauge which indicates changes of volume, and the body to be investigated is dropped into A. This instrument requires more care in manipulation than the former, especially in fixing on the gauge. The ex- periment need not be performed at this stage. 33. To Measure the Corresponding Temperature-changes in Water and Copper. — Weigh about 20 grams of copper wire rolled into a ball ; attach a thread of silk, place it in a large test tube together with a thermometer, and then immerse both for five minutes in boiling water. The thermometer will indicate the exact temperature. At the same time have ready a known quantity of water in a glass beaker, with a OBSERVATIONS OF CHANGE OF TEMPERATURE 41 thermometer showing its temperature. Convey the copper to the beaker as quickly as possible by means of the silk, and note the change of temperature taking place. The temperature of the known quantity of water rises, whilst that of the known quantity of copper falls, until there is thermal equilibrium ; but the resultant temperature shows that the fall is not equal to the rise, nor are the respective changes proportional to the relative quantities of copper and water present. Although it leads to greater accuracy to use a relatively large quantity of water in this experiment, we may infer that with equal quantities of water and copper different tem- perature-changes would be reciprocal. Observations with other substances indicate, similarly, that the same temperature changes (as marked by the thermometer) are not equivalent for different kinds of matter. It must be remembered that only approximate results will be obtained unless we prevent surrounding bodies, including the air, from taking part in the thermal changes without being estimated in our calculations. Calorimeters, such as already described, are intended to effect this requirement. A unit of temperature- change is required for purposes of measurement. Pure water at any temperature between 0° and 4° is selected as the standard substance in which it is to be observed. A change of 1° C. in 1 gram of water at any tempera- ture between 0° and 4° C. constitutes the unit temperature- change, and forms a basis for thermal measurements. If 2 grams of water are thus altered there are 2 units of tem- perature-change, and if 2 grams alter by 2°, as indicated by the thermometer, the numerical value of the total temperature- change is 4. Accurate observation shows that very nearly the same numerical values are obtained if the temperature- changes, which commence on a higher point of the scale, are taken as equal to similar changes between 0° and 4° C. In rough ex- periments this may always be done. A change from 20° to 21° may be considered equal to a change from 2° to 3°, 42 ELEMENTS OF LABORATORY WORK A given substance may be conveniently raised to a high temperature, and transferred to the known quantity of water with less risk of its temperature falling during the transfer, if, instead of the last process, we use a wide tube A (fig. 1 3), fitted at each end with a cork, through which an inner tube B passes. Fig. 13. The space between the two tubes is now filled with steam by connecting it at s with a flask of boiling water ; a cork, into which a thermometer c is fitted, serves to hold the body sus- pended in the inner tube, and to allow it to fall, when required, into the water, which should be placed directly underneath. We learn from the table below that a given change of temperature in 1 gram of water is equivalent to the same change of temperature in 1'62 grams of ethyl alcohol, 2 -2 2 of benzene, 10*64 of brass, and so on. These values will be found to bear no relation to densities or to the quantities of matter in equal volumes of the various bodies. They indicate a totally distinct relationship between various kinds of matter, and later observations in electricity and chemistry will show that this relationship may be discovered in other phenomena. OBSERVATIONS OF CHANGE OF TEMPERATURE 43 Thermal Equivalents. Numbers expressing the Relative Quantities of Various Kinds of Matter which are Equivalent in Thermal Change. Water is taken as Unity. So-called ' Specific Heats ' are the Reci- procals of these Numbers. Air ... 4214-7 Ice . ..;.... . 2-00 Aluminium . 4-950 Iron . . v » . 8-92 Antimony 18-343 Lead . 31-74 Arsenic . 12-285 Magnesium . 4-081 Bismuth 32-786 Mercury (liquid) . 31-328 Brass . 10-64 Platinum . . 30-864 Benzene 2-22 Silver . 17-889 Cadmium 10-649 Sodium . 3-408 Copper . 10-52 Sulphur . . 5-43 Ethyl alcohol 1-62 Tin . . 17-889 Glass .. 5-05 Water . ' , . 1-00 Gold . 30-864 Zinc • . . . . . 10-69 Hydrogen sulphate 3-33 We may, perhaps, now begin to regard thermal changes as conditional, not on the volumes nor the masses of the bodies taking part in them, but rather on something which is within the body itself. Equal masses are not equivalent, nor are equal volumes. Further investigation will show that under certain conditions the minute particles which are supposed to constitute matter are thermally equivalent. 34. To Measure the Numerical Value of the Temperature- change occurring in Surrounding Bodies when 1 gram of Ice Liquefies. — A weighed quantity of water in a glass beaker is prepared, and its temperature ascertained by a thermometer. Ice which has been standing in the room for some time, so as not to have a lower temperature than 0° C., and which has been dried, is added in quantity afterwards determined by re-weighing the beaker and water. When all the ice is melted, and the whole has been thoroughly stirred with the thermo- meter, the temperature is again noted. A known quantity of ice has changed to water without change of temperature (remaining at 0° C.), and has then 44 ELEMENTS OF LABORATORY WORK altered from 0° C. to the observed temperature of the mix- ture. These two changes have proceeded simultaneously with the temperature-change in the quantity of water first taken, which has fallen from its original temperature to that of the mixture. By making use of the definition of the unit temperature-change we can obtain a numerical value for the latter temperature -change, and likewise one for the water yielded by the ice in rising from 0° to the final temperature. The difference between the two magnitudes gives the numeri- cal value corresponding with the change of state of the quan- tity of ice which has been used ; and from this it is easy to calculate the numerical value for 1 gram of ice. The most accurate values obtained have been from 79 to 80, but this experiment will only give approximate results, since the changes produced in the air and the beaker itself have not been taken into account. Greater accuracy may, how- ever, be obtained by enclosing the beaker in non-conducting material, such as cotton-wool, and finding out how much water the glass of the beaker would be equivalent to, and adding this to the other quantity thermally changed. We must infer that the melting of ice is always accom- panied by changes equivalent to those here measured, what- ever the surrounding bodies may be. It is convenient in thermal measurement to consider the unit change of temperature as caused by a unit quantity of heat. We may then shortly describe the above process by saying that 80 units of heat are required to melt 1 gram of ice. If the temperature of a body rises, it is said to gain heat ; if it falls, to lose it. But as we are able to observe directly only such changes in the properties of bodies as we have agreed to class together as temperature-changes, or as caused by temperature-changes, it is important to remember that the terms, gain, or loss of ' heat,' are merely convenient expressions for changes of temperature. More exact know- ledge of temperature-change cannot be acquired until its co- relation with other physical changes is shown. We shall then learn what it is that is gained or lost during change of temperature, and why it is that the passage of ice, and of all OBSERVATIONS OF CHANGE OF TEMPERATURE 45 other solids, to the liquid state involves a thermal change in surrounding bodies without any change in their own tempera- ture, 35. To Measure the Temperature-change in a Known Quantity of Water corresponding with the Gasification of a Known Quantity of Water, or the Numerical Value of the Temperature-change involved in changing 1 gram of Water at 100° into Steam at 100°.— A known quantity of water is taken in a glass beaker, its temperature is ascertained, and then steam or water-gas is allowed to pass into it for a short time. The quantity of steam added and the change of temperature produced is easily deter- mined, but it is important that only water gas and not condensed steam be added, or the determinations will be inaccurate. With this purpose the tube A, leading the steam into the water, is a narrow tube, fitted with a cork into the bigger tube B, so that the steam leading into the water is maintained at 100°, and is shielded from the cooler air by the steam in B, which will be found to condense partly. The water in the beaker c should be shielded from the effects of the flame by which the water in the flask D is made to boil. This method is not direct, and we have to assume that the change is reversible. That is, the gasification of a given quantity is accompanied by the same temperature-change as when it is condensed, except that the direction of the change is reversed. In the first case the temperature would be lowered (as it was in the melting of ice), in the latter it is raised. The truth of this is proved by many observations. As in the case of the liquefaction of ice, there are two operations together balancing a third. The rise in tempera- ture of the known quantity of water co-exists with the con- densation of a known quantity of steam, together with the Fig. 14. 46 ELEMENTS OF LABORATORY WORK fall in temperature of the water formed from the steam, which must change from 100° to the final temperature of the mixture. Thence the numerical value of the temperature-change, corre- sponding with the condensation of a certain quantity of steam, is obtained by subtracting, from the total numerical value of the temperature-change in the water, the numerical value obtained from the condensed steam falling from 100° to the final tem- perature. The value for 1 gram is then calculated. The most accurate observations have shown the numerical value for 1 gram of water at 100° converted into steam at 100° to be 536. This number 536 has, unfortunately, been called the latent heat of steam ; and the number 80, the latent heat of water. Corresponding changes occur when any liquid passes to the state of gas. Table showing the Number of Grams of Water which would be changed from 1° to 0° C. by the Fusion of 1 gram of the following Solids : — Beeswax . . .97*22 Lead . . . 5-37 Ice . . . . 79-25 Sulphur . . . 9-35 Spermaceti . . 82'22 Silver . . .21-07 Tin . . . . 14-25 Zinc , 28-13 and by the Vaporisation of the following Liquids : — Bromine . . . 15'6 Ethyl alcohol . . 209 Ethyl ether . . 91 Mercury ... 62 Sulphur (liquid) . 362 Turpentine . . 69 Water . . . 536 The above numbers are also called the ' latent heats ' of fusion and vaporisation. OBSERVATIONS OF CHANGE OF TEMPERATURE 47 Temperatures at which Pressure Aluminium Antimony , Arsenic Brass Copper Gold Ice . . Iron . Lead Mercury . Platinum . Silver Sodium Sulphur Tin . Zinc . some Solids Melt under Normal of the Atmosphere. 600° C. about . 440° C. . 210° C. . 1,015° C. about . 1,050° C. about . 1,250° C. about 0°C. . 1,600° C. about . 335° C. .-39-5°C. . 1,700° C. about . 1,000° C. about . 95-6° C. about . 114-5°C. . 235° C. 450° C. Temperatures at which some Liquids Boil under Normal Pressure. Amyl alcohol 131-8° C. Glycerine 290° C. Ethyl alcohol 78-3° C. Hydrogen acetate . 120° C. Benzene 80-8° C. Hydrogen nitrate . 86° C. Bromine 63-0° C. Hydrogen sulphate 326° C. Carbon disulphide 48-0° C. Mercury 350° C. Ethyl ether 35-5° C. Turpentine . . 156° C. Density and Volume of Mercury at Various Temperatures. Temperature, ° C. Density Relative Volume 0 13-596 1-000000 4 13-586 1-000716 5 13-584 1-000896 10 13-572 1-001792 15 13-559 1-002691 20 13-547 1-003590 30 13-523 1-005393 40 13-499 1-007201 50 13-474 1-009013 60 13-450 1-010831 70 13-426 1-012655 80 13-401 1-014482 90 13-377 1-016315 100 13-353 1-018153 48 ELEMENTS OF LABORATORY WORK Density and Volume of Water at Various Temperatures. Temperature ° C. Density Relative Volume 0 •999884 1-000129 1 •999941 1-000072 2 •999982 1-000031 3 1-000004 1-000009 4 1-000013 1-000000 5 1-000003 1-000010 6 •999983 1-000030 7 •999946 1-000067 8 •999899 1-000114 9 •999837 1-000176 10 •999760 1.000253 11 •999668 1-000345 12 •999562 1-000451 13 •999443 1-000570 14 •999312 1-000701 15 •999173 1-000841 16 •999015 1-000999 17 •998854 1-001160 18 •998667 1-001348 19 •998473 1-001542 20 •998272 1-001744 21 •998060 1-001957 22 •997839 1-002177 23 •997614 1-002405 24 •997380 1-002641 25 •997133 1-002888 26 •996879 1-003144 27 •996616 1-003408 28 •996344 1-003682 29 •996064 1-003965 . 30 •995778 1-004253 40 •99236 1-00770 50 •98821 1-01195 60 •98339 1-01691 70 •97795 1-02256 80 •97195 1-02887 90 •96557 1-03567 100 •95866 1-04312 Mean Increase of Unit Volume for Rise of 1° C. in Tempera- ture, or Mean Coefficient of Cubical Expansion. Alcohol (ethyl) Brass Copper Glass •00108 •0000172 •00005 •000023 OBSERVATIONS OF CHANGE OF TEMPERATURE 49 Gold . . . -00004411 Hydrogen sulphate . -000489 Ice . . . . -0001585 Iron . . . -0000355 Lead . . . -000084 Platinum . . . -000026 Mercury . . . -00018 Silver '. . . -0000583 Tin . . . ~ . -000069 Zinc . . . . -000089 The coefficient of linear expansion, or the increase in unit length, is approximately one-third the cubical coefficient. Additional Exercises and Questions. 1. Show that we make use of the same reasons in determining that two temperatures are alike as in determining that two quantities of matter are alike. But show also that we cannot compare two tempera- tures as we compare two quantities of matter. 2. Compare the results given by a thermometer with your own sen- sations when various objects, metallic and otherwise, are touched. What explanation can be given of the apparent discrepancy ? Ascer- tain the temperature of your own body before offering an explanation. 3. Give the precise meaning to be attached to the terms ' heat ' and ' temperature.' In what way may ' heat ' be looked upon as a quantity ? 4. Classify the chief changes which may proceed simultaneously with changes of temperature in a body. 5. Observe the effect of raising the temperature of a tightly stretched wire. Suggest other methods of showing expansion and contraction with change of temperature. 6. Find the length of a brass and of an iron rod, first when they are placed in ice, and, secondly, after immersion in hot water of which the temperature is taken. Calculate from your observations the frac- tion of the length at zero by which each has increased during the observed change of temperature, and also the average increase for a change of 1°. The decimal fraction obtained from the latter calculation is called the coefficient of linear expansion. Measure by an eyepiece, connected with a vernier, travelling along a graduated bar. 7. Fit corks carrying glass tubes into flasks of equal capacity filled with water, turpentine, and mercury, so that no air remains in the flask and the liquids rise within the tubes to a convenient level. Rule lines at a distance of half a centimetre on strips of paper and gum them to 50 ELEMENTS OF LABORATORY WORK the tubes ; then place the flasks within a large vessel containing water, and observe the alterations of each level while the temperature of the water in the large vessel is being continuously raised by a flame. Keep a record of the heights at different temperatures, and trace curves which exhibit the relative changes of level. Observe also very carefully the changes of level taking place as the liquids are cooled by being surrounded by ice instead of water. 8. Heat the end of a glass rod until it is soft, and then push into it a piece of platinum wire. (Lengths suitable for subsequent use in the chemical laboratory should be used.) Observe that the platinum is tightly fixed after cooling, and give the reason. 9. Show from the relation existing between the volume of a cube and its linear dimensions that the coefficient of voluminal expansion is slightly more than three times the linear coefficient, provided the expansion is equal in all directions. 10. Observe the different lengths of time occupied in bringing about thermal equilibrium in the case of different kinds of matter. Goat rods of glass, iron, and copper with paraffin, pass them through a cork to the same distance, and fix the cork in a flask of boiling water. 11. Why is thin glass less likely than thick glass to crack from a rapid change of temperature ? 12. Knowing that most gases increase by about -00366 of their volume for an increase of 1° C., what is the density of air at 15° C. if it is -0012932 at 0° C. ? 13. Observe the melting-point of paraffin and beeswax by placing a small quantity of each in separate small tubes, fastening them to the bottom of a thermometer, and immersing them in a beaker of water which is gradually raised in temperature by a small flame. The water should be heated slowly and constantly stirred. 14. Suggest a method of showing change of temperature by the expansion of air. How would you compare the readings of your in- strument with those of an ordinary thermometer ? 15. Temperature might be ascertained by means of a vessel con- structed so that a liquid inside it would have to leave the vessel if it expanded. From the relation between the quantities remaining and the original quantity the voluminal expansion may be calculated, and hence the temperature may be determined, if the rate of expansion for the liquid is known, and if the starting temperature is known. Describe an instrument of this kind and the use to which it can be put. 16. Give descriptions of possible calorimeters, and mention the advantages and disadvantages of each. 17. The observed alteration of volume in a liquid contained in a vessel is not the real change, for the capacity of the vessel itself is simultaneously undergoing change. How may the absolute expansion OBSERVATIONS OF CHANGE OF TEMPERATURE 51 of a liquid be found if the coefficient of voluminal expansion for glass is known ? 18. Describe how the absolute expansion of a liquid may be found by weighing a piece of glass immersed in the liquid at different tempera- tures. What are the probable inaccuracies of the method ? 19. Mention the advantages and disadvantages of Lavoisier's calori- meter. Mention how some of the inaccuracies may be made relatively small. 20. How could you demonstrate that changes of temperature are changes which relate to quantity of matter and not to volume ? What hypothesis can you suggest as to the real process which underlies what we call change of temperature ? 52 ELEMENTS OF LABORATORY WORK CHAPTER IV OBSERVATIONS OF CERTAIN MUTUAL CHANGES COMMON TO ALL KINDS OP MATTER 36, Bodies displaced Equally from the Surface of the Earth reach it again Simultaneously if allowed to Fall. — A large electro-magnet may be used for suspending two bodies" at the same height. When the current is disconnected the bodies fall at the same rate. One body may be of iron, the other of wood with a piece of iron fixed so that the magnet will hold it. A piece of paper between the ends of the electro- magnet and the bodies ensures their simultaneous detachment. Variation, either in the quantity or kind of matter, does not change the result. All bodies let fall at the same instant and from the same height reach the earth at the same time, except so far as the obstruction of the air may intervene. Bodies which vary in falling in the air are found to be alike when tried in vacuo. If the displacement is varied the statement will be found to hold good. In this observation we have assumed the earth to remain at rest, while the two small bodies are said to be moving. By making this assumption, which our definition of movement justifies, we simplify all such investigations. The system under observation contains the earth and these two bodies. No change in the surroundings, however varied or repeated, has ever been found to annul either the power of return of any given body when removed from the earth, or the equal rate of return of two bodies equally removed. It is clear, then, that the earth and such bodies are alone concerned in this special change, and they constitute a material system in which MUTUAL CHANGES COMMON TO ALL MATTER 53 any vertical displacement is followed by a return to the original relative positions. 37. The Manner in which a Displaced Body returns to the Earth. — The Time of Fall. — A body allowed to fall from a height of 16 feet reaches the ground in one second. A body allowed to fall from a height of 64 feet reaches the ground in two seconds. In the last second it must therefore fall through 48 feet, if it takes, as may be proved, the first second in falling through 16 feet.1 The first fact may be demonstrated by suspending the body by an electro-magnet. Then break the current, and thus remove the support, at one tick of the seconds-pendulum. The body will reach the ground at the next tick. The second fact is not always easy to demonstrate on account of the distance being inconveniently great, but it may be accepted as the result of many experiments. More accurate measurements show that, if the resistance of the air be allowed for, the fall in a second is 490*5 centimetres, and in two seconds 1,962 centimetres. The result of all observations of the fall of bodies to the earth is to show that the rate of fall gradually increases along the course, and that the longer the course — or, in other words, the greater the original displacement— the greater the speed with which they reach the earth. 38. When a Body is displaced from the Surface of the Earth and then set free, it returns with a Uniformly Accelerated Speed in a Straight Line, — That a body, displaced a short distance from the surface of the earth and allowed to fall, returns in a straight line, is a matter of direct observation. That it returns with a uniformly accelerated speed is in- convenient to prove directly, on account of the magnitude being too great to measure in a room. The law may, however, be proved by retarding the motion and then measuring. This is best arranged by using Atwood's machine in conjunction with a pendulum beating seconds, or a clock. 1 It would not necessarily follow that it took one second to fall through 16 feet at the greater distance from the earth, but experiment shows that this is true within a moderate range. 54 ELEMENTS OF LABORATORY WORK Two equal masses are connected by a silk thread which passes over a pulley turning on friction-wheels. A small additional mass is made to rest on the mass near the scale. This causes an acceleration to be given to the masses, the heavier descending. By trial, the space passed over in one second may be noted, and the moveable stage placed there. Then the commencement and end of the fall will agree with two consecutive ticks of the seconds-clock. The space passed over during two seconds will be found to be four times that passed over during one second, and during three seconds, nine times, and so on. In order to give a long drop the pulley should be fixed as high as possible. These observed phenomena, together with those of the last section, may be most simply explained on the supposition that the acceleration which a body acquires by its proximity to the earth is independent of any motion which it may already have. A body, displaced 16 feet from the earth and allowed to fall, has at the moment it is stopped, i.e. at the end of one second, a speed of 32 feet per second, but if it has had a displacement of 64 feet, it will take two seconds to return, and will, at the end of the first second, have a speed of 32 feet per second, with which it commences the last second. Conse- quently it has at the end of two seconds a speed of 32 plus 32, i.e. 64, and at the end of t seconds a velocity of 32 t. In using Atwood's machine, the displacement of a body from the earth's surface corresponds with the distance between the starting-point and the stage which checks the fall. We may here state Newton's First Law of Motion, which is bound up with the above explanation : — 'Every body perseveres in its state of rest or of moving uniformly in a straight line, except so far as it is made to change that state by external force.' 39. Meaning of the Term « Force,' — When a body falls to the earth there is a change in the material system comprising the earth and that body. Each must be considered essential to the change — that is, it is a mutual change. The inevitableness of the return of a body to the earth gives rise to the statement that it is caused by the attraction MUTUAL CHANGES COMMON TO ALL MATTER 55 of the earth, or gravitation, but it is more exact to say that a mutual action, or a stress, exists between the two. The phrase attraction of the earth fails to convey the mutual nature of the change. We have seen that displacement between two bodies can only be measured by considering one of them to be at rest. So also mutual action is generally measured by its effect on one body. We may say that the earth moves to the displaced body, and consider the displaced body to remain fixed after it is re- leased ; or we may consider the earth to be fixed, and the body to move. We have no reason, so far, for taking one aspect of the change in preference to the other. We shall learn later that, relatively to any body not taking part in the mutual change, the earth must be considered to move, although to an infinitesimal degree, at the same time as the other body under- goes its much more apparent change. The displacements are, in fact, inversely proportional to the masses. Taking the customary and convenient conception of force, it may be defined as — whatever changes or tends to change the motion of a body by altering either its direction or its magnitude. But since observations show that change of motion in one body is always accompanied by change of motion, or change of some other kind, in another body, we must not forget that in using the term or idea, ' force,' we confine our attention to one side only of a two-sided event. This two-sided event is the mutual change that always occurs wherever stress manifests itself. It is to be noted in the case of the mutual action here investigated that the motion takes place in the straight line joining the centres of the bodies — in other words, the body moves towards the centre of the earth. 40. The Moveable Pulley. — A cord is fixed at one end, then passes over the moveable pulley A, and next over the fixed pulley B. The free end of the cord c and the pulley A are each furnished with a hook. If a known mass is attached to the free end of the cord it may be made to raise a mass nearly double its own in quantity. We must take into 56 ELEMENTS OF LABORATORY WORK Fig. 15. account the mass of the pulley, which is raised together with the attached mass. The more completely friction is avoided, the more nearly will a given total mass at A be balanced by one-half its mass at c, and the smaller will be the excess over one-half which is needed to cause the fall of c and the rise of A. While there is no movement, we have a system in equilibrium ; the stress between the earth and c balances the stress between the earth and A by the aid of the cord. It is easy to see that" in such an arrangement, where the three portions of the cord are all parallel, the mass at c would descend through twice the distance ascended by the mass at A. With a combination of pulleys, which consists of two blocks, each with three pulleys, and a continuous cord passing over each pulley, it is easy to see that the ascending mass would move through one-eighth the distance of the descent made by the smaller mass ; and, if it were not for the effect of friction, which is much greater in such a system, a given mass would balance one eight times larger. These experiments illustrate the need of considering both mass and distance in all such mutual changes. 41. The Lever. — The lever, like the pulley, shows that both mass and distance must be considered in all cases of mutual change. Its principle is illustrated by a rigid rod supported on an edge or small surface, called the fulcrum. If this rod is of constant section and homogeneous material it will be found to balance when supported at the centre, the stress on the one side of the fulcrum being just equal to that on the other. In any displacement from the horizontal position each particle on one side of the fulcrum has a corresponding , MUTUAL CHANGES COMMON TO ALL MATTER 57 particle on the other side, undergoing a displacement exactly equal, but opposite, to its own. If, however, the position of the fulcrum is altered, there is no longer equilibrium between the two opposing stresses, and the heavier side descends. This may be prevented by attach- ing a mass or restraint to the other side. Yarying masses may be attached at varying distances and their effectiveness deter- mined. By using a spring balance or dynamometer at different positions the same results may be made apparent. If the mass of the rod be very small in comparison with the adjustable masses kept in equilibrium by its agency, we may pay attention to these masses alone. We shall then find that, in cases of equilibrium, the vertical distances through which each mass moves, if the rod is displaced, are inversely pro- portional to the masses themselves. This may be shown by fixing to each mass a pencil, so that their displacement may be marked on two sheets of paper placed in position behind the lever. From these and similar observations it is known that the lever will be in equilibrium if the sum of the products of the numerical values of the vertical displacements and of the masses for all the particles of matter on the one side of the fulcrum be equal to the sum of the same products for every particle on the other side the fulcrum. If any considerable displacement occurs some of the matter on one side may change to the other side, and equilibrium be destroyed. The beam of a good balance will be found to exhibit all the properties of a lever balanced r at its centre on the smallest area which is practic- — able. Hence if the pans and the masses in them are together equal the lever is in equilibrium. It may be shown by geometry that the vertical displace- ment will always be proportional to the horizontal distance from the fulcrum— that is, DF : GE : : BD : BE. (See fig 16.) 58 ELEMENTS OF LABORATORY WORK The practical requirements for observations with the lever are as follows: — A wooden rod about 4 square centimetres section and about H metre long ; a wooden edge placed so as to act as fulcrum ; a pulley fixed so that the rod may be balanced if necessary by means of a cord passing over it. At the ends of the cord are fixed two hooks, one to receive the rod at its centre, and the other to hold a body just able to counterpoise the rod. In this way we get rid of the difficulty of calculating for the mass of the rod, and may pay attention solely to various masses which may be hung from the rod at various positions, while at the same time the position of the fulcrum may be altered. 42. The Pressure of Liquids. — When a liquid is at rest its free surface is horizontal, except where it is in near contact with a solid ; and this is true however much the surface may be modified by the shape of the containing vessel. In other words, all portions of the free surface of any homogeneous liquid at rest are in the same horizontal plane. But when we speak of a free surface we mean that portion of the liquid which is in contact with the atmosphere. The first and second of the figures below show a liquid with two equal free surfaces (A and B), each in contact with the atmosphere, and in the same plane. The third shows that they are still in the same plane when they are unequal. In the fourth case, the closed space B c must contain air, or other gas, in the same condition as the air outside the tube, or, as we have seen, the two surfaces A and B would not be in the same plane. In the fifth case the air has been driven out of the tube, while mercury has been poured in, and the space c D is a vacuum. We must conclude, in this case, that the column of mercury B C has the same effect on the imaginary surface B as the atmosphere would have had, if the surface had been exposed to it as in No. 1. In other words, the atmosphere at the surface A, and the column of mercury above B, are in equilibrium. Further investigation of these facts must be postponed until more is learnt of the structure of matter. We shall require help from the theory that matter is discontinuous MUTUAL CHANGES COMMON TO ALL MATTER 59 before we can gain clearer conceptions, either of the manner in which a gas can resist a liquid, as at A in No. 5, or of the nature of the equilibrium in such a case as No. 3. (5) Fig. 17. (4) 43. The Equilibrium of Two Liquid Columns in Communi- cation.— When a liquid — water, for example — is at rest in a bent tube of even bore of the shape A (fig. 18), the two surfaces are at the same level, and we may consider any two portions of the vertical columns which are equal in vertical height, as aft and cd, to balance one another — that is, the stresses between these two equal quantities of matter and the earth are equal. If, however, the tube is of the shape B (fig. 18), the sur- faces are similarly level, although equally long columns, a b and c d, do not contain equal quantities of matter. It is neces- sary to understand why two such columns are in equilibrium 60 ELEMENTS OF LABOKATOKY WORK We may be helped to do so by observing the result of adding to one of the columns a known quantity of water. Cork one of the branches tightly, and fill it with water by inverting the vessel. Add or remove water till the level stands a short way up the other branch. Then add successive equal quantities of water, say 5 c.c., from a burette, and mark each level upon a strip of paper gummed along the branch, or else mark the glass with a diamond. Calibrate the other branch similarly, starting, for convenience, at the same level. The distance between each mark in each branch may now be divided into five equal parts, and the columns will be calibrated in cubic centimetres with sufficient accuracy. a Fig. 18. B Water is now added to this calibrated vessel, and the level in each limb noted. Five cubic centimetres of water are now dropped from the burette into the narrow branch, and the levels again noted. Had there been no movement of the liquid, the addition of 5 c.c. of water would have raised the level through a vertical distance which is easily measured from the graduated marks by a scale. But this level has now changed through a measurable distance and we may say that 5 c.c. of water have moved through this distance, while the change of level in the other limb enables us to calculate what quantity of water has been simultaneously raised through a measurable distance. It should be found that the quantities of water are in- versely proportional to the distance through which they have been displaced, and we have the same kind of change as in the lever, illustrated under somewhat analogous conditions. In this calculation we assume that there is no alteration of MUTUAL CHANGES COMMON TO ALL MATTER 61 volume in the liquid during the experiment. With the con- ditions described there is no alteration, as the measurement of the total volume would show. We may consider a portion of the water to act as an incompressible body, which is depressed atone end by the added water, while at the other end it succeeds in raising a certain quantity. The relation of the quantity of water raised to the quantity depressed depends upon the sectional areas of the columns, and consequently upon the vertical displacements. It may be of value to note that the sectional areas of the columns in this experiment correspond with the arms of the lever. 44. The Internal Stress of Liquids.— The preceding obser- vations having shown some conditions of equilibrium of liquids afc rest, the internal state of such liquids remains to be inves- tigated. It may be noticed, in the first place, that in a given column of liquid the pressure increases with the depth, just as in the case of a solid. The pressure at the bottom of the regular- liquid column AB (No. 1, fig. 19) varies directly with the linear height A B, just as in the case of a homogeneous solid of similar shape. The bottom of the vessel supports the quantity of matter in the vessel just as if it were a solid rod receiving no support from the sides. The stress between the matter and the earth -is the same whether it is solid or liquid matter. With the arrange- ment here shown (No. 2, fig. 19) of a string passing over a pulley A and through a hole in the ground and greased plate P, fitting against the ground edges of the vessel v, the varying quantities of liquid added to v will be found to be balanced by proportional quantities of matter at (i) ^m v 62 ELEMENTS OF LABORATORY WORK the other end (B) of the string. If the two portions of the string are vertical, or at the same angle with the vertical, equal quantities of matter at each end counterpoise — that is, the plate and the liquid will be equal to the quantity of matter at B. There is, therefore, no vertical support to the liquid from the sides of the vessel. If we now immerse a thin plate in a liquid, and weigh it while immersed, as if its density were being ascertained, it will be found that it is counterpoised by the same quantity of matter at all depths. The next observation is that the pressure at the bottom of a vessel depends in no way upon the shape of the vessel, or the Fig. 19. quantity of liquid contained in it, but merely upon the linear vertical distance between the lower and upper surfaces of the liquid, and also, as we should expect, upon the area of the lower surface. Vessels of the shapes shown above (Nos. 3 and 4, fig. 19), together with the pulley and ground-glass plate, are sufficient to demonstrate this. The following facts are therefore clear : — 1. That the vertical sides of the vessel (No. 1) do not sup- port the liquid in the meaning of reducing the stress between the earth and the liquid. 2. That the sides of the vessel (No. 3) do reduce the stress to the extent that the bottom of the vessel only requires MUTUAL CHANGES COMMON TO ALL MATTER 63 to resist the stress between the earth and the imaginary column x Y. 3. That the pressure in a vessel of the shape shown in No. 4 is found to be the same as it would be if the sides were perpendicular, as c E, D F. The pressure in the part A K L B (No. 4) is evidently due to the stress between the liquid and the earth, and no difficulty arises in this case. But we need now to explain why the pressure on the areas c K and L D is the same as if the sides c A and D B were vertical as c E and D F. In order to do this we must make the following assumption : ' that the stresses be- tween the parts of a liquid at rest are always perpendicular to the surfaces of separation between those parts.' From this assumption we can deduce the following facts : — In the portion A c K are pressures perpendicular to A c and A K from the side A c and the column of liquid A B K L respectively, which pro- duce a resultant pressure downwards, as shown in the figure. The pressure from A c, due to the narrowing of the vessel at the top, is found from the observation to be exactly equal to the pressure which the side A c would bear from the presence of the same liquid in a vessel of the shape and dimensions ACE. From this it is evident that the whole pressure from the part A c K is due to two causes : the first is the pressure due to gravity, and the second is the resultant of the per- pendicular pressures from A c and A K. These two pressures are together equal to the pressure which a column of liquid represented by E K would exert on the bottom of the vessel in virtue of the stress existing between it and the earth. The fact that the pressure on the sides of a vessel varies with the depth also requires to be observed and explained. If we consider the liquid to be made of very small particles, it is evident the top particles press on the next, and so on until the pressure on the lowest particles is due to the sum of the pressures of all the particles above it. This pressure causes the particles to slip away at right angles towards the sides, thereby producing a pressure on the sides which increases with the depth. 64 ELEMENTS OF LABORATORY WORK 45. The Relation between Mutual Displacements, — We have observed that a small quantity of matter undergoing a large displacement may be the means of displacing a large quantity of matter. That is, mutual changes occur in which unequal masses are equivalent in virtue of unequal displace- ments. The examples investigated have been the pulley, lever, and the displacement of a large quantity of liquid by a smaller. The conditions necessary in these and all other examples of the same kind of mutual change are that the numerical value of the mass multiplied by the numerical value of the displace- ment shall give equal products for each of the moving masses, that is, mL = M£. This principle may be extended to phenomena which are not connected by material bodies. In the previous observa- tions we have bars, cords, &c., connecting the mutually chang- ing bodies. In these cases it follows of necessity that both changes must take place in the same time. The simultaneous- iiess of the changes is a consequence of their mutual nature. We may, therefore, substitute speed for displacement in our conception of the phenomena, for the numerical value of dis- placement divided by the numerical value of time expresses the magnitude of speed. But it is important to note that the direction in which the bodies move is not the same — that is, this complex quantity (mass x speed), which is called momentum, is positive in the one case and negative in the other. This principle obtains in every case of mutual change, whether the bodies concerned are connected in any way or not. The displacements are in opposite directions ; they are equal if the masses are equal, but if the masses are unequal the displacements are inversely proportional to them. This is the principle contained in Newton's Third Law of Motion, according to which reaction is always equal and opposite to action — that is, the actions of two bodies upon each other are always equal and in opposite directions. In order to demonstrate this principle completely, it would be necessary to find a system which is under the influence of its own mutual action alone. On the surface of the earth we MUTUAL CHANGES COMMON TO ALL MATTER 65 ^ • are limited in this and many other similar investigations by the enormous stress which exists between the earth and all bodies near it. We cannot, therefore, easily prove the equivalence of mutual changes. In all the pre- vious experiments the displacement which has been measured has been a displacement in the direction in which this stress acts, i.e. in a ver- tical direction. In the case of bodies moving without friction over a smooth horizontal surface, there is no displacement possible from the stress between them and the earth, and the displacements due to mutual changes will not be interfered with. Glass balls of different sizes rolling over a horizontal glass plate would approximate to these conditions, and with them we can prove roughly that a small fast-moving body can produce the same effect as a large slow-moving body. By causing balls of various sizes to strike others at different rates this may be shown in a rough manner. We may obtain similar results by fastening two unequal masses to a long cord passing over a pulley. If the heavier mass is supported, and the smaller mass allowed to fall for some time, and so acquire a speed before it begins to tighten the cord, it will be found that a rapidly-moving small mass is able to raise a much larger mass. The arrangement shown in fig. 20 will suffice for a number of observations. Similar results are observable in the use of a hammer or a pile-driver, Fig. 20. 66 ELEMENTS OF LABORATORY WORK 46. New Test for Equal Quantities of Matter. — Atwood's Machine. — By experiment with Atwood's machine it will be found that an additional mass, placed on one of the equal masses which are connected by the silk thread passing over the pulley, and allowed to fall for a measured time, will have acquired at the end of that time, together with these equal masses, a certain speed. This speed may be measured easily, for, if the additional mass be removed by a ring, the two equal masses continue to move uniformly with the identical speed which the system possessed at the moment of this removal. The uniform motion of the two equal masses after removal of the small mass which produced the acceleration, is a matter of direct observation which is in accordance with previous observations. Those masses which, under the same conditions, acquire equal speeds are equal masses. Those masses are equal which, when added for an equal time to this system containing two equal masses connected by a string, produce in it equal speeds. By the use of two similar pulleys, each with the same masses connected by a thread, a comparison of the speeds acquired may be made independently of the time taken. Direct observation of coincidence by sight and hearing will decide whether the speeds, and hence the masses, are equal. In this comparative method we are less dependent for accuracy on the smooth running of the pulleys. Provided they run alike, the conditions are the same for each change occurring. We shall find later that other stresses, besides that exist- ing between the earth and all bodies removed from its surface, may be utilised for measuring quantity of matter. We must not forget that this instrument enables us to surmise the manner in which a body falls to the earth by causing it to fall slowly. This retardation is produced by causing the body to form part of a system of three bodies, two of which are equal in mass and connected by a string so as to be in equilibrium. The speed which this body ac- quires under various conditions is not directly measured, but is taken from the uniform speed with which the system moves MUTUAL CHANGES COMMON TO ALL MATTER 67 according to Newton's First Law of Motion, after the disturb- ing body is removed. It is important to understand correctly the manner and degree in which this retardation is brought about. First of all, we learn from direct observation that the retardation is greater in proportion as the mass of the whole system is greater than that of the body under observation. That is, if the mass of the three bodies together is four times greater than the mass of the added body, then the speed acquired by this body in falling for one second will be 8 feet per second, instead of the 32 feet per second which it would gain in falling by itself for the same time. In order to have a clear concep- tion of the cause of this change of speed, it is advisable to regard the arrangement of two perfectly equal masses, con- nected by a non-extensible string which passes over a pulley, as a system in equilibrium and ready to move in a vertical direction, just as if it were released entirely from the stress which exists between the earth and all bodies near it. As a matter of fact, the stress cannot be annihilated, and we have here two such stresses, exactly equal, but made by the string, which is said to be in a state of ' tension/ to counteract each other. (We have a similar counteraction of two stresses when equal masses are placed in the pans of a balance.) Under these circumstances we may regard the system, as it now is, to be just the same as any body placed in such a position in space that it is free from all stresses and, indeed, from all liabilities. This, however, is only true for any disturbance in a vertical direction, but it is only for observing such disturb- ances that it is used. When we come to place the additional mass on one of these equal masses, we make the whole system, i.e. the three bodies, participate in the effect of the stress exist- ing between that additional mass arid the earth. In other words, the change is spread out over three bodies, and the actual rate of motion is diminished in exact proportion to the relative increase in the quantity of matter taking part in the given change. By these and similar observations we are led to the general- isation that, in any consideration of the effects of a given F2 68 ELEMENTS OF LABORATORY WORK stress (or force), we must pay regard both to the rate of change of speed and also to the quantity of matter in which it is produced. Additional Exercises and Questions. 1. Why does water remain in a pipette when the upper end is closed ? 2. Draw a diagram to explain how the reading of a barometer will be affected by a divergence of the instrument from the perpendicular. 3. Observe the level of the liquid in the various branches of the vessel shown in fig. 21. How do your observations explain the relation of pressure to dis- tance from surface ? 4. What would be the pressure on — that is, what would be the quantity of matter supported by — a sheet of 1 square centimetre area placed at a depth of 1 Fig. 21. metre in water ? What is the pressure when it is placed in mercury ? Why does the sheet not move downwards under this pressure, and how is that quantity of matter supported ? It is assumed that the liquid is over 1 metre in depth. 5. Explain why a body immersed in a liquid is partially or com- pletely supported by the liquid. To what extent is the body supported, and why does it depend on the volume ? 6. When a solid floats on a liquid, what will determine how much is submerged below the surface of the liquid ? 7. Observe and explain what takes place when a liquid (water, for example) in a beaker, and a solid with a piece of silk attached, are weighed when lying side by side in the pan of a balance ; and also when the solid is suspended by the silk from the hook at the end of the beam and immersed in the water. Also observe and explain what takes place when a beaker of water is weighed, and then a solid hanging from an independent support is placed in the liquid. Prove that what the water appears to gain in this case is exactly the same as the object appears to lose if it is made to hang from the beam, while the water is supported independently, as in determining density. 8. Fill with water a tube which has been closed at one end, and is about a metre long, place the thumb over the end, and remove the thumb when the open end is underneath the surface of water in another vessel. Observe that the water remains in the tube when it is placed upright. Fill a similar tube with mercury and invert it over mercury, and observe that the whole column of mercury in the tube is not supported but sinks to a certain level. Observe also what occurs when the tube is not completely filled with the water or mercury, and likewise the alteration MUTUAL CHANGES COMMON TO ALL MATTER 69 of level produced by lowering or raising the tube. Write out an explana- tion of your observations. 9. Ascertain that a vessel may be emptied of a liquid by means of a bent tube, one end of which is at the bottom of the vessel and the other at a lower level outside the vessel. The air requires to be removed from the tube. Observe the conditions necessary for the commencement of the operation, and explain by the use of diagrams the cause of the change which goes on. 10. Demonstrate by the use of bent tubes of the shape shown in fig. 22, and containing mercury, (1) That the pressure of a liquid varies as the depth ; (2) that the pressure is the same in all directions. 11. Compare the pressure of the coal-gas in the supply pipes with that of the atmosphere by noting the level of liquid (water or mercury) in each branch of a bent tube, one of which is exposed to the atmo- sphere, the other to the coal-gas. How will the re- sult be affected by a difference in the section of the two branches ? 12. Insert two tubes in two vessels containing dif- ferent liquids, connect them at the top by a T-shaped tube, and partially exhausb the air. Measure the length of each column, and calculate the relative densities of the liquids. 13. Describe from your own observations how air enters the lungs at an inspiration. 14. Explain clearly why a body immersed in a liquid has acting upon it in an upward direction a pressure, which would balance the downward pressure of a volume of the liquid equal to that of the body immersed. Make observations to demonstrate this statement. 15. Observe and explain what takes place when a tube closed at one end, and about 1 metre long, is completely filled with mercury and in- verted over a vessel of water. Proceed cautiously at first, only partially removing the thumb. 70 ELEMENTS OF LABORATORY WORK CHAPTER V OBSERVATIONS OF CERTAIN MUTUAL CHANGES EXHIBITED BY CERTAIN KINDS OF MATTER 47. When Certain Bodies are rubbed together and sepa- rated the Space near them exhibits Certain Properties. — The most distinctive feature, and the one most easily exhibited, of a so-called electrified body is that small portions of certain kinds of matter in its neighbourhood are set in motion. This property may be shown by bringing a piece of sealing- wax, which has been rubbed on flannel or cloth, near to a piece of pith suspended by a silk fibre, or dry lath balanced on a blunt point. Rapid movement towards the sealing-wax or electrified body is seen, and sometimes the body after contact moves away, and sometimes there is a repeated to-and-fro movement. The region in which such displacements take place is called the electric field. Amber, ebonite, glass, resin, gutta-percha, etc., rubbed with flannel, silk, fur, etc., exhibit the same properties as sealing-wax. These changes, however, do not take place until the object rubbed and the rubber are separated. When they are together brought near a light body no movement is noticed, although each apart may cause considerable move- ment. The act of separation is therefore essential. When a metal is rubbed by a piece of silk and tested like the sealing-wax, no change is perceptible, but if the metal, conveniently in the form of a rod, is firmly fixed to a glass rod, which is held in the hand while the metal is rubbed, a move- ment of a light body may be obtained. When this class of bodies is touched by the hand, it suddenly loses this property. SOME SPECIAL MUTUAL CHANGES 71 This explains why it does not gain the property when held in the hand while being rubbed. 48. Communication of the Property to Other Bodies.— When an electrified body is brought near to, or in contact with, certain bodies, they may be shown to exhibit properties similar to the electrified body itself. It is only those bodies, however, which cannot be electrified unless held by a handle of glass, ebonite, etc., which can have this property commu- nicated. That kind of matter which suddenly loses when touched by the hand, or, if held by the hand, cannot acquire, this property, which may be termed ' electrification,' is called ' elec- trically conducting matter,' or a ' conductor of electrification.' Good Conductors. Metals. Carbon. Water containing salts in solution. Sad Conductors, or Insulators. Gases. Oils. Ebonite. Paraffin. Resin. Gutta-percha. Caoutchouc. Porcelain. Glass. Sealing-wax. Silk. Sulphur. Wool. Shellac. 49. Investigation of the Electric Field by a Small Elon- gated Body, and also by Two Small Bodies.— If a light elon- gated body— for example, a piece of pith suspended by a silk thread at the end of a stick — is brought into the space between two bodies which have been rubbed and separated, it is always caused to set itself lengthways between them. If displaced, it returns to this position, sometimes with the ends reversed. If, however, instead of one elongated body, two small bodies, such as two pith balls suspended side by side, are 72 ELEMENTS OF LABORATORY WORK brought into the electric field, they will be found to diverge so that each approaches as nearly as possible to either of the two electrified bodies. Instead of two pith balls, two strips of gold leaf, hanging side by side, will be found to diverge very readily when placed in the electric field. The gold leaves belonging to the electroscope may be used. Each of these experiments is now tried with either of the two bodies separated considerably from the other. Bring an electrified body, either the object rubbed or the rubber, near to an elongated body or two small bodies delicately suspended. If a single small body is brought near to an electrified body Fig. 23. it moves towards it, provided the stress between that small body and the earth is not greater than the electrical stress. It either remains in contact with the electrified body, or, after contact, is repelled. If placed between two bodies that have been rubbed and separated, it will move quickly to and fro between them, if the distance is not too great. It must be noted, however, that it first moves towards that body which is nearest. If the small body is itself in this electrified condition it will be either attracted or repelled by the larger electrified SOME SPECIAL MUTUAL CHANGES 73 body. The smaller body may be brought to this condition either by friction or by being placed in contact with an elec- trified body. The same effect will be produced in each case. That is, it is now in a condition such that it may be either attracted or repelled, according to circumstances, whereas a body which is not electrified is never repelled by an electrical body. It will be seen that the behaviour just described explains why a body, which is not electrified, may be first attracted and then repelled by an electrified body. A and B in each of the above diagrams are mutually electrified bodies, and the condition of the electric field is in- dicated by the behaviour of the bodies placed in it. Additional Exercises and Questions. 1. Perform experiments with the view of finding out whether elec- trification is a property of matter or of space. Show, for example, that the space near an electrified body differs from other space. 2. Instead of saying that the condition of space is altered, we might say that an electrified body acts at a distance. Discuss this theory. 3. How would you investigate experimentally whether two bodies are in the same electric condition, and how would you ascertain if they are in equal electric conditions — that is, if they are equivalent in causing those changes which are characteristic of electrified bodies ? How would your results be explained if you attribute the changes in question to a condition of space rather than to the condition of the material bodies engaged ? 4. Do you consider the terms ' positive ' and ' negative,' as applied to electrification, suitable ? 5. Perform several experiments which show that electrification is a two-sided phenomenon. 6. Explain what is meant when it is stated that there are ' two kinds of electricity.' 50. The Existence of Electric Stress indicated by the Elec- troscope.— Two light bodies, for convenience, strips of gold leaf, are suspended side by side from a metal rod, and enclosed within a glass vessel for protection from currents of air. The metal rod may terminate either in a disc or a sphere. "When 74 ELEMENTS OF LABORATORY WORK an electrified body, e.g. a piece of ebonite or sealing-wax which has been rubbed with flannel, is brought near the top of this instrument, the gold leaves move simultaneously. If the disc is now touched with the hand, the leaves return to their original position ; but if the hand first, and then the electri- fied body, be removed, the leaves again simultaneously diverge during the removal of the electrified body, and remain apart for some time. It may be noted in the first observation, that the nearer the electrified body approaches the instrument the more the leaves diverge ; and in the second observation, that the leaves diverge the more widely the further away the electrified body is removed, after the disc has been touched by the hand. This instrument, which exhibits very conveniently the con- dition of the electric field, and may be used for purposes of comparison, is called an electroscope. It is essential that the metal rod and leaves be well insulated. We have observed from previous experiments that the effects produced by an electrified body depend upon the rela- tive position, nature, and quantity of matter acted upon. The use of the electroscope, however, discovers another very impor- tant condition essential to the manifestation of electric stress, and this is a change in the configuration of the system con- cerned. However great the stress may be, it would be unob- served so long as the system is unaltered in configuration. It is not manifested except by certain movements taking place in a neighbouring body, or bodies, concurrently with a dis- placement in the relative position of the electrified body. We have so far made use of the term, ' electrified body,' but it is now clear that it would be more correct to include in our observations all the bodies concerned in the mutual changes which are said to be due to electricity, and speak of them as c the electrified system.' There is no indication of such a thing as an electrified body existing entirely by itself, or of electric changes in which only one body is concerned. 51. The Quadrant Electrometer. — The electric stress which has been produced by friction, or any other cause, may be further investigated by the use of an electrometer. The thin SOME SPECIAL MUTUAL CHANGES 75 gold leaves are replaced by a thin flat strip of aluminium, which is suspended by two silk fibres so as to hang hori- zontally within four hollow horizontal metal quadrants. The opposite pairs of quadrants are united by a wire, but they are otherwise quite separate from one another, and supported on glass pillars. The whole is covered by a glass case, and also by a metal framework which places the whole of the space around the electrometer in more perfect connection with the earth. Two pairs of quadrants may, by means of connecting metal rods, be placed in electric communication with two bodies which have been electrified. These pairs of quadrants now electrically represent, in a more investigable form, the bodies with which they have been placed in contact. Or rather, we add to our system another symmetrical system, which partakes of its electrical condition and exhibits it in a convenient manner. The aluminium vane may, if necessary, be electrified by communication with an external body, through the medium of hydrogen sulphate (contained in a vessel underneath) and platinum wires. These together con- nect the moveable vane with a metal rod, which leads out wards and turns on a pivot. The vane is made to hang so that it is midway between the two pairs of quadrants when they are' not elec- trified. It moves to the one side or the other under different electric stresses ; and the deflec- tions are marked by the movement on a scale of a spot of light, which comes from a lamp, and is reflected from a small mirror attached to the plate. The essential structure of this instru- ment is here show in diagram (fig. 24). By the use of the quadrant electrometer we may perceive ---M IRROR. SECTION. PLAN. Fig. 24. 76 ELEMENTS OF LABORATORY WORK when there is an electric stress between two bodies ; for then the vane or indicator moves, together with the spot of light on the scale. But we may also determine by its use a much more important matter, viz. which of two electric stresses is the greater. If one pair of quadrants is introduced into an electric system, the indicator will move towards or away from that pair, according to circumstances. If the other pair of quadrants is introduced into another electric system, so as to occupy a corresponding position in it, there will be a stress between this pair and the indicator which will oppose the first stress. The deflection of the indicator will show the relation between these stresses. In the attracted-disc electrometer, the electric stress is compared with that of gravity — a stress which may be easily defined and measured, since it varies directly with the quantity of matter used. The electric stress between two opposed discs is accurately balanced, by a lever arrangement, with the stress due to a certain quantity of matter and the earth. The stress existing between parts of a system similarly electrified may also be exhibited by the instrument shown in the diagram. A thick copper or brass wire circle or ellipse has two plates, A and B, attached in such a position that similar plates, c and D, at the end of a thin pointer may face them. This pointer is carefully balanced on the steel point E, and the whole is now supported on an ebonite pillar F. We obtain a system in com- plete electric connection, and able to exhibit stress between its parts with- out losing that connection. It should be covered just as the gold-leaf elec- troscope by a glass coated inside with strips of tinfoil. A plate G is at- tached so that the system may be electrified with convenience, whereupon, the pointer is repelled to a distance varying with the magnitude of the electric stress. Observations made with Fig. 25. SOME SPECIAL MUTUAL CHAGENS 77 this instrument should be compared with those made with the gold-leaf electroscope. It will be found much less sensitive, on account of the greater quantity of matter displaced under the action of the stress. 52. Exploration of the Electric Field by Two Discs.— The neighbourhood of an electrified " body is in such a condition that not only do conductors, whether electrified or not, tend to move, but also an electric change is induced in them, whether previously electrified or not. Two similar metal discs with non-conducting handles are brought, with their faces in contact, into the electric field. If they are now separated in such a manner that they are placed at different linear distances from the electrified body, and then removed from the field, they will be found to possess the same properties as two bodies which have been together electrified by friction. This is proved by the behaviour of a small electrified body (a gilt pith ball), or by use of the electroscope or quadrant electrometer. If not separated before removal, no change takes place ; or if brought together after separation and removal from the field, no electrification can be further obtained. The same condition of the field may be shown by electrically connecting a conductor on a non-conducting support to a dis- tant electroscope or electrometer by means of a wire. On bringing the electrified body near the conductor, the leaves of the electroscope, or vane of the electrometer, will move and take up a fresh position so long as the electrified body is near. If the conductor, while in the field, be touched by the hand and then removed, it may be shown, by applying any of the previous tests, to be electrified. All the actions observed above will be found to diminish very rapidly as the distance from the electrified body increases, i.e. the nearer the body originating the changes, the greater will these changes be. We may have a series of these phenomena caused by the same body, either simultaneously, in case there are several suitable bodies near, or successively, in case the body induced is removed from the system and then treated as the originating 78 ELEMENTS OF LABORATORY WORK body in a new system. In other words, this inductive action may affect a large number of bodies placed at increasing distances from the inducing body, the action diminishing with the distance. It may also be noted that the action depends solely on the linear distance, and not at all on the direction, provided that other bodies be not introduced into the field. Additional Exercises and Questions. 1. Show that two mutually electrified bodies behave, when separated, as if they were joined by some extensible but elastic material. 2. Under what conditions may the electrification of a given body be communicated to a non-conducting body ? 3. In the electroscope and electrometer, the bodies between which mutual changes are taking place are shielded or screened either by wire- work or tinfoil. Give reasons for this in each case, and point out any difference in their application to the two kinds of instruments. 4. Make experiments with a view to discovering the amount of electric change which can be produced within a hollow metallic body by means of an electrified body held outside. For this purpose intro- duce any instrument or system, which is sensitive to electric changes, within a wire cage or any hollow metallic vessel. Compare results both with and without contact between the body inside and the cage, and also when the hollow vessel is in itself strongly electrified. 5. Place a sensitive electroscope in metallic contact with a hollow vessel, and observe the effect of placing within the vessel a ' charged body,' and also of putting it in contact with the vessel from the inside. 6. From your observations of electrificat ion what suggestion can you make as to their origin ? 7. What experiments demonstrate that the origin of electric changes lies in the condition of tke space around those bodies which manifest the changes, that this condition will vary with the nature of the sub- stan^es also occupying- the space in question, but that space which is filled by conducting matter cannot exhibit the properties of which it is otherwise capable ? 8. Show that conducting matter may become electrified by friction if it is insulated. Place a metallic plate upon a sheet of ebonite or paraffin ; connect the plate with an electroscope at a convenient dis- tance, and rub it with a piece of fur. The electrophorus may be utilised for the purpose, but take care that the cake of ebonite itself is not electrified. Passing through a flame will discharge it. SOME SPECIAL MUTUAL CHANGES 79 9. Demonstrate that dry glass is an insulator, while moist or strongly heated glass is a conductor. In order to do so, arrange a piece of glass so that it forms part of the matter connecting an electrified body with an electroscope. 10. Two plates are carefully insulated and supported on a wooden base. Connect one with an electroscope and then t lectrif y it. Observe the effects produced in the electroscope when the other plate is brought nearer to, and taken further away from, the plate connected with the electroscope. Frame some hypothesis in explanation of the changes observed. 53. Electric Phenomena Produced by another Method,— If two long strips of zinc and copper be placed, without touch- ing one another, in dilute hydrogen sulphate, and then con- nected with the quadrant electrometer, a movement of the vane will be seen, just as with bodies electrified by friction. If the two free ends of the strips are connected with two large plates placed face to face, a light suspended body may be caused to move, when placed between them, just as if these plates had been electrified by friction or induction. In the same way, too, the plates, if removed from the system by non-conducting supports, remain in the same condition for some time, but lose their property completely when made to touch. The space between the two strips or plates outside the liquid is an electric field of the same nature as the last investigated. Any arrangement of material by means of which these results may be obtained, is called an electric cell, and there is great variety in the systems capable of being used. Several cells may be combined into a battery, so as to give greater results. The Daniell cell consists of a copper plate, placed in a solution of copper sulphate, and a porous vessel containing zinc sulphate and a zinc rod or plate. All these are placed in an outer vessel, and connections are made from the copper and zinc. It will be found that the results, described above as obtainable from a cell, are independent of the size of any portion of the cell, and depend solely on the nature of the materials used. 80 ELEMENTS OF LABORATORY WORK In the Grove cell we have the zinc plate immersed in dilute hydrogen sulphate, in which is also placed a porous vessel containing strong hydrogen nitrate, and a sheet of platinum. The Bunsen cell resembles the Grove, except that the sheet of platinum is replaced by a plate of carbon. The Leclanche cell consists essentially of a carbon plate and a zinc rod immersed in a solution of ammonium chloride. The carbon plate, however, is packed with manganese dioxide and carbon fragments in a porous vessel. The Bichromate cell consists of carbon and zinc plates immersed in a mixture of potassium bichromate and hydrogen sulphate, or in hydrogen chromate solution. 54. Processes by which Electric Equilibrium is effected.— If two conducting bodies, mutually electrified either by friction, induction, conduction, or by communication with a cell, are insulated, and placed close together, they may be caused to resume their normal condition by means of a small insulated conductor (a gilt pith ball for instance) suspended by a silk thread between them. This conductor will move to and fro between them with considerable velocity, making repeated contacts with each, which gradually diminish and cease. At this point the two bodies will be found to be no longer elec- trified, for with electroscopes and electrometers no indications of that condition are given. These bodies may also be caused to resume their normal con- dition by placing a metal between them by means of an insulat- ing handle. The change in this case takes place with extreme rapidity. It is effected by a momentary contact. At the same time the process is not visible. The change takes place without any displacement of matter. Any number of bodies, put in electric connection with one another by means of metals, immediately assume the same electric condition, what- ever their original condition may have been. If a piece of very thin wire is placed in connection with the two bodies, equilibrium is not reached so rapidly, and may take a measurable time. During the process which brings about equilibrium, the wire may be shown to be in a condition SOME SPECIAL MUTUAL CHANGES 81 which is commonly described as having a current of electricity flowing through it. This description has been so long used that it has become a familiar term, but subsequent investigation will show how far it is suitable or correct. The nature of the material used for bringing about the equilibrium has an im- portant bearing. Under ordinary circumstances air lies between the two bodies, but in this case equilibrium is indefinitely retarded. The same will be the case with glass, ebonite, and all insulators or non-conductors ; but with con- ductors it takes place readily, and still more readily when the conductors are relatively large. Two processes by which electric equilibrium may be brought about are shown above (fig. 26). 55. An Electric Circuit, Conditions necessary for.— If strips of copper and zinc are placed in hydrogen sulphate and put in metallic connection with one another outside the liquid, changes may be observed in the liquid and also in the zinc employed. Investigation will prove these changes to be per- manent. When they cease, the system is no longer able to exhibit the electric properties of which it has already been shown to be possessed. The same statement holds good for any of the other elec- tric systems or cells. Co-existent with these changes there is one which is not apparent, but which may be perceived by special means. The space in the neighbourhood of the system is in a certain condition afterwards to be investigated, and we may speak of the bodies constituting such a system as an ' electric circuit.' The quantity of matter in a circuit may be increased without any alteration in the nature of the properties acquired, provided the additional matter inserted is conducting matter ; but the magnitude of the effects, characteristic of such a system, may be shown to vary with any change either in the 82 ELEMENTS OF LABORATORY WORK quantity, nature, dimensions, or temperature of any portion of that system. It will afterwards be shown that we may have an electric circuit — that is, a system of bodies exhibiting special proper- ties— without any permanent change of the kind about to be investigated. For the changes taking place in the cell some other kind of change may be substituted, so as to be correla- tive with the electric change. This may be a change of tem- perature or of position, as will be shown. The kind of change taking place in a cell may be illustrated by the changes occurring in a zinc, copper, and hydrogen sul- phate cell. When perfectly pure and homogeneous zinc is placed in dilute hydrogen sulphate, no action is- observed. The quantity of zinc, on weighing before and after immersion, is found unchanged. Ordinary zinc, however, is acted upon by hydrogen sulphate, and diminishes in quantity by entering into solution, while the hydrogen sulphate itself becomes changed, losing a gas — hydrogen — and yielding on evaporation a white solid — zinc sulphate. Precisely these changes take place when pure zinc and copper are placed in , hydrogen sulphate and connected electrically. Since copper itself undergoes no change, nor produces any change, in hydrogen sulphate, we may consider that the conjunction of the zinc and copper with hydrogen sulphate originates Fi 27 certain changes of the special kind known as chemical, and also that the behaviour of impure zinc is due to its impurities playing the part of copper in the above arrangement. 56. The Existence of Magnetic Stress Indicated by the Simultaneous Movement of Two Magnets, — When two magnets, freely suspended, are brought sufficiently near to one another, they will be found to mutually attract or mutually repel, according to circumstances. Or if one is set oscillating, the other will also oscillate. In addition, any freely suspended magnet will always set itself in the same position with regard to the earth, lying nearly north and south. If one of the ends of the magnet is SOME SPECIAL MUTUAL CHANGES 83 marked, it may be perceived that this end will always point in the same direction. If it is displaced from this position, it will oscillate for some time, and then come to rest. It is also capable of moving in a vertical plane if properly suspended ; it will be inclined in a degree which is found to vary in different places on the earth's surface. We have, then, indications of a stress existing between a given magnet and the earth, and also of a stress between one magnet and another. In these experiments, as in the experiments on electric stress, the suspension of the bodies used is necessary, in order to overcome the stress of gravitation existing between them and the earth. This stress is so powerful that those less power- ful are prevented from producing their special changes. When a suspended magnet is observed to place itself always in the same position with regard to the earth, and to oscillate about that position if displaced, we are unable to detect any change in the earth itself \ just as we are unable to perceive any change of the earth co-existent with the fall of a body, but the mutual nature of the change is very readily seen in the case of the magnetic stress between two magnets. A change, exactly corresponding with the oscillation of a magnet which has been displaced from its position of equili- brium, takes place when a suspended body, such as a pendulum, oscillates under the stress of gravitation. If that end of a magnet which moves so as to point to the north is brought near the corresponding end of another magnet, the stress will be such that they are mutually re- pelled. If the two ends which point southwards are brought together, they are likewise mutually repelled. A north and a south -pointing end, however, mutually attract. This property is easily shown by suspending the magnets from their centres. Likewise, magnets placed lengthways near each other are attracted or repelled according as their corresponding ends are reversed or together. We learn, therefore, that a magnet possesses polarity, or a dual variation in space, similar to an electric field, 84 ELEMENTS OF LABORATORY WORK 57. Deflection of a Freely Suspended Magnet by a Sub- stance forming part of an Electric Circuit,— When a lightly suspended magnet is brought near to a conducting body which is in connection with the copper and zinc of a cell, or which in any way forms part of an electric circuit, stress between them may be observed. The magnet always tends to take up the same position, for if displaced from this position it returns after some oscillation. The magnet tends to place itself at right angles to that axis of the conductor which lies between the points of connec- tion with the rest of the system. The relative distances from those points, or the plane in which the magnet is held, does not alter this tendency ; but on increasing the distance from the conductor itself the stress rapidly decreases. It is convenient to take a wire as the connecting con- ductor. The magnet will always tend to set itself at right angles to the wire. Since the stress between the wire and the magnet is the same in all positions, provided the vertical distance from the conductor be unaltered, the ends of the magnet are reversed when it is moved half-way round the wire, i.e. from above to below the wire, or from one side to the other. If, then, the wire is turned upon itself, so as to form a loop, the stress is intensified ; and still more so if the wire is wound into a coil containing many loops. A magnet suspended at the centre of a coil will indicate by its movement when the coil forms part of an electric circuit. Such an arrangement is seen in a galvanometer. All magnets, when freely suspended, are always so turned that their position with regard to the earth is the same. There is a distinct stress between them and the earth. Con- sequently, the displacement produced on a magnet by a con- ductor in a circuit must depend on the relative magnitude of the two stresses ; and consequently, the magnet will sometimes only tend to set itself at right angles to the coil. From this fact we learn also that the position of the con* ductor or coil in a galvanometer must not itself be at right angles to the position which a magnet assumes on account of SOME SPECIAL MUTUAL CHANGES 85 the stress between it and the earth, for then the other stress might be unnoticed. 58. Construction of a Galvanometer.— The stress existing between a coil of wire forming part of an electric circuit and a magnet is made use of in the instrument called a galvano- meter. The simplest form of galvanometer consists of a number of turns of copper wire, which is insulated by a silk or cotton covering, wrapped round a wooden bobbin and sup- ported vertically. The ends of the wire are connected by two binding screws, by means of which the galvanometer can be Fig. 28. EEPRESENTS AN INSTRUMENT FOR SHOWING THE ACTION, UPON A MAGNET. OF COILS FORMING PART OF AN ELECTRIC CIRCUIT. - A = magnetic needle with scale. B^B! = wooden bobbins, each with two sets of coils and binding-screws S to corre- spond, one set of coils containing twice as many turns as the other. B2, B2 = wooden bobbins with two coils like B! and Bn but the diameters are just half those of B! and B, and their supports enable them to be placed in the same plane as the larger bobbins. * G = groove in which the four bobbins may slide, so as to vary their position with regard to the magnetic needle. made to form part of an electric circuit. At the centre of this coil of wire is fixed a glass- covered box, containing a magnet suspended at its centre by a silk fibre. Underneath the magnet is placed a graduated circle, by which we may read the angle through which the magnet is deflected. Since the magnet will always be turned in the same direc- tion by the mutual action between it and the earth, the gal- vanometer is always placed so that its coil lies in this plane. Any movement of the magnet must then be due to the stress caused by the electric circuit. This stress will be found to 86 ELEMENTS OF LABORATORY WORK depend upon the number of turns of wire employed in making the coil, and also upon the diameter of the coil. Other things being the same, the stress varies directly with the number of turns, and inversely as the diameter of the coil. Yery sensi- tive galvanometers are constructed by using a very large number of turns, closely surrounding small magnets delicately suspended by silk or quartz fibres. The deflecting power of the coil is also made more apparent by using several very small magnets pasted at the back of a small mirror, from which a spot of light from a lamp is reflected to a scale. A small movement of the magnets gives a large deflection of the spot of light on the scale. When a steady deflection has been produced in a galvanometer, the stress between the magnet and the earth is just balanced by the stress between the magnet and the coil in an electric condition. 59. Meaning of ' Conductivity.'— If a delicate electrometer is placed in connection with any two points in an electric circuit, it will indicate the existence of a stress. If these two points are altered, so that the length of the conductor between them is increased, the stress will be observed to increase, while it decreases if the length of the conductor diminishes. The greatest value is obtained when the electrometer is connected with the zinc and copper plates themselves (or their equiva- lents). This stress continues so long as the system is unaltered, and so long as the correlative chemical changes in the cell proceed. That is, the same properties are exhibited by every portion of the circuit as are shown by the conductor connect- ing two mutually electrified bodies ; but while the latter con- dition is transient only, the other is maintained so long as certain changes proceed in the cell. This stress varies with the nature of the substances form- ing the system, as was observed in the use of the galvano- meter. When a bad conductor, such as bismuth, is inserted, the stress for the same length is much diminished, and may not be perceptible. At the same time, any alteration in the dimensions of the conductor inserted will affect the stress. The thinner the conductor, the smaller the stress, provided other things remain unaltered. Also, addition to the quantity SOME SPECIAL MUTUAL CHANGES 87 of matter forming the circuit may dimmish the stress, and so much may be added as to render it imperceptible. This, how- ever, will not readily happen unless the matter added is a bad conductor by reason of its nature or thinness. If any portion of the circuit is much changed in temperature, the stress varies, a rise in temperature generally causing a diminution. All these phenomena may be exhibited by using a galvano- meter as well as by using an electrometer. We observe, then, that different kinds of matter have dif- ferent effects upon the stress shown by an electric circuit. If that portion of the circuit which is called the cell or battery remains unaltered, the stress obtained will vary with the quality, dimensions, quantity, and temperature of the rest of the circuit. When the dimensions, quantity, and temperature are kept the same, then the stress varies with the nature of the matter employed. When the stress is large, the matter is said to have good conductivity, and the value of the stress varies with the degree of conductivity. In practical applica- tion the term 'resistance' is more general. The greater the stress, the lower is the resistance. The value of resistance will therefore be the reciprocal of that of conductivity, and the use of either will lead to the same result. It is easy to see that both terms have their origin in the hypothesis of a current. It is important to note that the relations existing between the stress and the matter in a circuit contained in it are also observed to exist between the rate at which the process of electric equilibrium takes place and the matter by which it is effected. Hence we may regard an electric circuit as caused by a system in which a state of equilibrium might readily occur but for some process by which it is constantly disturbed. 60. Change of Temperature in a Substance forming part of an Electric Circuit. — In addition to the stress which is shown either by the movement of a magnet or the index of an electro- meter, it will be found that the whole of an electric circuit changes in temperature. The change will vary in different portions of the circuit, according to the nature and dimensions of the substances comprising it. This change may be shown by using a thermometer, which, 88 ELEMENTS OF LABORATORY WORK when placed in the liquid of a cell, will indicate a rise of tem- perature when the circuit is closed. At the same time, another thermometer, in contact with another portion of the circuit, may indicate a rise in temperature, which will not necessarily be the same as that taking place in the cell. The extent of the change of temperature may vary very much in different portions of the circuit ; but the changes of temperature are alike in those portions where the dimensions and quality of the matter investigated are precisely alike. At the same time, the change of temperature varies with the stress in the circuit, or, as it is called, the strength of cur- rent ; and this change takes place proportionally throughout the circuit. The electric stress may readily be caused to diminish by adding to the circuit a body of low conductivity, such as a long, thin wire. A comparison may then be made of the relative changes of temperature in the same substance. The variation of the stress may be observed by the deflection of the magnet of a galvanometer, which is made to form part of the circuit. It is advisable to wrap a certain length of wire round the bulb of a thermometer and place them both in a vessel of water. The wire is then connected with the rest of the circuit. In this way a change of temperature is readily observed. The rise of temperature will be found to depend upon the time during which the circuit is closed. The conductivity of metals diminishes with a rise in tem- perature. The conductivity of saline solutions, on the other hand, increases rapidly with a rise in temperature. Approximate Relative Conductivity at 0° C. Mercury . 1-0 Silver, annealed 63-0 Copper „ 59-0 Gold 44-0 Aluminium, annealed 31'0 Platinum „ 10-0 Iron i 9-2 Zinc, pressed 16-0 Tin , 8-2 German-silver, \ ard or anr ealec I 4-2 Brass g 17-2 Lead, pressed . 4-6 SOME SPECIAL MUTUAL CHANGES 89 Resistance of Hard-drawn Copper Wire at 15° C. according to New Standard Wire Gauge. Resistance is the ^Reciprocal of Conductivity. Density of Copper =8 '95. S. W. G. Diameter in Centimetres Resistance in Ohms per metre Mass in Grams per metre Nearest B. W. G. 7/0 1-270 •000137 1134-0 6/0 1-179 •000159 976-3 5/0 1-097 •000184 846-3 4/0 1-016 •000215 725-6 3/0 •945 •000248 627-6 2/0 •884 •000283 549-6 0 0 •823 •000327 476-1 1 •762 •000381 408-1 2 •701 •000451 345-4 3 •640 •000541 288-0 4 •589 •000638 244-1 5 •538 •000764 203-8 6 •488 •000931 166-8 7 •447 •000111 140-5 8 •406 •00134 116-1 9 •366 •00166 94-0 9 10 •325 •00210 74-3 11 11 •295 •00255 61-0 12 •264 •00317 49-0 13 •234 •00406 38-4 14| 14 •203 •00536 29-0 15 •183 •00662 23-5 16 •163 •00838 18-6 16 17 •142 •0109 14-2 18 •122 •0149 10-4 19 •102 •0215 7-26 20 •0914 •0265 5-88 27 21 •0813 •0335 4-64 21 22 -0711 •0438 3-56 23 •0610 •0596 2-61 24 •0559 •0709 2-19 24 25 •0508 •0858 1-80 26 26 •0457 •106 1-47 27 27 •0417 •128 1-22 28 •0376 •157 •893 29 •0345 •185 •839 30 •0315 •223 •697 31 31 •0295 •225 •610 32 •0274 •294 •529 33 •0254 •343 •463 32 34 •0234 •406 •384 35 •0213 •486 •320 36 •0193 •594 •262 36| 37 •0173 •742 •210 38 •0152 •954 •163 39 •0132 1-27 •123 40 •0122 1-49 •104 90 ELEMENTS OF LABORATORY WORK 61. Formation of an Electric Current when Two Dif- ferent Metals are placed in Contact at each Extremity, and the Two Junctions maintained at Different Temperatures, — Copper and iron wires, joined together and connected at their free ends with a galvanometer, will also serve to exhibit a relation between thermal changes and electric changes. If the junction is now warmed by any hot body, such as a flame, the magnet of the galvanometer will move. If the junction is cooled, the magnet will move in the opposite direction. The simplest system would be a loop as shown (fig. 29, a), but the introduction of a galvanometer or electrometer into the circuit is needed to show the electric change produced by the change of temperature. The whole of the galvanometer coil may be considered as forming part of the copper wire, in GALVANOMETER. Fig. 29. which case the two junctions will be at A and B as shown (fig. 29, b). A system of this kind resembles the systems previously investigated, except that the cell is now absent. In the place of the cell, and fulfilling its function, we have a hot body and a junction of two kinds of matter. The greater the difference of temperature maintained be- tween the two junctions, the greater will be the electric stress produced up to a certain limit. The important correlation between electric change and thermal change is illustrated in another manner. If the temperature of junctions in a heterogeneous circuit containing a cell be carefully observed, it will be found that at some parts there is a fall of temperature, at others a rise. The direction of the change, however, is always the same for SOME SPECIAL MUTUAL CHANGES 91 the same arrangement of the circuit. In this case the electric stress causes the thermal change. In the previous case the thermal change caused .the electric stress. Additional Exercises and Questions. 1. How do you distinguish air, copper, brass, mercury, solution of copper sulphate in water, alcohol, turpentine, and glass with regard to conduction ? Give experiments which would support your views. 2. What may be observed when conduction takes place in homo- geneous metals ? 3. What analogy exists between a current of electricity and a current of liquid ? 4. Compare thermal conduction with electric conduction in the case of metals. 5. What units can you suggest in order to measure ' quantity of electricity ' and ' current ' ? 6. Describe by means of diagrams the stresses in an electroscope and an electrometer, (1st; when they are at rest and not electrified, and (2nd) when they are at rest and electrified. 7. What experiments show that the space around bodies forming part of an electric circuit differs from ordinary space, and also from the space in the neighbourhood of an electrified body? What further dis- tinctions can be drawn from the facts that conductivity increases with the sectional area, and that the whole of the body in an electric circuit changes in temperature and not merely the outside ? 8. Coil a long piece of insulated wire into a helix, connect it hori- zontally by its two ends with a small cell which can be made to float in water, and observe that the coil sets itself with its axis nearly north and south, as a freely suspended magnet would do. Observe also that two such floating coils attract and repel just as two magnets free to move would do. The cell may be made of any suitable materials. 9. Construct a coil of insulated wire containing many turns, connect the ends with a galvanometer placed at some distance, and observe what happens when a bar magnet is moved in the axis of the coil, or when the coil is moved towards or away from the magnet. Note the result of variation in the rate of the movement. 10. Substitute for the magnet in the last observation (9) another coil in which a current is flowing. We then have a current in one coil producing a current in a neighbouring coil. Observe also that a bar of soft iron placed within the coil possesses the properties of a magnet as long as the circuit is unbroken. It becomes an electro-magnet. Insert 92 ELEMENTS OF LABORATORY WORK a key, and observe what occurs when the circuit is completed and also when it is broken. 11. Introduce wires of different thickness and different lengths (e.g. Nos. 16, 20, 32, and 40 B. W. G.) into a given circuit together with a galvanometer, and observe the effects. 12. Give some demonstrations of Ohm's law — viz. that the 'strength of current ' varies directly as the « electromotive force ' and inversely as the resistance. 13. Construct a coil which possesses a resistance of 100 ohms by winding upon a reel some No. 32 silk-covered wire, German-silver pre- ferably. Compare the wire before winding with a standard 100-ohm coil. After adjustment wind doubly from the middle, so that the coil may not possess magnetic properties (in this case there will be an equal number of turns in each direction, and, therefore, magnetic equi- librium). Solder the ends to terminals and coat with paraffin. The coil will probably be slightly inaccurate when carefully tested, but the experience will be valuable. Kemember that the wire twisted round a binding-screw must not be counted as offering resistance. 14. Observe the effect of joining the terminals of a galvanometer by thick and thin wires while it is connected with the same battery. How would you prove that, when there is a choice of paths for the current, as in this case, the quantity along each path varies inversely as the resistance ? 93 CHAPTER VI OBSERVATIONS WHICH LEAD TO THE THEORY THAT ALL MATTER IS MADE UP OF VERY SMALL SEPARATE PARTICLES 62, When Liquids differing in Composition are placed in Contact a gradual Rearrangement of the Matter may proceed until the whole is homogeneous, i.e. until the Composition is the same in every Part. — The change by which two liquids spread themselves through one another so that in course of time the whole is alike in composition, is called diffusion. It will be found to take place in gases as well as liquids. Some liquids, however, remain distinct, and do not diffuse even when left in contact for a very long time. Such cases are illus- trated by mercury and water. Mercury added to water sinks below the water, and their surface of separation does not change. In other cases, however, the surface of separation disappears more or less rapidly, the different kinds of matter cross the original surface of separation in each direction, and gradually become evenly distributed. When a liquid and a gas are in contact the same kind of change may go on. For example, when water and air are in contact, some of the water passes into the air and some of the air into the water ; but the substances differ so much in condition that the laws which hold for substances in the same condition do not apply. The solution of gases in liquids, and the evaporation of liquids, are treated separately. But within certain limits we may consider that if we have any two kinds of matter, x and y, in contact there is a tendency for the original surface of separation to become divided into two surfaces, which ultimately diverge as completely as 94 ELEMENTS OF LABORATORY WORK possible. Finally, no region contains x alone and no region contains y alone — at any rate, so far as we can yet analyse. This action may be readily shown by placing a small flask containing alcohol within a large cylinder (fig. 30), and filling the cylinder gradually with water, which is denser than the alcohol, until its level is about 2 inches above the top of the flask. A glass bulb, blown so as to just float in water, and placed in the cylinder, will be found to sink lower and lower as the density of the liquid in the cylinder diminishes with the progress of the diffusion. When the diffusion is complete, the density of the liquid in the flask will be found, on removal and examination, to be the same as that in the cylinder. That is, the liquids will be evenly mixed by a process which cannot be directly traced nor explained, unless we admit that it is by the imperceptible movement of very minute particles of each liquid. This action may also be illustrated by placing, by means of a fine pipette, a coloured liquid, such as a solution of potassium bichro- mate, at the bottom of a cylinder already filled with water. With care, little disturbance of the water will ensue. The diffusion may "rig. soT then be observed bv tne gradual change to a uniform tint throughout. Other methods will suggest themselves. The rate of diffusion varies with the kind of matter used ; but in all cases the rate increases with the temperature. 63. When a Solid and a Liquid are placed in Contact, the Solid tends to gradually diffuse throughout the Liquid, in Amount dependent upon their Relative Quantity and their Nature and Temperature. — If water is the liquid selected, and sodium chloride the solid, it will be found that a small quantity of the solid, introduced into the liquid, will rapidly disappear or dissolve. A further quantity may be added and the same change ensues, and so on until a limit is reached. The solid does not then dissolve, but sinks to the bottom. MATTER FORMED OF SMALL PARTICLES 95 The solution of a solid in a liquid differs, therefore, from the mixing of two such liquids as alcohol and water, inasmuch as it cannot proceed indefinitely. It resembles it, however, in the peculiar thoroughness with which the solid permeates the whole of the liquid. In other words, the solid, or the dissolved portion of it, diffuses through the liquid, so that after a time the whole is homogeneous. This may be proved either by chemical means ; by the evenness of tint when the solid is coloured ; by the evenness of density ; or by taking equal volumes of the solution, evaporating, and weighing the solid residue. The last process is generally applicable. The rate at which a solid dissolves depends upon the extent of the areas in contact ; hence a powder dissolves more quickly than the same quantity of the substance in one piece. It also depends upon the quantity of the solid already dissolved. A given liquid cannot hold dissolved more than a certain quantity of a given solid. In considering the process of solution, it must be remembered that the layer of liquid in contact with the solid becomes saturated — that is, it contains its maximum quantity, except so far as it loses by diffusion. This process, however, is slow. Hence movement quickens solution. For the same reason solution is often quickened by suspending the solid at the top of the liquid solvent, so that the denser saturated portions may sink away from the solid. The limitation to the mixing of a solid with a given quan- tity of liquid must be looked upon as due to the solid itself rather than to any inability in the liquid. The knowledge which we have previously gained of the different behaviour exhibited by solids and liquids when acted on by stresses, gives a probability to the view that a solid consists of small particles which can only be separated with difficulty. The actions between a solid and its solvent, whatever they may be, which result in these firmly cohering particles being separated, are gradually weakened as more and more of the solid becomes mixed with the solvent. That the action is a complex one is proved by the fact that solubility is in no way proportional to tenacity. 96 ELEMENTS OF* LABORATORY WORK 64. The Solution of a Solid is attended with Change of Tem- perature. Also the Rate of Diffusion varies with Temperature. When ammonium nitrate is added to water the temperature is very much lowered ; a temperature as low as — 27° C. may even be reached. Ammonium chloride, sodium acetate, silver nitrate, and potassium iodide, among others, will pro- duce a fall of temperature. On the other hand, manganous sulphate, magnesium chloride, and a few others, when dissolved in water, cause a rise of temperature. The observations are easily made by using a thermometer to indicate the tempera- ture before and after the solid in question is dissolved. In all the above cases the solids dissolved resume their original condition on raising the temperature of the solution sufficiently to gasify the water, and the same observations may be made with other solids and other liquids. In certain cases, however, the solid cannot be restored to its original condition by raising the temperature of the liquid containing it. For example, when zinc and hydrogen sulphate are placed in contact, and the liquid afterwards raised in tem- perature, a solid quite unlike the zinc is obtained. Changes of this kind will require to be afterwards considered more fully by themselves. In either case the change coincides with a thermal change, and at the same time cannot be mentally grasped, except as a rearrangement of very minute particles ; those of one sub- stance making their way among those of the other substances imperceptibly, just as imperceptibly as electric and thermal changes proceed. We adopt, then, the theory that matter is discontinuous, i.e. built up of separate particles. So small, however, are the particles that no changes which affect them can be directly observed, and hence the difficulty in measuring or understanding them. It is important to note, in view of a possible connection between the temperature of a body and the motion of its minute particles, that the rate of diffusion of two liquids increases with the temperature. 65. The Quantity of a given Solid dissolved varies with the Temperature of the Solvent. The Point of Saturation is MATTER FORMED OF SMALL PARTICLES 97 reached by Different Quantities at Different Temperatures.— It will be convenient to take water as the solvent, and potassium nitrate as the solid. It will be found that water at about 55° C. will hold in solution three times as much potassium nitrate as the same quantity of water at 15° C. This may be shown by allowing water to remain in contact with excess of the solid (i.e. more than can be dissolved by the water) for several Fig. 31. hours. A known quantity of the solution, which will then be at the temperature of the room, is then removed by a gradu- ated pipette, placed in a crucible which has been previously weighed, and kept at a moderate temperature until all the water is gasified. Care must be taken that none of the solid is lost in the process. The crucible, with the solid, is then weighed, and the quantity held in solution thus determined. The quantity dissolved at a higher temperature may be ascer- tained by keeping the water, which is in contact with excess 98 ELEMENTS OF LABORATORY WORK of the solid, for some time at a temperature exceeding the temperature to be investigated. It may, for example, be boiled for several minutes. A thermometer is then inserted, and, as soon as the liquid has cooled to the desired tempera- ture, the same quantity of the solution is transferred by a warm pipette to a weighed crucible, evaporated, and measured as before. It follows from this that a saturated solution, as it cools, must liberate some of the solid from solution. This may be seen by allowing some of the warm solution to cool in a clean vessel. The solid then appears as crystals, first minute, then growing larger and increasing in number. By this and other methods such diagrams as that of fig. 31 have been drawn up. The curves represent the relative solubilities of various substances at various temperatures. 66. When Gases differing in Composition are placed in Contact, a gradual Rear- rangement of the Matter proceeds until the whole is homogeneous, i.e. until the Composition is the same in every Part. — In the same way as certain liquids diffuse throughout each other, so do gases ; but the diffusion is completed, in the case of gases, more rapidly, even when the surfaces in con- tact are very small. The manipulation of a gas is more difficult than that of a liquid, and direct proofs of the diffusion of gases are scarcely needed in the presence of many indirect proofs, but the following experiment illustrates the diffusion of two gases into one another : — Two dry glass flasks (A and B) of equal capacity, each fitted with a cork and glass Fig. 32. j^g to which a piece of caoutchouc tube with a clip is added, and containing air and ammonia respec- tively, are placed in communication by a narrow tube, and the clips opened so that the two gases may come into contact. MATTER FORMED OF SMALL PARTICLES 99 After some time the clips are turned, and the vessels discon- nected and opened under water. The water will be found to rise about half-way inside each vessel, on account of the solubility of a portion of the contents of each vessel. Thus it is demonstrated that the ammonia which previously filled the upper vessel has evenly distributed itself throughout both vessels. The experiment also illustrates the fact that the gases are soluble in liquids, for the water entering into the vessels replaces the ammonia removed by solution. It is con- venient to use, as the source of the ammonia for filling B, a strong solution of the gas in water, placed in a flask, fitted with a delivery tube which leads to the top of B, inverted over it. On raising the temperature of this solution, ammonia will be driven off and completely fill the vessel B, expelling the air downwards. This depends upon the fact that the quantity of gas dissolved by a liquid varies with the temperature. The higher the temperature the smaller is the quantity held in solution. Table of Solubility of Air in Water. Unit Volume of Water at 760 m.m. pressure dissolves at :• Temperature Volume of Air Temperature Volume of Air 0 •02471 11 •01916 1 •02406 12 •01882 2 •02345 13 •01851 3 •02287 14 •01822 4 •02237 15 •01795 5 •02179 16 •01771 6 •02128 17 •01750 7 •02080 18 •01732 8 •02034 19 •01717 9 •01992 20 •01704 10 •01953 67. Atmospheric Pressure and its Variations.— An instru- ment for indicating the pressure of the atmosphere is called a barometer. A glass tube, of the form shown in fig. 33, closed at the end A and open at the end B, is nearly filled with mercury H 2 100 ELEMENTS OF LABORATORY WORK o O o O fc CO 0 rH 1 o CO CO CO CO o CO co Ol S CO •V CJ CM CO § CO i CO 1C rH -H CO 5 0 t- 0 O O 0 0 o 0 0 0 * T S 3S 6 co fc. rH g 07 C5 co C5 CO 0 CO 01 CO CO 0 CO OS rH Ol rH <~~> 07 00 (^) o Ol 0 CO 00 »~ ^o rH O 6 6 0 6 6 6 CM 6 2 CO •h 6 CO C5 Ol r:- »O O fc- co Ci co tV 00 lj« "73 "tt ^ a o o S i — > "y &. r^ i 1 a £1 (3 d 1 .S mono fl 01 a a> ^ V d CJ | •R ' o p O CC cf: £ a d PJ ft -t he p s g I X 2 w S ! I 1 I 1 i 1 1 p fl i MATTER FORMED OF SMALL' "PARTICLES by inclining it suitably. Any air now remaining may be swept out, by closing the open end with the thumb, and causing the air in the shorter branch to pass to the top of the longer branch and down again. Mercury is now poured out until it stands about half-way up the shorter branch, and the tube is supported vertically. It will be noticed that there is an empty space at the top A, provided the tube be long enough to allow the vertical distance between the two columns to be more than 760 m.m. If the tube be now attached to a graduated scale this vertical distance may be exactly measured, and observations will reveal variations from time to time. The vertical distance between the two surfaces of mercury may be most accurately measured by using a cathetometer, which is an instrument consisting of an accurately graduated and rigid bar firmly fixed on a support carrying levelling screws, by which it may be made perfectly vertical. Spirit levels fixed upon a moveable portion will show when this condition is reached. To the moveable portion is rigidly fixed the reading telescope, which revolves in a horizontal plane only, and a vernier which is so arranged that the vertical movement of the telescope may be accurately read. The cross- wires of the telescope are first of all focussed upon some distant object, and then the telescope replaced in position. The vertical distance between any two points is then equal to the distance obtained from the readings of the vernier, although the telescope may have been moved horizontally through any angle in making the cross-wires coincide with the required points. 68. The Use of the Cistern Barometer. — The cistern baro- meter consists of a long straight tube, closed at one end, which has been completely filled with pure mercury and then inverted in a cistern holding mercury. The atmosphere, pressing upon the surface of the mercury in the cistern, supports a column of mercury within the tube, just as the atmospheric pressure on the surface of the mercury in the shorter limb of the tube, 102 ELEMENTS OF LABORATORY WORK which was used in the last experiment, maintained a longer column of mercury in the other limb. The height of the column supported may be noticed to vary slightly at different times, provided the tube be long enough. In order to accurately measure this variation in the distance between the level of the mercury in the cistern and that in the tube, certain details of construction are required. The bottom of the cistern A is formed of leather, which can be raised or lowered by a screw B working against it. By this means the surface of the mercury in the cistern may be always made to touch an ivory pointer c, placed immoveably with regard to the scale. The distance is then always measured from the bottom of this pointer to the top of the column of mercury within the tube, and since the scale is rigidly fixed to the tube (for it is marked on the brass tube partly encasing it), a band with a horizontal lower edge, moving over the tube and graduated so as to form a vernier, enables the exact position of the column with regard to the scale to be read. When the centre of the mercury surface and the front and back of the band all seem to be at the same level, their vertical heights coincide. It will be noticed that the sur- face of the mercury is somewhat convex. We measure from the centre of the surface, which will be the highest point, provided the tube be vertical. This is ensured by allowing the tube with its brass case to hang freely. The accurate comparison of the pressure of the atmosphere at different times requires **; more than the reading of the height of the column of mercury it supports. The height of the column of liquid supported under these conditions has been shown to be inversely proportional to the density. The MATTER FORMED OF SMALL PARTICLES 103 density of mercury varies with its temperature. Hence the height must always be corrected to the same temperature for the comparison to be exact. In addition, the scale itself varies with change of temperature. If we know the coefficient of expansion of the brass of which it is made, correction is very easy. It is useful to take the heights of the columns of two barometers at the same time and note that they are alike, in so far as they are correctly constructed, although the tubes may vary in diameter. 69. The Volume of a given Mass of Air maintained at the same Temperature varies inversely as the Pressure, that is, the Density of Air varies directly as the Pressure —A long thick glass tube of even bore, closed at the end A and enlarged at the other end B (fig. 35), has mercury carefully poured in until it stands at the same level in both limbs. B This may be readily ascertained by a scale fixed behind, or better, by using the cathetometer. The height of the barometer is now taken, and then mercury added until the difference between the two levels is equal to the observed height of the barometer. It will now be found that the air in the shorter limb occupies half its previous volume, and it is evidently subject to double its original pressure — that is, double the pressure of the atmo- sphere. It is ^-necessary to calibrate the shorter limb in order to measure the volume exactly. If, instead of adding a column of mercury equal to that supported in the barometer, we pour in mercury to half this height, the gas will be found to occupy two-thirds its original space ; for the change of pressure is in the ratio of 1 to 1J or 2 to 3, and, therefore, the volume changes in the ratio of 3 to 2. It must be remembered, how- ever, that a given change of pressure might not produce the same change of volume at different temperatures. In order to ascertain this, the changes in volume may be observed when the tube is surrounded a§ completely as is practicable by snow or ice, Fig. 35. 104 ELEMENTS OF LABORATORY WORK Observations at higher pressures require inconveniently long tubes ; but they have been found by special experiment not to agree exactly with the results at low pressures. The same results for low pressures, and the same slight divergence from the general rule at high pressures, has been observed in the case of most gases. We may say, for practical purposes, how- ever, that the volumes of all gases vary inversely as the pressure. It is, of course, assumed that no mixture or union of the bodies in contact (mercury and air) takes place ; and also that the temperature is the same at each measurement of volume. (2, • >• VOLUME •« _ fr fig. 36. The various curves represent the relation between volume and pressure, for various temperatures, of a given gas. The vertical distances of a given point, in any of these curves, from a b and a c, represent the magnitude of the pressure and volume respectively. In order to measure corresponding changes we must take care in every case that these changes only are being observed, or, at any rate, we must take into account those modifications which cannot be avoided, 70, Graphic Representation of Correlative Changes by Dia- gram.— This mode of representing correlative changes may be illustrated by the following example : — Two straight lines ab,ac are drawn at right angles to one another. The units of length along a b are made to stand for units of volume, while the units of length along a c stand for units of pressure ; that MATTER FORMED OF SMALL PARTICLES 105 Diagrams slwwing that Boyle's law is not quite true. The product of he numerical values of pressure and volume, p v, varies with pressure as shown. From Amagafs observations. NITROGEN. 20 40 60 I 0 120 14-0 160 ISO 200 220 240 260 280 300 320 press lire 4 • HYDROGEN. 80 100 120 140 160 l«0 200 220 240 260 28C pre*sttre> Fig. 37. is, the magnitude of any given volume and of any given pressure is graphically represented by the magnitude of linear Distance in the direction a b and a c respectively. The^ results 106 ELEMENTS OF LABORATORY WORK of a series of observations are recorded by marking along a b the distances corresponding with the volumes, and along a c the distances corresponding with the pressures, in each case according to a given scale, and then erecting at these distances perpendiculars which shall meet in points which mark by their linear distance from a b and a c the condition of the body with regard to volume and pressure at the respective observations. It is obvious that an endless number of observations would yield a continuous line instead of isolated points. Instead of this, a number sufficiently large to detect any irregularity is taken, and then the line joining the points recording these ob- servations becomes the probably true representation of the state at all intermediate stages. Such diagrams are given above (figs. 36, 37). Table showing Value of Product p v for Air at Various Pressures and at Ordinary Temperatures.^ Pressure in Pressure in Atmospheres pv Atmospheres pv 1-00 1-0000 110-82 •9830 31-67 •9880 133-51 •9905 45-92 •9832 176-17 1-0113 59-53 •9815 233-68 1-0454 73-03 •9804 282-29 1-0837 84-21 •9806 329-18 1-1197 94-94 •9814 400-05 1-1897 1 From Amagat's observations. 71. The Measurement of the Change in Volume of a given Mass of Air, when changed from the Temperature of the Room to that of Boiling- Water, while the Pressure remains Unaltered. — A round- bottomed flask is tightly fitted with an indiarubber cork, and its position in the welted neck of the flask marked. This cork is to be fitted with a short thermo- meter, and also with a short glass tube, to which is joined an indiarubber tube with a clip, as shown (fig. 38). The glass tube is not to project below the bottom of the cork. The capacity of the flask up to the point marked on the neck, together MATTER FORMED OF SMALL PARTICLES 107 that of the tubes as far as the clip, is measured by filling with water and then emptying the water into a graduated vessel. The flask is thoroughly dried inside, and, with the cork inserted and the clip opened, it is immersed for several minutes in a vessel of boiling water, and the temperature observed. The clip is then tightly closed and the flask quickly removed. The flask is then placed with the mouth of the tube under water of the same temperature as the room, the clip is opened, and the flask is allowed to cool to the temperature of the room. The level of the water outside is made to agree with that of the water inside the flask, and at this point the clip is closed. The water which has entered the flask is measured by means of a graduated vessel, and, when its volume is deducted from that of the flask, we obtain the volume of air, at the temperature of the room, which will fill the flask when raised to the temperature indicated by the thermometer. This will be nearly the same as that of boiling water (100° C.). That is, we have the <$? CLIP means of measuring the change of volume which occurs when a certain volume of air undergoes a certain , • , r™ SI V- THERMOMETER. change or temperature. The pressure at each temperature is the same, as it is directly exposed to the atmosphere at the higher temperature, and is Fig. 38. brought into equilibrium with it, before measuring at the lower temperature. If accuracy is not ex- pected, the thermometer may be dispensed with, and the higher temperature taken as 100°, but the use of a thermometer is recommended. Suitably short ones may be obtained. The same method may be used for other gases. 72. The Temperature-changes resulting from Changes in the Volume of Gases. — When temperature changes in gases are in question, it must be remembered that the quantity of matter constituting a given volume of gas is very small compared with that of the containing vessel. A small change of 108 ELEMENTS OF LABORATORY WORK temperature in a gas would not be easy to observe, on account of the speedy adjustment of its own temperature with that of the vessel ; hence all comparisons and measurements of the changes become extremely difficult. It is easy to show that the diminution in the pressure on a gas, with its consequent expansion, takes place together with a fall in temperature. If a thermometer is placed under the cover of an air-pump, and a portion of the air removed by means of the pump, the thermometer may easily be made to mark a fall of 8° or 10°. In this case we have a diminution of pressure on the small quantity of air remaining which enables it to expand and fill the given space. In" so doing it becomes considerably colder. The same result may be shown by exhausting the air from a vessel by means of a filter-pump. If the pressure upon a gas be increased — that is, if its volume be diminished — the temperature increases. This may be easily shown by using a force-pump to compress a large quantity of air within a given space containing a 'thermometer. The temperature will be found to rise just as distinctly as it fell during the converse process. Many modifications of these experiments may be made, and they may be extended to other gases with the same results. It is of great importance to consider these results side by side with the observations that an increase in the temperature of a gas, from contact with a hot body, causes its volume to increase, provided the pressure remains the same ; while a decrease in temperature causes a contraction in volume. These apparently divergent facts are reconciled if we take into con- sideration certain external changes, which must be considered at a later stage. Similar results, with certain modifications, are found in dealing with liquids and solids. For example, the stretching of a wire cools it, while examples of compression causing a rise of temperature are common. Friction may be looked upon as a special case of compression. But the greater simplicity, to be subsequently demonstrated, in the structure of gases makes them easier to investigate than solids or Jiquids. MATTER FORMED OF SMALL PARTICLES 109 73. The Measurement of the Pressure of Aqueous Vapour in contact with Excess of Water at different Temperatures. — When a small quantity of water is introduced into the vacuum of a barometer, it will be found that the column of mercury is depressed through a distance which does not change on the introduction of more water, provided the temperature of the whole be unaltered. But if the temperature be caused to rise, it will be found that there is an increase of the depression of the mercury column, caused by the pressure of the water vapour ; and if a temperature of 100° C. be reached, the pressure of the contained vapour would be equal to that of the atmosphere, i.e. the column of mercury inside be depressed to the level of the mercury outside. It will also be noticed that, if the tube itself be raised or lowered, the height of the column of mercury is unaltered. That is, the pressure of the vapour in presence of water remains the same, whatever the change in the space throughout which the pressure has to be exerted. The quantity of liquid may be noticed at the same time to diminish or increase as the space is increased or diminished. In each experiment there must be excess of water. Any vapour which behaves in this manner is called a saturated vapour. These results are inde- pendent of the presence of air, as may be shown by allowing a small quantity to enter the tube. In conducting these experiments firm stands for the tubes are essential, and a tube with a vacuum free from water is necessary for compari- son. In order to show that the pressure is inde- pendent of the space through which it is exerted, provided only there be excess of water, the cistern shown (fig. 39) is used. In order to show that the pressure of the vapour at 100° is equal to that of the atmosphere, complicated apparatus is re- quired. What is strictly true is that water boils at that temperature at which its saturated vapour has a pressure equal to that which its surface bears. By diminishing Fig 39. 110 ELEMENTS OF LABORATORY WORK Pressure of Aqueous Vapour in M. M. of Mercury. T.°C. M.M. T.°0. M. M. T. ° 0.- M.M. T. °C. Atmos. -10 2-08 16 13-54 90 525-39 100 1-0 -9 2-26 17 14-42 95 633-69 110 1-4 -8 2-46 18 15-36 99 733-21 120 1-96 -7 2-67 19 16-35 99-1 735-85 130 2-67 -6 2-89 20 17-39 99-2 738-50 140 3-57 -5 3-13 21 18-50 99-3 741-16 150 4-7 -4 3-39 22 19-66 99-4 743-83 160 e-r -3 3-66 23 20-89 99-5 746-50 170 7-8] -2 3-96 24 22-18 99-6 749-18 180 9-9 -1 4-27 25 23-55 99-7 751-87 190 12-4 0 4-60 26 24-99 99-8 754-57 200 15-4 1 4-94 27 26-51 99-9 757-28 210 18-8 2 5-30 28 28-10 100 760-00 220 22-9 3 5-69 29 29-78 100-1 762-73 230 27-5 4 6-10 30 31-55 100-2 765-46 5 6-53 35 41-83 100-3 768-20 6 7-00 40 54-91 100-4 771-95 7 7-49 45 71-39 100-5 773-71 8 8-02 50 91-98 100-6 776-48 9 8-57 55 117-48 100-7 779-26 10 9-17 60 148-79 100-8 782-04 11 9-79 65 186-94 100-9 784-83 12 10-46 70 233-08 ! 101 787-59 13 11-16 75 288-50 105 906-41 14 11-91 80 354-62 110 1,075-37 15 12-70 85 433-00 120 1,489-60 Boiling points of some Saturated Solutions. Salt Dissolved Quantity in 100 parts of water at Boiling-point Boiling-point Potassium acetate 800 169° Sodium acetate . 209 124-4° Ammonium nitrate . . 209 164° Calcium nitrate . . * 362 115° Potassium nitrate . 335 116° Sodium nitrate . . 224-8 121° Potassium carbonate 205 135° Sodium carbonate . 48-5 104-6° Potassium chlorate 61-5 104-2° Ammonium chloride 89 114-2° Barium chloride . 60 104-4° Strontium chloride 117-5 117-8° Calcium chloride . . 325 179-5° Potassium chloride 59-4 108-4° Sodium chloride . . ; 40-2 108-4° Sodium phosphate .. . 112-6 106-6° Potassium taitrate . 276-2 114-7° MATTER FORMED OF SMALL PARTICLES 111 the pressure upon the surface, boiling will commence at a correspondingly lower temperature. In the same manner as above it may be shown that the saturated vapours of other liquids exert a final pressure, which is proportional to the temperature, and that the temperature at which any liquid boils is the temperature at which its saturated vapour exerts a pressure equal to that upon the free surface of the liquid. 74. The Enunciation of Avogadro's Theory. — The observa- tion that most gases change their volume in almost exactly the same degree, when they undergo the same changes of tempe- rature or pressure, led to the theory of Avogadro. Accord- ing to this theory, similarity of behaviour is caused by similarity of structure. We must regard a given volume of a gas as a system of very small invisible particles, separated from each other by a distance which diminishes when the pressure increases or the temperature falls, and grows larger when the pressure decreases or the temperature rises. Dif- ferent kinds of gases will have different kinds of particles ; but equal volumes of all gases, at the same temperature and pressure, will contain the same number of particles. The theory does not extend to the composition or structure of the particles, or to other changes consequent on a change of temperature. With these it is not concerned. It aims merely at explaining the observation that gases undergo the same change in volume when equally changed in temperature and pressure. Further investigations are necessary before the accuracy or limitation of the theory can be tested. It has the undoubted advantage of simplicity. It offers no precise explanation of the manner in which changes of volume are produced, nor of the exact condition of the system at any given moment. It assumes that a given change is effected by an average change in the distance between the particles. Some may be wider apart and some closer together than the average. Since nothing like any heterogeneity of structure, much less isolation of particles, can ever be detected, it is indis- pensable to the theory that the particles must be considered as extremely small. 112 ELEMENTS OF LABORATORY WORK Avogadro's theory, then, assumes that equal volumes at the same temperature and pressure of those gases which undergo the same volume-change, when they are equally changed in temperature or pressure, contain an equal number of particles. It is obvious, if this be true, that the relative quantities of matter contained in equal volumes of different gases under the same conditions of temperature and pressure, will be the same as the relative quantities of matter contained in separate particles of these gases. If the theory be true, we may learn the masses of relative particles which are so small as to be far removed from the possibility of direct observation. If we admit that the observations of changes of pressure and temperature in gases lead to this conclusion, it remains to be shown how our conceptions of these changes are aided. Other observations have indicated to us that these particles are in constant motion. They must, therefore, approach the sides of the containing vessel with a frequency which is directly proportional to their number. If the volume of a system of these particles is halved, the number of their impacts on the sides of the vessel is doubled. When we speak of the pressure being doubled, this appears to be what is meant. Again, when the temperature of a gas changes, the speed of its particles is supposed to change, an increase of speed being the real change known to us hitherto as a rise of temperature. An acceleration in the average speed of a system of particles will increase the number of impacts against the sides of the containing vessel just as much as a diminution in the capacity of the vessel. Hence, the volume remaining the same, the pressure increases with rise in . temperature ; or the pressure remaining the same, the volume increases. We are driven to the conclusion that the expansion of a gas during a rise of temperature, while its pressure is un- changed, is a change of the same nature as that which occurs when a moving body, coming in contact with another body, sets that body in motion. If this be so, the converse changes which have been observed are such as might be expected. That is, the forcible diminution of the volume of a gas should cause its temperature to rise, and, using the same reasoning, MATTER FORMED OF SMALL PARTICLES 113 an increase in the volume should cause a fall of temperature. In the former case the speed of the particles which come in contact with the moving boundary is increased, in the latter it is diminished. The temperature- changes stated are matters of direct observation, whether the hypothesis be correct or not. The ordinary change of temperature, consequent on con- tact with a body of different temperature, must be regarded, in the same way, as a change in the rate of motion of the particles through collision with particles moving at different rates. The particles from which the change is derived are not necessarily those of a gas. This explanation must be looked upon as partial only ; after further investigations it may be made more complete. It must be distinctly understood that, although all obser- vations point to the probability of solids and liquids being made up of minute particles similar to those constituting gases, there is no reason yet adduced to suppose that Avo- gadro's hypothesis can be directly applied to them. The wide differences in the behaviour of various solids and liquids for the same temperature and pressure changes, would rather show that much wider investigations must be made before any theory as to their structure can be proposed. Whatever their structure may be, it is undoubtedly unlike that of gases in many respects. ~ This is shown by the scarcely perceptible compressibility which distinguishes most solids and liquids from gases, and by the very slight trace of cohesion existing between the particles of gases. At the same time, it is important to remember that most kinds of matter may be made to pass from one state to the others by alteration of temperature, and under certain circumstances the change of state may be gradual and even imperceptible. Additional Exercises and Questions. 1. Connect a porous earthen war vessel, such as is used for electric cells, with a thick glass tube by means of an indiarubber cork ; fill the tube and vessel with coal-gas, and place it over water or mercury. Note that the quantity of gas inside diminishes until a limit is reached. I 114 ELEMENTS OF LABORATORY WORK Prepare a similar apparatus, but maintain an atmosphere of coal-gas outside the porous vessel by the assistance of a vessel enclosing it, and note that a quantity of gas passes to the inside of the porous vessel. Write out a probable explanation of your observations, and suggest methods of continuing the research. 2. Ascertain by experiment the alteration of pressure produced by a given change of temperature in a quantity of air maintained at the same volume. Use a bent tube containing mercury and connect it with a flask ; bring the air in the flask to its original volume by causing it to support a lengthened column of mercury. 3. Make experiments with a view to compare the physical properties of indiarubber, glass, copper, and sealing-wax. Indiarubber tubing, glass tubing or rod, and copper wire may be used. Pay special ..attention to elasticity, rigidity, ductility, malleability. As a result of your observa- tions, define the properties mentioned in a more accurate and complete manner, and suggest explanations derived from the theory that matter is formed of very small particles. 4. Construct apparatus, and make observations of the amount of evaporation taking place from a liquid — water, for example — into a known quantity of air at different temperatures. 6. Show by experiment that equalisation of pressure in gases takes place rapidly, while the process of diffusion is comparatively very slow. How is this explained 1 Modify the apparatus of fig. 32. 6. Find out, by weighing the solid left after evaporation, the relative quantities of common salt dissolved by water at the temperature of the room, and by boiling water. 7. Prepare crystals from powdered copper sulphate. What bearing has the molecular theory of matter upon the formation of crystals ? 8. How does the rate of evaporation and of solution depend upon (1) rate of diffusion and (2) temperature ? 9. In what sense can one gas be said to act as a vacuum towards another ? 10. Describe methods by which the rate of diffusion of gases or liquids may be determined. 11. Give a list of the chief facts which are reasonably explained by the molecular theory of matter. 12. Describe the various kinds of changes which might be expected to take place in a system of molecules if it resemble a system of visible bodies. 13. Describe some process of determining the mass of a given volume of water-vapour or steam. How will the presence of water-vapour in the air affect the height of the barometer ? 14. State why the surface of mercury in a glass tube is convex while that of water is concave. MATTER FORMED OF SMALL PARTICLES 115 15. Make the following observations and give explanations in each case : (a) That mercury will not run through a fine gauze or cambric, while water does so. (#) That a plate, suspended by beeswax and twine from the end of a balance so that its lower surface is completely in contact with the surface of some water, will require a considerable mass to be placed in the other pan of the balance, before it is detached from the surface of the water. (