THE 
 
 THEEMAL MEASUKEMENT 
 OF ENERGY. 
 
3LonUon: C. J. CLAY AND SONS, 
 
 CAMBKIDGE UNIVEKSITY PKESS WAREHOUSE, 
 
 AVE MAKIA LANE. 
 
 50, WELLINGTON STREET 
 
 ILetpjtfl: F. A. BROCKHAUS. 
 gorfe: THE MACMILLAN COMPANY. 
 E. SEYMOUR HALE. 
 
 [All Rights reserved.] 
 
THE 
 
 THEEMAL MEASUREMENT 
 OF ENERGY. 
 
 LECTURES DELIVERED AT 
 THE PHILOSOPHICAL HALL, LEEDS 
 
 BY 
 
 E. H. GRIFFITHS, M.A., F.R.S. 
 
 FELLOW OF SIDNEY SUSSEX COLLEGE, CAMBRIDGE. 
 
 CAMBRIDGE : 
 
 AT THE UNIVERSITY PRESS. 
 1901 
 
CambriUge : 
 
 PRINTED BY J. AND C. F. CLAY, 
 AT THE UNIVERSITY PRESS. 
 
PEEFACE. 
 
 following Lectures were delivered in Leeds, during 
 the Spring of this year, at the request of the 
 Technical Instruction Committee of the West Riding 
 County Council. 
 
 At the close of the course I received, from those who 
 had attended it, a request that the lectures should be 
 published ; this request was subsequently repeated in a 
 letter from the Secretary of the Technical Committee. 
 I therefore now give the lectures (with a few trifling 
 exceptions) in the form in which they were delivered. 
 
 It did not appear possible in such a course, and if 
 possible I should not have considered it advisable, to 
 enter on any detailed criticism of all the various deter- 
 minations of the heat equivalent; suffice it to say, the 
 selection of examples was in no sense arbitrary. 
 
 Some reference to the educational aspects of the 
 subject are, I hope, justified by the fact that the greater 
 portion of my hearers were teachers of science. 
 
 It is natural that an audience should criticise its 
 lecturer ; but the reversal of the process may appear to 
 
 360480 
 
vi Preface 
 
 be almost an impertinence. Nevertheless, I will venture 
 to record some of the impressions I received during my 
 visits to Yorkshire. Informal classes were held at the 
 close of each lecture, and from the experience thus gained, 
 as well as from a study of the large number of letters 
 forwarded to me during the course, I was in some degree 
 able to appreciate the keenness and ability which were 
 the characteristics of those with whom it was my good 
 fortune thus to come into contact. 
 
 The reflection that hundreds of such teachers should 
 have been willing to sacrifice their Saturday afternoons to 
 the study of certain physical measurements which did not 
 even possess the charm of novelty, may somewhat lighten 
 the gloomy prospect sketched for us by those who hold 
 pessimistic views as to the future of Intermediate 
 Scientific Education in this country. 
 
 I take this opportunity of thanking Mr F. H. Neville 
 "and Mr W. C. D. Whetham, not only for their assistance 
 in the revision of the proof-sheets, but also for many 
 valuable suggestions and criticisms. 
 
 E. H. GRIFFITHS. 
 
 SIDNEY SUSSEX COLLEGE, 
 CAMBRIDGE, 
 May, 1901. 
 
CONTENTS. 
 
 LECTURE I. 
 
 Introductory Kemarks. Importance of accuracy in Physical Measure- 
 ments. Brief Historical Survey. Newton. Rumford. Davy. Mayer. 
 Condition of our Knowledge in 1840. Importance of Joule's Work. 
 Energy of a System. Examples of the Transformation of Energy 
 by the agency of Friction, Percussion, Compression, Expansion, 
 Electric Current, Electrical Separation, Movement of Conductors in 
 a Magnetic Field, Sound Waves, Eadiant Energy, and Chemical 
 Action. pp. 1 25. 
 
 LECTURE II. 
 
 Relation between Potential and Kinetic Energy. The C.G.S. System. 
 Meaning of the phrase " The Mechanical Equivalent." Experi- 
 mental difficulties involved in (a) the Measurement of Work ; (b) the 
 Measurement of Quantities of Heat. Primary and Secondary Heat 
 Units. Meaning of a Scale of Temperature. Distinction between a 
 Scale and the True Scale. Garnet's Cycle. All Reversible Engines 
 equally efficient. An Absolute Temperature Scale. The Gas Thermo- 
 meter. Mercury and Platinum Thermometers. A Simple Form of 
 Heat-Engine. pp. 26 53. 
 
 LECTURE III. 
 
 Table of Values obtained by different observers. Direct and Indirect 
 Methods of Measurement. Principles which should guide us when 
 making a selection. Brief descriptions of the Methods of Joule, 
 Hirn, Rowland, Reynolds and Moorby, Griffiths, Schuster and 
 Gannon, Callendar and Barnes. Table of Results. pp. 54 94. 
 
viii Contents 
 
 LECTURE IV. 
 
 Distinction between Capacity for Heat and Specific Heat of Water. 
 Changes in <r t consequent on changes in t as deduced from the 
 experiments of Kegnault, Eowland, Bartoli and Stracciati, Griffiths, 
 Ludin, and Callendar and Barnes. 
 
 Keduction of the results, given in Lecture III., to a common temperature. 
 Possible errors in Electrical Units. Values of C t from to 100. 
 Final Conclusions regarding the Secondary Thermal Unit. The 
 First Law of Thermodynamics and Perpetual Motion. The Second 
 Law. Illustrations of its Application. The Dissipation of Energy. 
 
 pp. 95120. 
 
 APPENDIX I. 
 
 The Thermal Unit. pp. 121, 122. 
 
 APPENDIX II. 
 
 Approximate Methods of determining the Mechanical Equivalent. 
 
 pp. 123133. 
 
 APPENDIX III. 
 
 Copy of [Resolutions passed by the Electrical Standards Committee of 
 the British Association in 1896. pp. 134 135. 
 
 ERRATUM. 
 981-35 ,, . 1-0034 , 981-35 , 1-0033 
 
 987^00 ' ' -T- 97800 ' 
 
LECTURE I. 
 
 Introductory Remarks. Importance of accuracy in Physical 
 Measurements. Brief Historical Survey. Newton. Rumford. 
 Davy. Mayer. Condition of our Knowledge in 1840. Im- 
 portance of Joule's work. Energy of a System. Examples 
 of the Transformation of Energy by the agency of Friction, 
 Percussion, Compression, Expansion, Electric Current, Elec- 
 trical Separation, Movement of Conductors in a Magnetic Field, 
 Sound Waves, Radiant Energy, and Chemical Action. 
 
 THE truth of the principle of the Conservation of 
 Energy is now-a-days so firmly established, that there is 
 some danger of students of natural knowledge regarding 
 it as a doctrine to be accepted without question, rather 
 than as a proposition capable of demonstration. It must 
 be remembered that the proof, like that of all other 
 natural laws, is a purely experimental one, and as all 
 numerical relations dependent on experimental results are, 
 at their best, but approximations, it is well to occasionally 
 collect, and not only collect but also weigh, the evidence 
 at our disposal. 
 
 It is possible that such an enquiry may to some 
 appear as a matter of historical, rather than of immediate, 
 G. 1 
 
2 Mevm'remwit of Energy 
 
 interest. I shall, however, endeavour to show that much 
 has been accomplished, even within the past few years, 
 and that our progress in recent times has been real ; 
 although that progress partakes rather of the nature of 
 an accurate survey of country whose main outlines are 
 already familiar than of any advance into unknown 
 territory. 
 
 It is not on that account, however, of the less conse- 
 quence, for settlement is often as true an indication of 
 progress as discovery itself. 
 
 It has been well said that the surest evidence of 
 advance in any branch of knowledge is increase in the 
 accuracy of our measurements of the phenomena involved, 
 and, judged by this test, there is much to be proud of 
 as we contemplate the knowledge of to-day and compare 
 it with the somewhat indefinite condition of our thermal 
 measurements some thirty, nay, twenty years ago. 
 
 In this course of lectures I shall endeavour to place 
 before you our reasons for satisfaction, and my chief desire 
 is to enlist your sympathies and your enthusiasm in the 
 doctrine of the importance of accurate measurement and 
 in the belief that, in physical science, accurate measure- 
 ments are the steps by which we mount to heights 
 otherwise inaccessible. 
 
 An illustration of the truth of this statement (if 
 illustration is needed) is to be found in the history of 
 the discovery of argon by Lord Rayleigh. 
 
 Who would have supposed it possible that his insistent 
 endeavour to determine the density of nitrogen with the 
 closest accuracy would lead to the discovery of a new 
 
Lecture I 3 
 
 element in the atmosphere ? a discovery which also led 
 indirectly to the detection and isolation of other elements 
 previously unknown. 
 
 As it happens, many of the results due to recent 
 advances in physical science (such as the Rontgen rays, 
 wireless telegraphy, &c.) have been, if I may so venture 
 to describe them, of a sensational character, and there is, 
 to my thinking, a danger that our younger scientists may, 
 in their admiration for such achievements, neglect the 
 more laborious and less attractive methods of research 
 and measurement by which alone such discoveries are 
 rendered possible. 
 
 To-day I am speaking to those who have responsi- 
 bilities as teachers, and I trust that they will join with 
 me in preaching, whenever possible, the doctrine that 
 accurate measurements are necessary to physical sal- 
 vation. Remember that he who accurately determines 
 the value of any physical constant has placed a weapon 
 of precision at the service of mankind. 
 
 One further remark by way of introduction. I propose, 
 when possible, to illustrate what I have to say by means 
 of simple experiments. The majority of these experi- 
 ments require no complicated apparatus and could be 
 performed with appliances to be found in almost every 
 laboratory. Bearing in mind that this course of lectures 
 is addressed to teachers, I have chosen such experiments 
 not on account of their novelty or attractiveness, but 
 by reason of their educational value and practicability. 
 That the more simple an experimental illustration the 
 greater its utility both to teacher and pupil, is a statement 
 
 12 
 
4 Measurement of Energy 
 
 sufficiently near the truth to be accepted as a working 
 hypothesis. 
 
 The discovery of the principle of the Conservation of 
 Energy may be said to date from the time when Newton 
 enunciated bis third law. "Action and reaction are 
 equal and opposite " is, in fact, the whole matter in a 
 nutshell, although all the consequences involved in this 
 statement were only fully comprehended and established 
 in the latter half of the last century. 
 
 It is as Professor Tait has pointed out 1 a matter for 
 regret that Newton's own explanation of the terms action 
 and reaction has been so little considered and discussed 
 by succeeding generations. He stated that there are two 
 entirely distinct senses in which these words may be used, 
 and that, whichever interpretation we accept, the law 
 still holds true. Action in the one sense is a force only, 
 and to this interpretation attention is, and has been, 
 almost universally directed. 
 
 Newton's second interpretation of his third law is 
 very different from this, and is of great importance. It 
 is as follows : 
 
 "If the activity of an agent be measured by the 
 product of the force into its velocity and if similarly the 
 counter activity of the resistance be measured by the 
 velocities of its several parts, whether these arise from 
 friction, adhesion, weight, or acceleration, &c., then activity 
 and counter activity in all combinations of machines will 
 be equal and opposite." 
 
 1 Eecent Advances in Physical Science, p. 33. 
 
Lecture I 5 
 
 We must remember that by the velocity Newton 
 meant the velocity in the direction in which the force 
 is acting (i.e. the component velocity in the direction of 
 the force). 
 
 A most important consequence of this interpretation 
 is that the rate at which an agent does work is the rate 
 at which the kinetic energy of a body increases. In other 
 words the kinetic energy is increased by an amount equal 
 to the work done in producing motion where the only 
 resistance is that due to acceleration. Where the work 
 is spent against friction, however, the visible energy of 
 the system suffers decrease. If Newton had known of 
 experimental evidence which indicated that the visible 
 energy thus apparently destroyed was proportional to the 
 heat developed against friction, it is possible that he 
 might have enunciated the principle of the conservation 
 of energy in its modern form 1 . 
 
 1 In the year 1606 (36 years before the birth of Newton) an anonymous 
 author published a poem entitled "Hallo, my Fancy! " 
 
 You will find this remarkable production in Gilfillan's "Less-known 
 British Poets," and the 13th verse runs as follows : 
 " What multitude of notions 
 
 Doth perturb my pate, 
 Considering the motions 
 
 How the Heavens are preserved, 
 
 And this world served, 
 In moisture, light, and heat ! 
 If one spirit sits the outmost circle turning, 
 Or one turns another continuing in journeying, 
 If rapid circles' motion be that ivhich they call burning ! 
 
 Hallo, my fancy, whither wilt thou go ? " 
 
 Here we have an attractive, although possibly unprofitable, subject for 
 speculation. How far would the progress of science have been accelerated 
 
6 Measurement of Energy 
 
 The sure and rapid growth of our scientific knowledge 
 in recent times is in a great measure due to the firm 
 establishment of the principle of the conservation of 
 energy. Had the truth of this principle been demon- 
 strated by Newton, the progress of natural knowledge 
 might have been quickened by a century ! 
 
 Returning from such imaginings to sober reality, we 
 find that from the time of Newton until the commence- 
 ment (one might almost say the middle) of the nineteenth 
 century, natural philosophers were heavily handicapped 
 in their progress by the theory of caloric then firmly 
 established. Theories of all kinds are useful scaffoldings ; 
 but he would be a bad architect who, instead of regarding 
 the scaffolding as a temporary expedient, allowed its 
 existence to cramp or influence the nature of his edifice. 
 
 The existence of an imponderable, indestructible fluid 
 termed caloric was practically assumed in all discussions 
 on natural phenomena, and many ingenious hypotheses 
 and far-fetched explanations were put forward to account 
 for the numerous difficulties which, in consequence, 
 presented themselves. 
 
 For example, percussion was supposed to alter the 
 condition of a body and lessen its capacity for heat. 
 Thus in hammering a nail the caloric was simply squeezed 
 out of the iron as the molecules were forced more closely 
 together. 
 
 This explanation, however, did not appear to be 
 
 and what would have been our position to-day, had Newton but read 
 that line " If rapid circles' motion be that which they call burning," and 
 allowed his fancy to dwell thereon ? 
 
Lecture I 7 
 
 satisfactory in the case of lead, whose density is not 
 increased by hammering. 
 
 When heat was developed by friction, part of the 
 material was rubbed into powder and the Calorists 
 insisted that the capacity for heat of the powder was 
 smaller than that of the solid from which it was abraded. 
 The absence of any experimental evidence of the truth 
 of this hypothesis does not appear to have troubled them 
 in any way ! Such efforts to maintain the scaffolding 
 unaltered necessarily hampered and retarded the efforts 
 of the builders. 
 
 Count Rumford was the first to publicly question the 
 popular caloric theory, when in 1798 he gave an account 
 of his experiments. He placed a hollow gun-metal 
 cylinder beneath a blunt steel borer and observed that 
 after the cylinder had made about a thousand revolu- 
 tions its temperature had risen from 60 to 130 F., 
 while the scaly matter abraded by the friction weighed 
 only 837 grains troy. " Is it possible," he writes, " that 
 such a quantity of heat as would have caused 5 Ibs. of 
 ice-cold water to boil could have been furnished by so 
 inconsiderable a quantity of metallic dust merely in 
 consequence of a change in its capacity for heat l ? " 
 
 The Calorists, however, were not convinced. Even 
 when Rumford proved that the capacity for heat of the 
 solid was the same as that of the dust, they said that, 
 although the heat required to change the temperature 
 of equal masses was the same, yet the solid metal 
 contained a greater quantity of heat than the dust. 
 1 Rumford's Complete Works, Vol. i. p. 478. 
 
8 Measurement of Energy 
 
 Rumford answered that if the heat were rubbed out 
 of the material, a time must come when all its heat 
 would be exhausted, whereas there was no evidence that 
 such was the case. He also proceeded with further 
 experiments in which the metal was immersed in water 
 and, if we work out the results of those experiments, we 
 find that 940 foot-pounds of work would raise one pound 
 of water through 1 F. 1 . His final argument was as 
 follows : 
 
 " In reasoning on this subject we must not forget to 
 consider that most remarkable circumstance, that the 
 source of heat generated by friction in these experiments 
 appeared evidently to be inexhaustible. 
 
 " It is hardly necessary to add, that anything which 
 any insulated body, or system of bodies, can continue to 
 furnish without limitation cannot possibly be a material 
 substance 2 . It appears to me to be extremely difficult, 
 if not quite impossible, to form any distinct idea of 
 anything capable of being excited and communicated in 
 the manner in which the heat was excited and communi- 
 cated in these experiments, except it be motion." He 
 adds, " I am very far from pretending to know how or by 
 what means or mechanical contrivance that particular 
 kind of motion in bodies which has been supposed to 
 constitute heat is excited, continued, and propagated." 
 
 The historical importance of Rumford's experiments 
 
 1 Rumford's experiments were qualitative, not quantitative. He made 
 no attempt at the determination of any numerical relation. 
 
 2 In an earlier portion of his paper (p. 479, ibid.) Eumford calls 
 attention to the significant fact that the rate of production of heat 
 remained constant so long as the work was done uniformly. 
 
Lecture I 
 
 Fig./. 
 
 Fig. 1. 
 
 "Fig. 1 shows the cannon used in the foregoing experiments in the 
 state it was in when it came from the foundry. 
 
 Fig. 2 shows the machinery used in the experiments No. 1 and No. 2. 
 The cannon is seen fixed in the machine used for boring cannon, u 
 is a strong iron bar (which, to save room in the drawing, is repre- 
 sented as broken off), which bar, being united with machinery (not 
 expressed in the figure), that is carried round by horses, causes the 
 cannon to turn round its axis. 
 
 m is a strong iron bar, to the end of which the blunt borer is fixed ; 
 which, by being forced against the bottom of the bore of the short 
 hollow cylinder that remains connected by a small cylindrical neck 
 to the end of the cannon, is used in generating heat by friction. 
 
 Fig. 3 shows, on an enlarged scale, the same hollow cylinder that is repre- 
 sented on a smaller scale in the foregoing figure. It is here seen 
 connected with the wooden box (g, h, i, k), used in the experiments 
 No. 3 and No. 4, when this hollow cylinder was immersed in water. 
 
 p, which is marked by dotted lines, is the piston which closed the 
 end of the bore of the cylinder. 
 
 n is the blunt borer seen sidewise. 
 
 d, e is the small hole by which the thermometer was introduced 
 that was used for ascertaining the heat of the cylinder. 
 
 Fig. 4 is a perspective view of the wooden box, a section of which is seen 
 in the foregoing figure. (See g, h, i, k, Fig. 3.) 
 
 Figs. 5 and 6 represent the blunt borer ?i, joined to the iron bar m, to 
 which it was fastened. 
 
 Figs. 7 and 8 represent the same borer, with its iron bar, together with 
 the piston, which, in the experiments No. 2 and No. 3, was used to 
 close the mouth of the hollow cylinder." 
 
10 Measurement of Energy 
 
 is so great that it may interest you to see this copy of 
 his original drawings. The description of the figures is 
 extracted from his paper entitled "An Inquiry concerning 
 the Source of the Heat excited by Friction 1 ." 
 
 Rumford's work was of the highest value. As Professor 
 Tait remarks 2 , it was throughout free from that a priori 
 style of reasoning which had hitherto been so fatal to the 
 progress of natural science. Had Rumford shown that the 
 heat developed by the solution of a powder in acid was 
 equal to that developed by the solution of the same mass of 
 the solid, he could have claimed the sole credit of having 
 established the doctrine of the n on- materiality of heat 3 . 
 Nevertheless Rumford's conclusions remained for another 
 forty years as subjects for ridicule rather than for ad- 
 miration. 
 
 Almost immediately after the publication of Rumford's 
 paper, Sir Humphry Davy proved experimentally that 
 two pieces of ice may be melted by rubbing them 
 together, and thus he gave conclusive proof (although 
 there is evidence that he himself at the time did not 
 perceive it) that heat is not a form of matter, and 
 therefore his experiments are historically of the first 
 importance. In a second series of experiments he so 
 
 1 Rumford's Complete Works, Vol. i. p. 492. 
 
 2 Recent Advances in Physical Science, p. 42. 
 
 3 This statement, however, requires some qualification, as it is not 
 certain that the heat developed in both cases would be the same. For 
 example, the heat developed by the solution of a steel spring when 
 wound up would differ from that developed by the solution of the same 
 spring when not in a state of strain. In other words, it is not sufficient 
 that the masses should be equal, their physical conditions must also be 
 identical. 
 
Lecture I 11 
 
 contrived that the friction between the lumps of ice 
 took place in the exhausted receiver of an air-pump. 
 He says : 
 
 " From this experiment it is evident that ice by 
 friction is converted into water, and according to the 
 supposition its capacity is diminished ; but it is a well- 
 known fact that the capacity of water for heat is much 
 greater than that of ice ; and ice must have an absolute 
 quantity of heat added to it before it can be converted 
 into water. Friction, consequently, does not diminish the 
 capacities of bodies for heat." 
 
 It was not, however, till 1812 that he enunciated this 
 proposition : " The immediate cause of the phenomenon 
 of heat then is motion, and the laws of its communication 
 are precisely the same as the laws of the communication 
 of motion 1 "; and, on reflection, it seems extraordinary 
 that the publication of the works of Rumford and Davy 
 produced so little effect, and that their conclusions should 
 have been regarded merely as ingenious hypotheses until 
 the time of Joule. 
 
 It would be impossible in any historical summary, 
 however brief, to omit the name of Dr Julius Mayer 
 (1842), as he was the first to employ the phrase, the 
 mechanical equivalent of heat, and thus enunciate in a 
 distinct form the law of the Conservation of Energy 2 . 
 
 It is doubtful, however, if Mayer has deserved all the 
 credit which was in consequence at one time assigned to 
 him. The data on which his conclusions were based were 
 
 1 Elements of Chemical Philosophy, 1812, pp. 94, 95. 
 
 2 Ann. Ch. Pharm., XLII. 233. 
 
12 Measurement of Energy 
 
 not sufficient, while certain of his assumptions were 
 undoubtedly erroneous. Mayer denied on more than one 
 occasion that heat depends on motion, and yet he has been 
 called by some " the discoverer of the modern theory of 
 heat." Nevertheless he, as it happens, rendered a service 
 to the cause of science by distinctly, although perhaps 
 over-boldly, enunciating a theorem of the highest import- 
 ance. In this case no evil consequences resulted from 
 the premature publication, for the work of Joule and 
 of Colding (already partially accomplished) afforded 
 satisfactory and complete experimental evidence of the 
 truth of the proposition advanced by Mayer. 
 
 Let me here briefly summarise the condition of our 
 knowledge at the time of the advent of Joule. 
 
 Although not generally apprehended, the principle of 
 the Conservation of Energy had, in its main features, 
 been enunciated by Newton. Rumford and Davy had 
 demonstrated that heat is not matter; but their con- 
 clusion was not generally accepted. The school of 
 Calorists still existed, and although the general prin- 
 ciple of Conservation of Energy had been enunciated 
 by Mayer, his data were so scanty, and often erroneous, 
 that his conclusions carried but little conviction to men 
 of science. What the situation demanded was rigorous 
 experimental proof that apparent disappearance of energy, 
 when work was done against friction, was invariably 
 accompanied by the generation of a proportional amount 
 of heat, and that this quantity of heat was independent 
 of the manner in which the work was done, or the nature 
 
Lecture I 13 
 
 of the materials employed. Hence the singular import- 
 ance of Joule's experiments. 
 
 The actual numerical values obtained by him are, we 
 now know, somewhat inaccurate, but, at the same time, 
 marvellously near the truth when we consider the con- 
 ditions under which he worked, and more especially the 
 unsatisfactory state of therm ometry in his time. 
 
 It is not so much the accuracy as the variety of the 
 evidence supplied by Joule which claims our admiration. 
 He did not content himself with the examination of some 
 single case of transformation of energy. He investigated 
 the heat caused by the friction between solids, and also 
 that developed in overcoming fluid resistance, not only in 
 the case of one fluid but of different fluids. 
 
 Again, the manner of doing work was varied from the 
 descent of weights to that performed by an electric current 
 in overcoming resistance. Although many stones have 
 been laid by other workers it may be said, I think without 
 exaggeration, that the piers were built by Newton and 
 the keystone of the arch supplied by Joule. 
 
 The principle of the Conservation of Energy states 
 that in all its forms energy remains a constant quantity, 
 however many transformations it undergoes. In other 
 words, if energy is made to pass from any condition such 
 as that of matter in motion into any other condition such 
 as molecular, or electrical energy, the numerical value of 
 the resulting effect depends simply on the quantity of 
 energy so transformed, not on the method of transfor- 
 mation, the materials, time, or any external conditions. 
 
14 Measurement of Energy 
 
 All natural phenomena have their origin in the trans- 
 ference of energy from one form to another, and energy 
 is only available when it is capable of transformation. 
 The total energy of the molecules of air in this hall is, 
 no doubt, very great; but we have not the means of 
 readily translating that energy into other forms and 
 hence can make no practical use thereof. When we 
 refer to the " available energy of a system" we mean that 
 portion of it which we can utilise. 
 
 It must be remembered that all our measurements 
 are but relative ; when we speak of a mass at rest we 
 mean that its motion is that of the surface of the earth 
 at the same place. We then say that it has no kinetic 
 energy, whereas, in reality, all matter that we know of 
 is in rapid motion and the kinetic energy of any mass 
 which appears to us to be stationary is in reality very 
 great 1 . It is well therefore to keep this relative nature 
 of our measurements in mind, although when, in the 
 future, I speak of the kinetic energy of a system it will 
 be understood that I refer the motion of its parts to that 
 of the surface of the earth at the same place. 
 
 I now wish to draw your attention to the more 
 
 1 For example, take a lump of our best coal and give it a velocity of 
 about 5 miles per second ; its energy due to movement would then be about 
 the heat equivalent of its complete combustion. Now, if we regard the 
 sun as fixed, the velocity of the earth in its orbit is between 19 and 20 
 miles per second. Hence the energy of a mass of coal due to its velocity 
 (although it appears to us to be at rest) is far greater than its chemical 
 energy. In other words, suppose the earth to be constructed entirely of 
 the best coal, the heat generated by the sudden stoppage of its movement 
 would be about 15 times as great as the heat which would be developed by 
 its complete combustion ! 
 
Lecture I 15 
 
 common phenomena of the transformation of energy. 
 The examples which we shall consider are probably 
 known by all of you ; but their importance is so great 
 that it is a tale worth telling, although twice told, and 
 I would ask you more especially to fix your attention 
 on the fact that the cases we consider present one cha- 
 racteristic feature, viz. that when we convert a given 
 quantity of energy from the form A to the form B some 
 portion of it is, at the sapie time, converted into heat. 
 
 Experiment. This arrangement of a rotating tube 
 filled with water is probably familiar to most of you. 
 You see that as the tube is rotated great heat is deve- 
 loped at the place where it is clasped by the wooden 
 pincers, so that the contained water is boiled and the cork 
 explosively expelled. Let us suppose that but 1 grm. of 
 water was here raised to boiling point and converted into 
 steam, then the work which my assistant has done was 
 sufficient to raise a weight of about 640 grms. (i.e. about 
 1*4 Ibs.) from the bottom of a coal-mine 1,400 ft. deep. 
 
 Simple as this experiment is, it is important educa- 
 tionally if we show that the result is the same, no matter 
 what the material of the pincers or of the tube, provided 
 that the work done against friction remains constant. 
 Here then we have the familiar case of conversion of 
 work directly into heat. The source of the energy is 
 to be found in the chemical separation of the substances 
 eaten by the operator. 
 
 Experiment. Here, again, you see that by hammering 
 the lead its temperature is sufficiently raised for it to ignite 
 
16 Measurement of Energy 
 
 the phosphorus 1 place upon it. This is an example of the 
 conversion of kinetic energy into heat. 
 
 Experiment. By suddenly compressing the air in this 
 tube, the heat generated is again sufficient to raise the 
 temperature to the ignition point of phosphorus. 
 
 A neat application of this method of transforming 
 energy comes to us from the other side of the Atlantic. 
 When driving piles they make the upper portion of the 
 pile hollow, and a heavy cylinder, which just fits the 
 hollow tube, is supported above the pile, while a little 
 gunpowder is placed at the bottom of the hollow. When 
 the cylinder is released, it compresses the air within the 
 hollow of the pile so rapidly that the heat generated 
 explodes the gunpowder and the force of the explosion 
 drives the cylinder up to its original position (where it is 
 caught), while the reaction drives the pile further into 
 the ground. 
 
 Experiment. Here I have a bottle of carbon-dioxide, 
 the pressure within the cylinder being at least 60 or 70 
 atmospheres. As we open the tap the contents stream 
 out at the nozzle, there is rapid evaporation, a large 
 volume of air under atmospheric pressure is displaced, 
 and thus mechanical work is done. Heat, therefore, dis- 
 appears at such a rate that the temperature of the 
 emergent substance is reduced below 80 and solidifi- 
 cation takes place. You see the resulting carbon-dioxide 
 snow, and when I add some of it to this mercury, you 
 perceive that I am able to lift the frozen lump of mercury 
 
Lecture I 17 
 
 by the wire placed in it. This is, of course, a converse 
 case to the last, where we raised the temperature of a gas 
 by compression. 
 
 In considering this experiment it is important to 
 remember that the heat which has thus disappeared 
 corresponds to that developed by the work done when the 
 cylinder was originally charged. If the vessel had been an 
 adiabatic or perfectly non-conducting one, and had there- 
 fore retained its contents until to-day at the temperature 
 to which they were raised at the time of charging, the sole 
 effect of now allowing the contents to escape would have 
 been to lower them to practically their original tem- 
 perature. Hence, on the whole, we have had no real 
 disappearance of heat; in fact, could we minutely trace 
 all the steps of the cycle, we should find that a certain 
 quantity of energy had been degraded. By the whole 
 cycle of operations we have therefore increased rather 
 than diminished the earth's store of heat. 
 
 Experiment, Another form in which energy presents 
 itself is in the separation of electrically charged bodies. If 
 I inductively charge this electroscope and then remove the 
 negatively electrified ebonite rod, I have to overcome the 
 attraction of the positively charged electroscope. Work 
 is thus done upon the system in consequence of its 
 electrical condition, as is shown by the divergence of 
 the gold leaves whose centres of gravity are thus 
 raised. When I connect the electroscope with earth, 
 that energy is lost and, could we examine with sufficient 
 accuracy the temperature of the wire connecting it with 
 G. 2 
 
18 Measurement of Energy 
 
 earth, we should find that it had been increased. When 
 a body at a higher potential is discharged, the heat 
 generated is usually rendered evident by the familiar 
 phenomenon of the spark. Thus we continually find 
 that as we alter the energy of an electric system, some 
 of that energy appears as heat. 
 
 The conversion of the energy of an electric current 
 into heat is now-a-days so familiar a phenomenon that 
 it is almost unnecessary to call your attention to it. All 
 our electric lighting stations are engaged in converting 
 some of the heat generated, by the union of the carbon 
 and hydrogen of coal with the oxygen of the atmosphere, 
 into mechanical energy; this in its turn is changed into 
 the energy of an electric current, which is again degraded 
 into heat in our incandescent lamps, a very small per- 
 centage of the total energy appearing as visible radiant 
 energy. The electric current here is merely the most 
 convenient method of converting mechanical energy at 
 one place into heat and some visible radiant energy at 
 another. 
 
 Experiment. I have here a fly-wheel so connected 
 with a number of magnets that the latter rotate with 
 great rapidity as the fly-wheel revolves. You will see 
 that the resistance to movement is small and that the 
 fly-wheel continues to rotate for some time after the hand 
 has been removed. We could form an idea of the energy 
 of this rotating system by finding the distance through 
 which it would raise a known weight. 
 
 The magnets are revolving within the coils of an 
 
Lecture I 19 
 
 incomplete electrically conducting circuit but without 
 touching them. We will now cause the fly-wheel to 
 rotate at, as nearly as possible, the same rate as before, 
 and then join the ends of the circuit and thus allow the 
 induced currents, formed by the rotation of the magnetic 
 field, to pass through the coils. These currents will 
 always be established in such a direction as to resist the 
 motion of the magnets. Hence more work is now done 
 per revolution by the revolving fly-wheel than before I 
 closed the circuit and thus the wheel is brought to rest 
 as if by the application of a powerful brake. As a 
 consequence, the energy of the fly-wheel disappears after 
 a very few revolutions and at the same time you see by 
 the glowing of this wire that heat has been developed in 
 the electric circuit, this heat being the equivalent of the 
 energy which, in the previous case, enabled the fly-wheel 
 to perform many more revolutions 1 . 
 
 I particularly wish to draw your attention to the fact 
 that the manner in which that work is being done is of 
 no importance. The heat generated will be the same, 
 whatever the cause of the stoppage, if it can be shown 
 that the energy of the rotating wheel has not appeared 
 in other forms. It is this independence of the nature 
 of the material, or the manner in which the resistance is 
 overcome, which is the true test of the principle of the 
 conservation of energy. 
 
 Experiment. In a cup formed in the top of this 
 
 1 When the electric circuit was incomplete the fly-wheel performed 
 27 revolutions; when the circuit was closed it came to rest after 
 5 revolutions. 
 
 22 
 
20 Measurement of Energy 
 
 copper cylinder, which is rotating in a strong magnetic 
 field, I place a piece of phosphorus. I think you will 
 see that, in consequence of the resistance offered by the 
 currents due to its rotation in the magnetic field, the 
 work done on the copper is sufficient to raise its tempera- 
 ture sufficiently to ignite the phosphorus. 
 
 Sound-waves are, themselves, carriers of energy and, 
 as is well known, a certain amount of heat is developed 
 by the production of sound. The dissipation of energy 
 in the sound-wave itself is, however, very small, otherwise 
 the waves would die away with extreme rapidity. It is, 
 nevertheless, certain that when sound-waves impinge on 
 solid bodies a certain amount of heat is developed. 
 
 Experiment. Here is an example of such a propaga- 
 tion of energy. I set this tuning-fork in vibration and, 
 when I stop it, I think you will distinctly hear the same 
 note given out by the second fork. 
 
 Again, by suspending a pith-ball against one prong 
 of the receiving fork, we can (with the aid of the lantern) 
 render visible to the eye the vibrations set up by means 
 of the energy transmitted from the first fork to the 
 second. I have not been able to devise any method of 
 showing you that heat has in this case been actually 
 generated in the receiver, but as you can see the rapid 
 hammering of the metal by the ball, it is easy to under- 
 stand that such impacts must be accompanied by the 
 evolution of some heat. 
 
 Of all forms of energy we, on this earth, are most 
 indebted to the radiant form ; the source alike both of the 
 
Lecture 1 21 
 
 energy of the food we eat and of the coal we burn, it is at 
 once, the greatest and the highest of the forms in which 
 energy presents itself. We have few machines which 
 work by the direct transmutation of radiant energy 
 to lower forms, yet we must remember that the action 
 of all water-mills, turbines, &c. is dependent on the 
 transformation of radiant into potential energy a trans- 
 formation performed for us by nature, without our 
 assistance. As our coal supply becomes exhausted I 
 think it possible that engineers will have to turn their 
 attention more seriously to the direct conversion of the 
 energy so freely supplied to us by the sun. 
 
 You know that power is now transmitted from the 
 Falls of Niagara to towns at considerable distances, and 
 here we have an example of an indirect use of radiant 
 energy. As the solar radiant energy reaches our earth it 
 is almost entirely degraded to the heat form. A portion 
 of this heat is transformed, by means of evaporation, into 
 potential energy of masses of water at a high elevation, 
 and some of this energy is retained by the water after 
 it has fallen on the American Continent, since it is then 
 at a higher level than the ocean from which it sprang. 
 During its further descent at Niagara this water is so 
 directed that it causes the rotation of conducting bodies in 
 a magnetic field ; thus a portion of its energy is converted 
 into the energy of electricity in motion and, in this 
 transformation also, a portion is degraded into heat. 
 
 Again, the energy of this electric current is, at distant 
 places, almost wholly converted into heat, either by the 
 use of incandescent lamps, or by overcoming the friction 
 
22 Measurement of Energy 
 
 of various pieces of machinery. Here we have an 
 interesting series of transmutations ; but I would press 
 on your notice the fact that no single one of them has 
 been accomplished without the payment of a forfeit in the 
 shape of a certain per-centage of the total energy de- 
 graded into the form of heat. 
 
 How small a fraction of the earth's share of the solar 
 energy is directly utilised by man is evident from the 
 following considerations. 
 
 According to Lord Kelvin's calculations the energy of 
 the sun's radiation is equal to about 7000 H,P. per square 
 foot of its surface. 
 
 Some observations (by J. Y. Buchanan 1 ) taken in Egypt 
 with an improved form of calorimeter, lead to the con- 
 clusion that each square metre of the earth's surface, 
 which is exposed perpendicularly to the sun's rays, re- 
 ceives radiant energy equivalent to 1 H.p. 
 
 Now, the area of the great circle of the earth is 
 roughly 130 x 10 12 square metres; thus the working value 
 of the sun's radiation to us is about 130 billion H.P. If 
 we deduce from this the H.P. radiation per 1 square foot 
 of the sun's surface, we obtain a value very decidedly less 
 than that obtained by Lord Kelvin. It is probable, there- 
 fore, that the result obtained by Buchanan does not err 
 on the side of excess. 
 
 I am aware that such figures as a billion convey little 
 
 meaning to our minds. Recently, I came across an 
 
 example which illustrated in a somewhat novel manner the 
 
 vastness of this number. Do you suppose that there are 
 
 1 Proc. Camb. Phil. Soc., 1900. 
 
Lecture I 23 
 
 a billion bricks in all London ? I admit that I should have 
 considered it possible. Now, assuming the area of London 
 to be 100 square miles, simple arithmetic will tell you 
 that 1 billion of ordinary sized bricks placed together 
 would cover London in a solid mass to the depth of 
 25 feet. Remembering this, I ask you to reflect on the 
 magnitude of the stream of energy thus continuously 
 poured upon the earth ; 130 billion H.p. ! 
 
 I find that the latest estimate of the total population 
 
 130 x 10 12 
 
 of the earth is 1500 millions. This would give 
 
 lo x 10 8 
 
 H.P. per individual. In other words, if the radiant solar 
 energy, falling on the earth were wholly converted into 
 mechanical energy, each individual's share would enable 
 him to lift a weight of 33,000 Ibs. through a vertical 
 distance of 100,000 feet (nearly 20 miles) every minute of 
 his life. 
 
 Experiment. In this familiar apparatus (Crooke's 
 Radiometer) you see apparently a direct transformation 
 of radiant energy into mechanical motion ; in reality, the 
 change has taken place in two steps. The radiant energy 
 is changed into the heat form (more being thus converted 
 on the black, than on the bright, side of the vanes) and 
 a portion of the heat thus generated increases the rapidity 
 of the motion of the molecules of the gas there present, 
 thus setting up, on opposite sides of the vanes, a difference 
 of pressure sufficient to cause rotation ; but this kinetic 
 energy again becomes converted into heat by the friction 
 of the bearings. 
 
 The form of energy chiefly used by the engineer 
 
24 Measurement of Energy 
 
 is that of chemical separation. The burning of coal is 
 the conversion of such energy into the heat form, the heat 
 being probably of kinetic origin and due to the impact of 
 atoms. We must bear in mind, however, that in such 
 cases we always have a breaking up of existing molecules, 
 as well as the formation of new ones. 
 
 When we oxidise zinc by the action of dilute sulphuric 
 acid, we start with molecules of zinc, sulphuric acid, and 
 water, and we finish with zinc sulphate, hydrogen, and 
 water. The chemical energy of the products will be less 
 than that of the original substances and the difference is 
 accounted for by the heat developed by the reaction. If 
 we connect the zinc externally with a plate of some other 
 metal immersed in the acid we obtain an electric current, 
 and by means of this current we can perform mechanical, 
 or other, work in which case less of the lost energy of the 
 compounds will appear directly as heat. 
 
 Experiment I cause this current to decompose 
 water and in consequence less heat will (for a given 
 consumption of zinc) be developed in the battery and 
 circuit than would be the case if I merely connected the 
 ends of the battery wires. The energy thus again appears 
 as that of chemical separation, although some portion has 
 certainly gone downhill as heat during the process. 
 I apply a light to the soap-bubbles which contain the 
 separated gases. You all know the exceedingly sharp 
 explosion thus obtained. Here nearly all the apparently 
 missing heat reappears at the place of explosion, although 
 a fraction may be generated elsewhere by means of sound- 
 waves. 
 
Lecture I 25 
 
 To-day we have concerned ourselves chiefly with the 
 transference of various forms of energy into heat and we 
 have found that, in nearly all cases, such conversion is easy 
 of accomplishment. We have seen that the change from 
 any form A to another form B involves the appearance 
 of some of the total energy as heat. Each time we alter 
 our investment in energy, we have thus to pay a commis- 
 sion, and in future lectures I hope to be able to show you 
 that the tribute thus exacted can never be wholly 
 recovered by us and must be regarded, not as destroyed, 
 but as thrown on the waste-heap of the Universe. 
 
 In conclusion, it is necessary to remember that, although 
 the doctrine of the indestructibility of energy is established 
 beyond all question, it in no way involves the assumption 
 that energy in different forms is equally available. 
 
LECTURE II. 
 
 Kelation between Potential and Kinetic Energy. The C.G.S. 
 System. Meaning of the phrase "The Mechanical Equiva- 
 lent." Experimental difficulties involved in (a) the Measure- 
 ment of Work ; (6) the Measurement of Quantities of Heat. 
 Primary and Secondary Heat Units. Meaning of a Scale of 
 Temperature. Distinction between a Scale and the True Scale. 
 Carnot's Cycle. All Keversible Engines equally efficient. An 
 Absolute Temperature Scale. The Gas Thermometer. Mercury 
 and Platinum Thermometers. A Simple Form of Heat-Engine. 
 
 IN my last lecture I gave a very brief outline of the early 
 history and the general principle of the Conservation of 
 Energy. I propose to-day to direct your attention more 
 particularly to the nature of the measurements which 
 have to be made before we can obtain the numerical 
 relation between the mechanical, and the thermal, forms 
 of energy. 
 
 Let us first consider the measurement of the potential 
 and kinetic energy of a system. 
 
 The most common English method of stating potential 
 energy is in foot-pounds. This is unfortunate, as we 
 require further information (viz. the local value of g) 
 
Lecture II 27 
 
 before we can attach any definite value to an expression 
 of this kind. 
 
 The ratio of the value of 1 ft.-lb. of work here (or 
 rather in Manchester) to its value at the Equator is 
 
 981-35 ^ . 1-0034 
 
 that is, - - , and this ratio increases m 
 
 i 
 
 magnitude as we approach the Poles. If, therefore, the 
 potential energy of a system is given in ft.-lbs., and 
 the position of the observer is not stated, there exists 
 an uncertainty of about 4 parts in 1000, and even 
 when the position is known, a troublesome reduction 
 to a common standard is necessary. It is far better to 
 adopt at once a non-gravitational and absolute unit, such 
 as the " erg," or dyne-centimetre. 
 
 Now a mass of 1 gramme, if acted on by its own 
 weight, would in this room move with an acceleration 
 of 981*4 cm. per sec. per sec. Hence, as I support this 
 1 gramme weight in my hand, I must be giving it an 
 equal upward acceleration ; that is, I am exerting upon it 
 an upward force of 981*4 dynes. Suppose therefore that 
 I lift a mass of 100 grammes through a vertical distance 
 of 101 '9 cm., I have caused a force of 98140 dynes to move 
 through a distance of 101*9 cm.; hence I have done almost 
 exactly 10 7 ergs, that is, 1 joule of work. It may be 
 convenient to remember this example, viz. that a joule 
 of work is done (approximately) whenever we lift 100 
 grammes through a vertical distance of 102 cm., the 
 exact distance depending, of course, on the local value 
 of g ; also, if I perform this work in one second, then the 
 power (or rate of doing work) is 1 watt. 
 
28 Measurement of Energy 
 
 I propose to adopt the erg, or its multiple the joule, 
 as our unit in all cases, and to express the results obtained 
 by different observers in terms of that unit 1 . 
 
 The potential energy of a system may be denned as the 
 work it can do in consequence of its position or configu- 
 ration; the kinetic energy of a system is that due to motion. 
 
 We know from a study of the phenomena of accelera- 
 tion that if a mass m is shot upward with a velocity v, it 
 
 v 2 
 will rise through a vertical distance s such that s = . 
 
 * t/ 
 
 Now, this mass is pulled towards the earth with a 
 force mg; hence if allowed to descend through the vertical 
 distance s it could do mg . s units of work. By its ascent 
 to its highest position, therefore, its potential energy must 
 have been increased by this quantity, mg . s. This increase 
 was entirely due to its motion when starting upwards. 
 Hence the kinetic energy of a mass m moving with a 
 velocity v is equivalent to the potential energy 
 
 ?; 2 1 
 mg.s = mg.-^ = 2 mv ' 
 
 Thus since mg =/dynes (in the C.G.s. system) we know 
 that ^mv- =fs ergs. 
 
 1 The conversion from ergs to foot-pounds is always a troublesome 
 one and involves a knowledge of g at the place of observation. As it is 
 often necessary to convert the mechanical equivalent expressed in ergs to 
 foot-pounds at Greenwich (# = 981*24) the following factors may be found 
 useful. 
 
 Mechanical equivalent in ergs x -0000334363 = mechanical equivalent 
 expressed in foot-pounds at Greenwich. 
 
 Mechanical equivalent in foot-pounds at Greenwich x 29907*6 = me- 
 chanical equivalent expressed in ergs. 
 
Lecture II 29 
 
 It is important to notice that ^mv" is not a directive 
 or vector quantity ; it can never be negative. Hence the 
 kinetic energy of a system is the sum of the kinetic 
 energy of its parts, independently of the directions in 
 which those parts are moving, although the availability 
 (or what Lord Kelvin terms the motivity) may depend 
 upon the direction of such movements. The energy of a 
 swarm of gnats is the same whether they are all moving 
 in different directions, or all in the same direction. In the 
 first case we may not, but in the second case we may, be 
 able to utilise that energy. 
 
 We are now, I think, in a position to define the me- 
 chanical equivalent and I propose to do so as follows : 
 
 " The mechanical equivalent is the number of ergs 
 which, if wholly converted into heat, would generate one \/ 
 thermal unit." 
 
 In order, therefore, to obtain the value of this 
 constant, we have two distinct sets of measurements to 
 perform. 
 
 (a) The accurate measurement in ergs of the change 
 in the mechanical energy of a given system ; 
 
 (b) The measurement of the quantity of heat gene- 
 rated by the complete conversion of that number of ergs 
 of energy into the form of heat ; and I may add that it 
 is the second of these measurements which has presented 
 the greatest difficulties. 
 
 I remember, some years ago when examining in the 
 Cambridge Local Examinations, I asked for a definition of 
 the mechanical equivalent. I received many curious 
 
30 Measurement of Energy 
 
 answers ; but one, in particular, impressed itself upon my 
 memory, viz., "The object of the mechanical equivalent 
 is to waste as much work as possible." Now, the most 
 lenient of examiners could scarcely have endowed this 
 answer liberally with marks; at the same time it has often 
 struck me that there is a good deal of truth in it. If we 
 start on a determination of this important constant, our 
 object is to transform the whole of the energy we measure 
 into heat, and that heat all generated at one place. We 
 do want to " waste as much work as possible." 
 
 If we have a mass at a high elevation, then, if we know 
 the value of g, we have seen that we can calculate with 
 accuracy its available energy, that is, the number of ergs 
 of work it can do in descending through a given distance. 
 Suppose, in its descent, it turns a paddle-wheel ; some of 
 the energy we measured will have been dissipated by 
 sound-waves, some by friction at bearings exterior to the 
 calorimeter, some perhaps by the mass having a certain 
 amount of kinetic energy at the end of its descent. The 
 difficulty, in fact, is not so much that of " wasting all the 
 work " as of wasting it at the place where we measure its 
 equivalent. 
 
 The various devices by which these difficulties have 
 been overcome will be considered in my next lecture. 
 To-day I more especially wish to fix your attention on the 
 method by which we measure the heat generated, on the 
 assumption that we are able to convert all the energy of 
 the system into heat. Two distinct methods of measuring 
 quantities of heat suggest themselves : 
 
 (1) Determination of the quantity of heat required 
 
Lecture II 31 
 
 to change the physical condition of a body (to melt, for 
 example, a given mass of ice), or, 
 
 (2) Observation of the heat required to raise a 
 certain mass of some selected substance, such as water, 
 through a given range of temperature. 
 
 The first of these methods possesses one great 
 advantage, it is independent of all temperature measure- 
 ments. 
 
 Unfortunately there are practical difficulties. For 
 example : The magnitude of the unit thus obtained is, 
 in many respects, inconvenient, and we do not as yet know 
 a satisfactory method of determining its value with 
 accuracy. It has also been recently proved that the 
 density of ice is variable 1 . 
 
 Nevertheless, so great is the advantage due to the 
 absence of thermometric measurements, that some of our 
 leading authorities are still in favour of the adoption 
 of such a unit. (See Appendix I.) 
 
 The second method of measuring heat (by the rise in 
 temperature of a known mass of water) is, however, the 
 one which has been most universally adopted from the 
 time that calorimetry became a science. And, in this 
 matter, I suppose we must yield to custom. The choice 
 is an unfortunate one, for not only is the accurate 
 measurement of temperature one of the most difficult of 
 all measurements, but also the material selected, viz. 
 water, is capricious in its behaviour. 
 
 It must be remembered, however, that the true primary 
 unit is the heat-equivalent of 1 erg. 
 
 1 Physical Review, vm. 1899, pp. 2138. 
 
32 Measurement of Energy 
 
 We must therefore regard such units as secondary 
 ones, chosen simply for convenience ; j ust as, for example, 
 the ohm and the volt are arbitrary multiples of the 
 C.G.S. units of resistance and potential difference, so 
 the thermal unit, as ordinarily defined (viz. the quantity 
 of heat required to raise 1 gramme of water through 1 at 
 a certain temperature) is some multiple of the heat-equi- 
 valent of one erg. 
 
 The ratio of the ohm, or the volt, to the corresponding 
 C.G.S. unit is, however, unaffected by the properties of any 
 material substance ; whereas the ratio of this secondary 
 thermal unit to the primary one is dependent upon the 
 behaviour of a particular compound, and this dependence 
 has been a cause of difficulty and confusion. There is, I 
 am afraid, little hope of any change ; nevertheless I am 
 convinced that the only satisfactory method would be to 
 wipe the slate clean and start afresh. Let our secondary 
 unit of heat be the joule, or 10 7 ergs ; we should then give 
 the capacity for heat and latent heat of fusion etc. of a 
 substance as so many joules. This alteration in nomen- 
 clature would certainly tend to simplification, especially in 
 the study of steam-engines and other practical applications 
 of thermodynamics. 
 
 In the meantime we must take things as we find 
 them (or rather as the majority insists on regarding 
 them), and, therefore, try to determine the real value 
 of this secondary watery unit : in other words, how 
 many ergs will raise 1 grm. of water through 1 at a 
 certain temperature? 
 
 Here, of course, comes the question what is one 
 
Lecture II 33 
 
 degree of temperature ? If the whole of this course 
 of lectures was devoted to the reply the time would be all 
 too short. Let us put the question in a more practical 
 form and ask " How do we form a scale of temperature ?" 
 I would answer as follows : 
 
 We observe some property of a body (such as length, 
 pressure, electrical resistance, etc.) which undergoes altera- 
 tion with change of temperature. We then find the 
 condition of the body at two fixed, or recoverable, tempe- 
 ratures, and we make the assumption that at other 
 temperatures the change in the body is proportional 
 to the change in temperature. 
 
 Now, is there any case in which this assumption is 
 true ? If so, how are we to prove it ? 
 
 There is one test we can apply, which will tell us, at 
 all events, that the various scales thus obtained do not 
 agree and that, therefore, no two of them can be correct. 
 We have one fundamental definition of equality of tempe- 
 rature about which there can be no doubt, viz. if A and B 
 are at equal temperatures, then if A and B are placed in 
 contact their temperatures will not alter. 
 
 Suppose you observe the position of the mercury 
 in a glass thermometer, first in melting ice, and then 
 in steam at standard pressure. Make a mark half-way 
 between these two points. Now place this thermometer 
 in some water and change its temperature until the 
 mercury stands at this half-way mark. Repeat these 
 operations, using some other kind of matter, say a gas, 
 as the thermometric substance ; you will obtain two lots 
 of water whose temperatures are presumably equal, for, 
 G. 3 
 
34 Measurement of Energy 
 
 according to the scales thus formed, they are each half- 
 way between the temperatures of melting ice and steam. 
 Mix these two masses of water ; iu this case, where a gas 
 has been used as the second material, you will find that 
 the temperature of the first mass rises, while that of the 
 second falls ! How, therefore, can we find out which (if 
 any) of our various property-of- matter scales are true ? 
 What is the ideal scale to which all must be referred ? 
 
 It is one of the many claims which Lord Kelvin has 
 upon our gratitude that he was a leader amongst those 
 who furnished us with this ideal, or absolute scale. Most 
 of you are probably acquainted with that imaginary, but 
 nevertheless exceedingly useful piece of mental apparatus 
 named Carnot's engine. Although this fairy engine was 
 built of impossible substances aud based on wrong con- 
 ceptions as to the nature of heat, I doubt if many of our 
 existing engines have done more useful work, and I 
 would earnestly impress upon you the necessity, if you 
 wish to obtain a real grasp of thermodynamics, of study- 
 ing Carnot's cycle until you feel that you have fully 
 mastered it. 
 
 Time will not permit us to fully enter into this matter; 
 but I ask the forbearance of those who are already well 
 acquainted with this portion of our subject while I briefly 
 describe the nature and application of Carnot's engine ; 
 especially as I propose to present it to you in a somewhat 
 different form from that usually given in the text-books. 
 
 In an ordinary steam-engine we are confronted by 
 a complex problem ; details as to the nature of steam, 
 construction of valves, conductivities of substances, etc. 
 
Lecture II 
 
 35 
 
 distract the attention from the real essence of the matter. 
 Now, in Carnot's engine we get rid of all this, just as in 
 geometry we reason on the properties of straight lines, 
 without bothering our heads as to the effect of the 
 irregularities which in practice invariably present them- 
 selves. 
 
 ft 
 
 HOT TO COLD (ADIABATIO J 3 | 
 
 CLOSED 
 
 4 V COLD (ISOTHERMAL) 
 / (K. OPEN) 
 
 HOT (ISOTHERMAL) / 2 
 (L. OPEN) \ 
 
 Fig. 2. 
 
 Suppose the walls of this central vessel (V) to be con- 
 structed of a perfectly non-conducting (or adiabatic) 
 substance. Let the sides of this vessel come into contact, 
 on the right hand, with a perfectly conducting hot body 
 
 32 
 
36 Measurement of Energy 
 
 X, on the left with a perfectly conducting cold body F. 
 Let us, however, have the power of sliding away, by means 
 of the handles L and K, the adiabatic faces which prevent 
 any passage of heat to or from X and Y. It must be 
 understood that no work is done in removing or replacing 
 these adiabatic shutters, we simply issue a command and 
 they are gone. Further, they are shutters whose removal 
 allows the passage of heat only; not of &ny material which 
 is within the vessel V. 
 
 Thus, for example, remove K. Now the gas, or other 
 material within the vessel, is brought into thermal contact 
 with the cold body and we will suppose that it at once 
 assumes the same temperature ; but when K is replaced 
 the contents of V are uninfluenced by the presence of Y. 
 In the same manner, remove the shutter at L, the contents 
 are at once brought into contact with and assume the 
 temperature of the perfectly conducting hot body X ; 
 but in neither operation does any material leave, or 
 enter, V. 
 
 A tube (also formed of the adiabatic substance) is fitted 
 into the upper part of Fand closed by an adiabatic piston. 
 Suppose that we find K open and L shut, so that we know 
 that the contents of F are at the temperature of the cold 
 body ; close K and suppose that the piston then stands at 
 A. Now commence your cycle. Force the piston down- 
 wards; work is thus done on the contents and the 
 heat produced by this work will cause the temperature 
 within the vessel to rise. Let this continue until the 
 temperature within F is that of the hot body and let the 
 piston then be at B. Now, slide L away, and then allow 
 
Lecture II 37 
 
 the piston to rise ; work is done by the contents and heat 
 disappears, although the temperature is kept constant by 
 the transference of heat from X to F. Let this stroke 
 terminate at any position you please, say at C ; then close 
 L, and still further diminish the external pressure. As 
 the piston again rises, heat again disappears, but in this 
 case the temperature will fall. Allow this process to 
 continue until the contents arrive at the temperature of 
 the cold body. Let this happen when the piston is at D. 
 Now slide K away and force the piston downwards until 
 it is at its starting point A. Although work is thus 
 done on the system, the temperature of V is not increased, 
 as the heat generated passes into F. Finally close K. 
 We have now completed a cycle, for the material in F is 
 exactly in the same condition as regards quantity, tempe- 
 rature, pressure, and volume as when we started. The 
 total effect has been the removal of heat from the hot 
 body and the addition of some heat to the cold one, and 
 that without exposing the working substance in F to con- 
 tact with bodies at a different temperature from its own. 
 
 Let us consider the four steps. 
 
 (i) A to B | contents cold to hot, adiabatic. 
 
 (ii) B to C f ,, hot isothermal. 
 
 (iii) C to D f hot to cold, adiabatic. 
 
 (iv) D to A \ cold isothermal. 
 
 From this summary it is evident that the average 
 temperature (and therefore pressure) during the two 
 upward strokes (2nd and 3rd) is greater than during the 
 two downward ones (1st and 4th). Now as the lengths of 
 the total upward and downward movements are the same, 
 
38 Measurement of Energy 
 
 it follows that the total work done during the rising strokes 
 exceeds that done during the falling ones. Thus work has 
 been done by the system, while heat has been taken from 
 X and some heat passed into F. 
 
 If the working substance in F is a gas the relation 
 between the volume and pressure of the contents, at each 
 stage of the operations, can be represented diagram matically 
 as in Fig. 3. For example, the ordinates at A, B, C and D 
 are proportional to the pressures within V when the piston 
 was in the positions indicated by the same letters in 
 Fig. 2. 
 
 \ 
 
 .VOLUME 
 Fig. 3. 
 
 The quadrilateral figure ABCD 1 is bounded above and 
 below by isothermal, and at its sides by adiabatic, curves ; 
 
 1 The meaning of the dotted lines within the quadrilateral will be 
 explained in a subsequent lecture, for our present purposes they may be 
 disregarded. 
 
Lecture II 39 
 
 the enclosed area represents the excess of the work done 
 during the upward, over that done during the downward 
 strokes. 
 
 Now, if you consider the operations, you will find that, 
 by commencing with the piston at C (Fig. 2) and the 
 contents at the temperature of the hot body, it is possible 
 to complete the cycle by taking all the steps in reverse 
 order 1 . In this case, heat will be passed into the hot, 
 while some heat will be taken from, the cold body. Hence 
 the average pressure during the downward, will be greater 
 than that during the upward, strokes and work is done on, 
 instead of by, the working substance. 
 
 If you construct the corresponding diagram, you will 
 discover that the resulting quadrilateral figure is the same 
 as that obtained from the first or forward cycle. When 
 sketching it, however, your pencil will pass through any 
 point on its perimeter in the opposite direction to that 
 previously followed. Thus work has been done on, or by, 
 the working substance, according as we have travelled 
 round the work-space in the same, or the opposite, 
 direction to the hands of a clock. 
 
 Carnot, at the time he wrote his paper, considered 
 that this transference of heat from a high to a low 
 temperature was analogous to the falling of a given mass 
 of water from a high to a low elevation, and that the work 
 done in the transfer was not due to any consumption of 
 
 1 The operations are as follows : 
 
 (1) C to B | L open contents hot. 
 
 (2) B to A f shutters closed ,, hot to cold. 
 (8) A to D f K open cold. 
 
 (4) D to C | shutters closed ,, cold to hot. 
 
40 Measurement of Energy 
 
 the substance called caloric, but was simply performed by 
 it when sliding down a temperature gradient. We now 
 know that the heat delivered to F is less when the cycle 
 is completed than that taken from X, and the difference 
 is the heat-equivalent of the work done during the cycle. 
 Also, when we do work on the system during the reverse 
 cycle more heat will be given to X than was taken 
 
 f TZ j -f j.1. i_: Heat added to X , . 
 
 from F, and if the ratio : rr = =. during a 
 
 Heat taken from F 
 
 reversed cycle has the same value as the ratio 
 
 Heat taken from X , . . '. 
 
 , . . , TF- during the direct operation, 
 Heat added to F 
 
 we know that the engine is a perfect one and that it has 
 the highest possible theoretical efficiency. 
 
 This is a very important point in our argument, so let 
 us consider it more fully. Suppose it possible to obtain a 
 better engine, better in the sense that it converts into 
 work during a forward cycle a larger proportion of the 
 heat received from X than is thus converted by the 
 reversible engine. 
 
 Now let this better engine be so coupled up with the 
 reversible one that it works it backward, stroke for stroke. 
 The reversible engine will each time remove a larger 
 quantity of heat from F during its backward cycle than 
 the more efficient engine puts into F during a forward one. 
 Thus the quantity of heat in the hot body can remain 
 constant while the quantity in the cold must steadily 
 diminish. True, the compound engine thus formed will, 
 on the whole, do work ; but only by the transference of 
 heat from a colder to a hotter body. Now, this is contrary 
 
Lecture II 41 
 
 to all experimental evidence, for we have overwhelming 
 proof that, in no case, can work be accomplished by the 
 transference of heat from cold to hot bodies. Hence the 
 assumption that there can be a more efficient engine than 
 a reversible one leads to a conclusion which we believe to 
 be false. 
 
 Let us put the matter in another way. We have seen 
 that our imaginary compound engine will do work. Let 
 us use up this excess of energy by making it work 
 another reversible engine backwards. On the whole, the 
 system is now doing no work at all, and yet heat is being 
 steadily transferred from a colder to a hotter body. This 
 again is so against all experience that we are justified in 
 saying that it is impossible. 
 
 Hence a reversible engine must be the best of all 
 possible engines, arid, therefore, all reversible engines are 
 equally efficient. 
 
 Lord Kelvin, as far back as 1848, pointed out that we 
 here have a basis for a scale of temperature which is 
 independent of the properties of any form of matter. For 
 since all reversible engines have the same efficiency, that 
 efficiency must be independent of the nature of the 
 working substance, and depend only on the temperatures 
 of the hot and cold bodies. Now the efficiency is the 
 ratio of the work done to the heat taken in, and the 
 work done must, by the Principle of the Conservation of 
 Energy, be equivalent to the difference between the 
 quantity of heat taken in (Qi) and that given out 
 
 Thus the ratio ~ must also depend only upon the 
 
42 Measurement of Energy 
 
 temperatures of the two bodies. We can, therefore, 
 define the ratio between the temperatures of those two 
 
 bodies as the ratio -^. It remains to be seen, however, 
 
 Va 
 
 if there is any close relation between the scale resulting 
 from this definition and the property-of-matter scales in 
 ordinary use. 
 
 One interesting and important consequence of this 
 method of measuring temperature is that it leads naturally 
 to the idea of a body containing no heat whatever, and 
 the temperature of which, therefore, must be the lowest 
 possible temperature. 
 
 For, suppose our reversible engine to deliver during a 
 forward cycle no heat at all to Y. Here the ratio 
 
 Heat taken from X . . . 
 
 -^r : ^r- becomes infinite and thus, 
 
 Heat given to Y 
 
 temperature of X 
 temperature of Y ~ 
 
 This is only possible under the given conditions, when 
 temperature of Y is zero. Thus not only the relative 
 values of any two temperatures, but also the zero point, 
 are defined for us on the absolute scale in a manner 
 independent of all properties of matter. 
 
 In arriving at these conclusions no assumption has 
 been made as to the size of the degrees on this scale. We 
 may, therefore, choose any arbitrary value we please. 
 If we prefer to call the difference between the temperature 
 of steam under standard pressure and that of melting 
 ice 100, we can find how many of such degrees lie 
 
Lecture II 43 
 
 between freezing point and absolute zero. Suppose this 
 number to be T then 
 
 Absolute temperature of boiling point _ T -\- 100 _ Q l 
 Absolute temperature of freezing point T Q 2 
 
 where ft is the heat taken in, and Q. 2 the heat given out 
 by a reversible engine working between standard boiling 
 and freezing points of water. 
 
 Now, if we assume as the working substance a perfect 
 or ideal gas, viz. one which obeys Boyle's Law at all 
 temperatures, we can show that the value of this ratio 
 
 ft. . ,373 2 T +100 373 
 
 ' 
 
 ft 1S 
 
 thus T= 273 (more accurately 273'7). 
 
 Hence a body at - 273 G '7 C. is the coldest body 
 possible. 
 
 Remember that this conclusion is based on the 
 behaviour of an ideal gas, and it remains to be seen 
 how far the gases we are acquainted with fulfil the 
 above conditions. 
 
 I must not go into details of the comparisons that 
 have been made ; it is sufficient to say that the tempera- 
 ture-scale most closely in agreement with the absolute 
 one, is that obtained by assuming that the pressure of a 
 gas, such as hydrogen, is, at constant volume proportional 
 to its temperature. 
 
 Scales thus constructed differ slightly according to 
 the nature of the gas ; hence the phrases hydrogen scale, 
 nitrogen scale, etc. We may, however, consider it as 
 
44 Measurement of Energy 
 
 established that when the gas is hydrogen the resulting 
 scale differs so slightly from the absolute one at ordinary 
 temperatures that it is sufficiently accurate for our pur- 
 pose 1 . (For example, the absolute zero on this scale is 
 at - 273'13.) 
 
 From what has been said, it appears that our de- 
 finition of the C.G.S. primary unit must be as follows : 
 
 "If a reversible engine does 1 erg of work during a 
 forward cycle when the temperature difference between 
 the hot and the cold bodies is 1 of the absolute scale, 
 then the primary thermal unit is the excess of the heat 
 received over that ejected." 
 
 True, the unit thus indicated is a very small one : it 
 would only raise the temperature of 1 gramme of water 
 by about -^ millionth of a degree. Fortunately, however, 
 the usefulness of a thing is not proportional to its size 
 (remember for example that the C.G.S. unit of potential 
 
 difference is but ^ of a volt). 
 
 It is now necessary to determine the value of our 
 secondary watery-unit in terms of this primary one. 
 
 Our definition of this unit will be, "The number of 
 primary units (or ergs) required to raise 1 grm. of water 
 through 1 of the constant volume hydrogen thermometer 
 at a fixed temperature on that thermometer." 
 
 Now, how is this number to be accurately ascertained ? 
 The first practical question is " in what way are we going 
 to measure this 1 rise in temperature ?" It is very easy 
 
 1 See Report of Electrical Standards Committee, Appendix I., B. A., 
 
 1897. 
 
Lecture II 45 
 
 to talk about finding it by means of a gas thermometer ; 
 but that is a most difficult instrument to use. I know of 
 no physical apparatus which is so simple in theory, but so 
 appallingly difficult in practice. A rough approximation is 
 very easily obtained by means of it, but if the idea is to 
 secure an accuracy of say T 0^th of a degree, the under- 
 taking is a very serious one. Its direct employment 
 in experimental work is rarely feasible, and the only 
 course is to standardise a mercury, or other thermometer 
 by comparisons with it, conducted under the most favour- 
 able circumstances, and then use that thermometer for 
 the experimental work. 
 
 Even when a comparison with the hydrogen scale has 
 been satisfactorily accomplished (and such cases are rare) 
 sufficient allowance has often not been made for the 
 erratic behaviour of all in ere ury-in -glass thermometers. 
 
 Our knowledge of the peculiarities of mercury thermo- 
 meters has, in recent years, been greatly increased. The 
 investigations of MM. Guillaume, Chappuis, and Fernet 
 have not only indicated causes of error hitherto un- 
 suspected, but have also given us methods of observation 
 and correction by which it is possible to eliminate the 
 effects of such errors. The determination of a single 
 temperature by a mercury-in-glass thermometer is, how- 
 ever, a complicated and laborious one at the best. The 
 following table is an example of such a determination 1 
 and it will be seen that some of the operations are of a 
 kind that it would be difficult to carry out under ordinary 
 circumstances. 
 
 1 Phil. Trans. Roy. Soc. t Vol. 184, p. 429. 
 
46 Measurement of Energy 
 
 Temperature reading by thermometer P. 
 
 Zero point 
 
 millims. millims. 
 
 Barometer (corrected) 754'1 7541 
 
 Water pressure (in terms of mercury) ... 121 4 -4 
 
 Total external pressure 766*2 758-5 
 
 Observed reading 14*025 - -Q36 
 
 Calibration correction -'026 
 
 External pressure correction - '001 
 
 Internal +'026 + -008 
 
 Zero + 028^ -Q28 
 
 Fundamental error correction -'006 
 
 Sum corrections 4- '021 
 
 Correction for stem temperature . . - -002 
 Hence reading on mercury scale... =14'044 
 Correction to H scale - -067 ; to N scale - -059. 
 
 Hence temperature is 
 
 Hydrogen scale. Nitrogen scale. 
 
 13-977 13-985 
 
 The observations here recorded were made with a 
 Tonnelot hard-glass thermometer. Had one of our 
 ordinary English soft-glass thermometers been used, 
 many of the corrections would have been larger and also 
 more uncertain than those given in this Table. 
 
 If you reflect on all the preliminary labour which had 
 to be accomplished before it was possible to apply these 
 corrections, as for example in the standardisation, cali- 
 bration, determination of the coefficients for changes in 
 the internal and external pressures, the comparison with 
 the gas scales, etc., I think you will admit that the 
 popular belief in the simplicity and accuracy of the 
 
Lecture II 47 
 
 mercury-in-glass thermometer is based . on ignorance 
 rather than on knowledge. 
 
 The want of sufficient appreciation of these experi- 
 mental difficulties has rendered useless much work that 
 would otherwise have been of the greatest value. 
 
 Investigators seeking the value of the mechanical 
 equivalent have taken elaborate precautions as regards 
 the direct measurement of the work done, whereas they 
 have paid too little attention to their thermometric 
 standardisations and corrections. Even such masters as 
 Joule and Rowland have erred in their thermometry to 
 an extent which has seriously affected the accuracy of 
 their conclusions. 
 
 In recent years a valuable weapon has been placed in 
 our hands, viz. the platinum-resistance thermometer. 
 
 The change in the electrical resistance of a platinum 
 wire, due to changes in temperature, is a quantity which 
 can be determined with a high degree of accuracy, and 
 although the resulting scale departs as largely from the 
 hydrogen scale as does that of the mercury thermometer, 
 the platinum thermometer has certain marked advan- 
 tages. It is not erratic in its behaviour, its readings 
 are more constant under varying conditions, and, by 
 suitable arrangements, it renders evident much smaller 
 temperature differences than could be determined by 
 other methods. Hence, if the relation between the 
 increase in electrical resistance of the platinum wire 
 and the increase in temperature on the true temperature- 
 scale has been accurately ascertained, the precision of 
 temperature determinations obtained by the use of 
 
48 Measurement of Energy 
 
 platinum thermometers exceeds, in my opinion, that 
 obtainable by any other method ; at all events at ordinary 
 temperatures. 
 
 I have thought it necessary to dwell, at some length, 
 upon this matter of the practical determination of 
 temperature, as I propose, when discussing the values 
 of the mechanical equivalent obtained by different ob- 
 servers, to attach great weight to the more recent 
 determinations. Although, in some cases, the measure- 
 ments of the work expended may be less satisfactory than 
 in earlier experiments, the thermal measurements are of 
 a higher order of accuracy. 
 
 In my first lecture I endeavoured to show you that 
 it was a comparatively easy matter to completely convert 
 any form of energy into heat. 
 
 To-day our enquiry into the meaning of the phrase 
 'a temperature scale' has led us to very important 
 conclusions concerning the reverse process. We have seen 
 that it is only possible to convert heat into mechanical 
 work provided that we can obtain bodies at different 
 temperatures, and further, that the fraction of the heat 
 supply which can be thus converted is dependent on the 
 temperature-difference. In other words, if we have a 
 source of heat at temperature 6 on the absolute scale and 
 a condenser, or sink, at temperature t ; then if we have a 
 perfect engine at our disposal the maximum amount of 
 heat we can utilise when any quantity of heat Qi is taken 
 
 Q j. 
 
 from the source, is x Q^ 
 
 V 
 
 It is seldom that the difference of temperature between 
 
Lecture II 49 
 
 the source and condenser of our steam-engines is as much 
 as 120 C.; thus a perfect engine could only, under such 
 circumstances, utilize less than J of the heat passed into 
 it. I shall show you in my last lecture that, unless 
 we can discover perfectly conducting materials as well as 
 perfect non-conductors, it is certain that no real engine 
 can approach to the efficiency of a reversible one. Thus, 
 in practice, our engines transform into mechanical work 
 but a very small fraction of the heat-energy which they 
 receive. 
 
 In the phrase " mechanical equivalent" therefore, the 
 meaning of the word "equivalent" is restricted to a 
 numerical relation only. 
 
 If we say that 1400 ft.-lbs. are equivalent to 1 thermal 
 unit, it does not follow that you would as soon have the 
 one as the other. It is probable that you could make 
 some profitable use of the 1400 ft.-lbs.; but it is only 
 under exceptional circumstances that you could do 
 anything whatever with your thermal unit. 
 
 I have here an apparatus which is probably the 
 simplest form of heat-converting engine yet constructed. 
 It more nearly resembles Carnot's engine in its action 
 than any other engine I know ; but, at the same time, 
 the differences are vital, and I am afraid the efficiency of 
 this engine is but a small fraction of that of a reversible 
 one. At the same time, we have here no valves and the 
 contents are in the same condition after, as before, a cycle; 
 only, unfortunately, those contents have been constantly 
 in contact with conducting bodies at different tempera- 
 G. 4 
 
50 Measurement of Energy 
 
 tures and, therefore, it would be of no use to compare the 
 quantities of heat received and ejected, even if we were 
 able to do so. 
 
 Fig. 4. 
 
 The .apparatus consists of a large U tube partially 
 filled with mercury. A perforated cork is inserted at 
 one end of this tube and the neck of a glass bulb passes 
 through the cork. Thus, when the surface of the mercury 
 at A descends, some of the air in the bulb passes into the 
 upper part of the U tube, and vice versa. If the flame of 
 a Bunsen burner be now placed beneath the bulb, the 
 column of mercury begins to oscillate, the amplitude of 
 the oscillations being considerable 1 , and although the 
 
 1 In the apparatus shown at Leeds the amplitude of the oscillations 
 was about 8 cm. 
 
Lecture II 
 
 51 
 
 centre of gravity of the mercury is not permanently 
 raised, it is obvious that work must be done in main- 
 taining this oscillation against the frictional resistance 1 . 
 As the mercury passes down from B to C the space 
 thus vacated is filled by hot air from the bulb. This 
 air is cooled both by the work it has done and by 
 the contact with the cold surfaces in the tube. As the 
 
 v 
 
 Fig. 5. 
 
 mercury rises from G to B this air, whose temperature 
 will now have been considerably reduced, is passing back 
 into the bulb. Hence we see that the average tempera- 
 ture and, therefore, the average pressure of the air is 
 greater during the descent than during the ascent of the 
 mercury in the closed limb. Hence in a complete cycle 
 
 1 An oscillation of this kind was observed some years ago by 
 Mr A. Vernon Harcourt when passing electric sparks through a mixture 
 of hydrogen and nitrogen confined above a column of mercury. At first 
 he attributed the effect to an explosive action, but further experiments 
 proved that the movement was maintained when other gases were used 
 and the heat applied externally. 
 
 42 
 
52 Measurement of Energy 
 
 t 
 
 more work is done on the mercury as it is forced from 
 B to C than it does upon the gas during its return, and 
 therefore the movement can be kept up in spite of 
 friction, etc.; the indicator diagram being probably some- 
 what of the type shown in Fig. 5. 
 
 The oscillation can only continue so long as the 
 temperature of the bulb exceeds that of the tube. The 
 movement of the contained air during each stroke tends 
 to diminish this difference and, therefore, the motion 
 would soon cease, but for the constant loss of heat by 
 conduction and radiation from the tube, and the gain of 
 heat by the bulb. 
 
 The action of hot-air engines is of the same nature, 
 although it is obscured by the many moving pieces. 
 Considering the small difference in temperature that 
 must exist after they have been running for a con- 
 siderable time, the power developed by such engines 
 is surprisingly great. 
 
 I am afraid that to-day's lecture may, to some of those 
 present, have appeared a needless repetition of truths 
 already known and appreciated. I have, nevertheless, 
 ventured to inflict it upon you, for I believe that the 
 difficulties of temperature measurements are, as a rule, 
 greatly underestimated. Whatever views we may hold 
 regarding those difficulties, it is, however, impossible to 
 deny the importance of this subject when we reflect 
 on the number of physical constants whose accurate 
 determination is dependent upon the measurement of 
 temperature. 
 
Lecture II 53 
 
 NOTE. At the close of this lecture two rough experimental 
 determinations of the ' mechanical equivalent' were performed as 
 an introduction to the methods of the observers whose work I pro- 
 posed to discuss during the following lecture. I have in Appendix II. 
 given an account of those experiments in the hope that it may be 
 found useful by teachers, although neither the apparatus nor the 
 methods present any specially novel features. 
 
LECTURE III. 
 
 Table of values of J obtained by different observers. Direct and 
 Indirect Methods of Measurement. Principles which should 
 guide us when making a selection. Brief descriptions of the 
 Methods of Joule, Hirn, Eowland, Keynolds and Moorby, 
 Griffiths, Schuster and Gannon, Callendar and Barnes. Table 
 of Results. 
 
 IN my first Lecture I called your attention to the 
 transformation of various forms of energy into heat, a 
 process involving what is commonly called degradation 
 of energy. In the second Lecture our enquiry as to 
 the nature of a temperature scale led to the consideration 
 of the converse operation, a transformation involving what 
 we may term elevation of energy. 
 
 We found that the process of degradation could be 
 accomplished with comparative ease; whereas, at all 
 events under the conditions holding on our earth, the 
 process of elevation is one which presents peculiar diffi- 
 culties. 
 
 Now, unfortunately, or possibly fortunately (for the 
 sight of brave men struggling with adversity is grateful 
 to the Gods), it is the transmutation from the lower to 
 the more exalted forms of energy which almost entirely 
 engages the attention of our engineers. 
 
Lecture III 55 
 
 The physicist, however, is not hampered by the 
 conditions which bind the engineer; hence, in the de- 
 terminations of the mechanical equivalent, he has, in 
 general, trodden the downward path. 
 
 The experimental investigations may be placed under 
 two headings, Firstly those in which the thermal effect 
 is directly produced by the expenditure of mechanical 
 work, and secondly where it is due to the expenditure 
 of energy other than mechanical. In the latter case it is 
 necessary that the numerical value of this energy should 
 already be known in dynamical units ; - as, for example, 
 where the work is done by means of an electric current. 
 The first may be termed the direct, and the second the 
 indirect method. 
 
 The direct method naturally carries greater weight 
 when our one object is the determination of the numerical 
 constant giving the relation between work done and 
 equivalent heat ; but the indirect methods are also of 
 high importance, for they enable us to test the accuracy 
 of various physical standards, such as electrical resistance 
 etc., and also to express all forms of energy in terms of a 
 common denominator. 
 
 Tables I. and II. are (with the exception of the results 
 of experiments completed since 1893) taken from Preston's 
 Theory of Heat, and I believe they contain all the deter- 
 minations that have any pretensions to accuracy. 
 
 Unfortunately the values in this table are all given in 
 kilogramme-metres, and therefore no exact comparison 
 between them is possible unless the value of g is known 
 at each place where the observations were conducted ; for 
 
56 
 
 Measurement of Energy 
 
 TABLE I. (DIRECT METHODS.) 
 
 Date 
 1843 
 
 1845 
 
 1847 
 1850 
 
 1857 
 
 1858 
 
 1860-61 
 
 1865 
 1870 
 
 1875 
 1878 
 
 Observer 
 Joule 
 
 Favre 
 
 Him 
 
 jj 
 Favre 
 
 Him 
 
 Edlund 
 Violle 
 
 Puluj 
 Joule 
 
 Method 
 
 Besult 
 
 Friction of water in tubes . . . 424*6 km. 
 Electromagnetic currents ... 460 
 Decrease of heat produced by a 
 pile when the current does 
 
 work 442*2 
 
 Compression of air 443*8 
 
 Expansion of air 437*8 
 
 Friction of water in a calorimeter 488*3 
 
 428*9 
 
 11 55 11 11 
 
 Friction of mercury in a calo- 
 rimeter 
 
 Friction of iron plates in a 
 calorimeter 
 
 Decrease of heat produced by 
 a pile doing work ... 
 
 Friction of metals 
 
 423*9 
 424*7 
 425*2 
 
 424*464 
 
 371*6 
 
 400*450 
 
 Friction of metals in mercury 
 
 calorimeter ... ... ... 413*2 
 
 Boring of metals 425 
 
 Water in friction balance ... 432 
 Escape of liquids under high 
 
 pressure 432, 433 
 
 Hammering lead 425 
 
 Friction of water in two cylinders 432 
 
 Expansion of air 440 
 
 Steam-engines 420*432 
 
 Expansion and contraction of 
 
 metals 428*3,443*6 
 
 Heating of a disc between the 
 
 poles of a magnet 435 
 
 Friction of metals 425*2,426*6 
 
 Friction of water ... 423*9 
 
Lecture III 
 
 57 
 
 TABLE I. (continued}. 
 
 Date Observer Method Kesult 
 
 1878 Rowland Friction of water between 5 
 
 and 36 429'8, 425 -8 
 
 1891 D'Arsonval Heating of a cylinder in a 
 
 magnetic field 421 '427 
 
 1892 Miculescu Friction of water 426*84 
 
 1897 Reynolds and ,, Meancapa- 
 
 Moorby city to 100 426*27 
 
 TABLE II. (INDIRECT METHODS.) 
 
 Date 
 1842 
 
 1857 
 
 1859 
 
 1867 
 
 1878 
 
 Observer 
 Mayer 
 
 Quintus 
 
 Icilius 
 Weber 
 Favre } 
 Silbermaiij 
 Bosscha 
 
 Joule 
 Bosscha 
 Lenz- Weber 
 
 Joule 
 Weber 
 
 1888 Perot 
 
 Method 
 By the relation of J 
 
 for 
 
 Result 
 
 365 km 
 
 gases 
 Heat developed in a wire of known 
 
 resistance ......... 399*7 
 
 Heat due to electric currents ... 432-1 
 Heat developed by zinc on sulphate 
 
 of copper ......... 432'1 
 
 Measure of E.M.F. of a Daniell's 
 
 cell ............ 432*1 
 
 Heat developed in a Daniell's cell 419'5 
 E.M.F. of a Daniell's cell ... 419'5 
 Heat developed in wire of known 
 
 resistance ......... 396-4,478-2 
 
 429-5 
 
 428-15 
 
 By the relation L = r(v 2 - 
 Heat of electric currents 
 
 dt 
 
 424-63 
 
 1889 Dieterici Heat of electric currents ... 432*5 
 
 1893 Griffiths ... 427*45 
 
 1894 Schuster and Electric current, E. & C. being 
 
 Gannon known 427*19 
 
 1899 Callendarand 426*52 
 Barnes 
 
58 Measurement of Energy 
 
 I find by one or two reductions that they have not been 
 corrected to a common latitude. If the English ones 
 are multiplied by 981'24 x 100, and the French by 
 980*94 x 100, the result will give the value in ergs with a 
 sufficiently close approximation for the purposes of a 
 rough comparison, for it must be remembered that the 
 temperature scales differ considerably, as also the mean 
 temperature of the temperature range. 
 
 In these tables the values vary from 365 to 488 kms. ; 
 how then are we to decide which to select ? 
 
 There are some would-be physicists who apparently 
 believe that if you obtain a sufficient number of observa- 
 tions and find the mean (especially if you apply the 
 method of least squares) you will probably be about right. 
 I do not see, however, that there would be any advantage 
 in following this course where we have to deal with such 
 divergent results as these. It should ever be remembered 
 that a few good experiments are probably better than the 
 mean of one hundred faulty ones, for it is quite possible 
 that the errors of all the faulty ones are in the same 
 direction. 
 
 To assist us in making a selection, I propose to ask 
 the following questions : 
 
 (1) Are the temperature determinations sufficiently 
 accurate ? 
 
 The answer will lead to wholesale rejection, especially 
 in the earlier experiments. 
 
 As I have previously indicated, the difficulty and 
 importance of temperature measurements were not suf- 
 ficiently appreciated until within very recent times, and, 
 
Lecture III 59 
 
 unfortunately, an error in thermometry is, as a rule, 
 a fatal one ; for each thermometer has its own peculiarities 
 and special causes of error; thus, no later increase in 
 knowledge enables us to correct results unless the actual 
 thermometers have been preserved and the conditions, 
 under which they were used, fully recorded. 
 
 Fortunately in two of the most important cases (viz. 
 Joule's and Rowland's) the thermometers actually used 
 have been preserved. 
 
 In the former, however, our information is not complete 
 for we are not sufficiently acquainted with the exact 
 conditions under which their readings were observed by 
 Joule. In the latter, a restandardisation has been ac- 
 complished under Rowland's own direction, and thus the 
 corrections can here be applied with far greater certainty. 
 In both cases, as I shall show you later, the results as 
 originally published have, in consequence, undergone 
 considerable modification. 
 
 (2) Has the author given us sufficient data to enable 
 us to judge the probable accuracy of all the various 
 measurements involved by his method of experiment ? 
 
 In this respect, also, the earlier determinations are at 
 a disadvantage, as compared with the later ones, for the 
 importance of full information concerning the details of 
 physical measurement has only been generally recognised 
 in recent times. 
 
 (3) Are we certain that the energy of the bodies 
 under observation has undergone no modification during 
 the experiment in consequence of molecular changes ? 
 
 If we could accurately determine both the kinetic 
 
60 Measurement of Energy 
 
 energy expended in hammering a nail and, also, the heat 
 developed, it is not certain that the resulting value of the 
 constant would be correct; for the condition as regards 
 density, strain, &c. of the nail (and possibly of the hammer- 
 head) might have undergone alteration and, in con- 
 sequence of new molecular conditions, have gained, or lost, 
 in energy. 
 
 Now, we know that no permanent shearing strain can 
 exist in a fluid, and if the external pressure is unaltered, 
 the density will have undergone no change except that 
 due to change of temperature. Hence, conclusions drawn 
 from observation of work expended in heating a liquid are, 
 cceteris paribus, of leading importance. 
 
 I will not trouble you with further details of the 
 considerations which have led to the selection of the 
 experiments which I am about to discuss. Suffice it 
 to say that a careful study of the writings of most of those 
 authors who are mentioned in these tables has led to the 
 selection from table I. of the work of Joule, Rowland, 
 and Reynolds and Moorby, and from table II. the 
 determinations of Griffiths, Schuster and Gannon, and 
 Callendar and Barnes 1 . 
 
 I believe that the results obtained by Rowland, after 
 the revision of his thermometry, should be considered 
 as of leading importance in the estimation of the 
 
 1 Those who may wish to obtain information concerning the work of 
 the other observers mentioned in Tables I. and II. should consult the 
 summary given by Prof. Ames in the Rapports presentes au Congres 
 International de Physique, Paris, 1900, Tome i. 
 
 In my criticisms on the works of the above authors I have ventured 
 to quote largely from this excellent Eeport. 
 
Lecture III 61 
 
 numerical value of the constant; while the indirect 
 methods of Griffiths, and above all of Callendar and 
 Barnes enable us to trace the changes in the capacity for 
 heat of water and thus render it possible to make a com- 
 parison of the values obtained by the different observers 
 in terms of the constant primary unit. I propose, there- 
 fore, to consider in some detail the determinations I 
 have mentioned and also, for special reasons, the work 
 of Him. 
 
 JOULE \ The form of apparatus first used by Joule 
 (in which the descent of a weight caused the rotation of 
 a paddle) is the one ordinarily given in the text-books 
 and is, I am sure, familiar to all. 
 
 Now, text-books are curious things. If a description 
 of a piece of apparatus, or the value of any natural 
 constant once appears in any text- book, it is apparently 
 a law that it should continue to appear in all text-books 
 for the remainder of time. Thus the apparatus used by 
 Joule in 1845-7 is almost invariably presented to us, 
 while the improved type used by him for his later, and 
 more accurate, work is generally ignored. 
 
 The method finally adopted by Joule consisted in stir- 
 ring water by means of a paddle which was rapidly turned 
 by hand-wheels, shown at d and e (Fig. 6) ; the vessel 
 was suspended by a vertical shaft 6, which also carried ' a 
 large fly-wheel /. The mass of the water and the water- 
 equivalent of the calorimeter were carefully determined, 
 the rise in temperature was noted on a mercury-in-glass 
 
 1 Scientific Papers, vol. i. pp. 632657. 
 
62 
 
 Measurement of Energy 
 
 thermometer, and the work consumed in heating the water 
 was measured by a dynamometer, which consisted of an 
 arrangement for balancing the moment acting on the 
 suspended calorimeter (owing to the revolution of the 
 paddle) by a moment produced by the tension of the 
 
 Fig. 6. 
 
 cords fastened tangentially to the calorimeter. The cords 
 passed over pulleys and supported weights k. If this 
 moment is constant and is called M, and if the number 
 
Lecture III 63 
 
 of revolutions per second of the paddle is N, the work 
 done per second is ZirMN. 
 
 In order to reduce the metallic friction as far as 
 possible, the base of the calorimeter rested on a hydraulic 
 supporter, which consisted of two concentric vessels v and 
 w, the space between them being filled with water. The 
 three uprights attached to w pressed against the base of 
 the calorimeter and reduced the pressure on the bearing 
 at o nearly to zero. 
 
 Joule's calorimeter had a water equivalent of 313*7 
 grammes of water at 15'5C. ; the mass of water used in 
 an experiment was about 5124 grammes, each experiment 
 lasted 41 minutes and the observed rise in temperature 
 was about 2'8C. The mean of his results gave 772*65 
 foot-pounds at Manchester, as the quantity of work 
 required to raise the temperature of one pound of water 
 1 degree F. on his mercury-in-glass scale at 61*69 F. 
 Changing to the centigrade scale and to the C.G.S. system, 
 Joule's result may be stated as follows : the quantity of 
 work required to raise the temperature of 1 gramme 
 of water 1 degree centigrade on his mercury-in-glass 
 thermometer at 16'5 is 4'167 x 10 7 ergs. 
 
 In 1895 Professor Schuster 1 compared Joule's thermo- 
 meter with a Tonnelot thermometer which had been 
 standardised in terms of the nitrogen thermometer of 
 the Bureau International at Sevres; and in this way 
 was able to recalculate Joule's value for the mechanical 
 equivalent. Rowland also, when reviewing this experi- 
 ment of Joule's, called attention to certain errors in the 
 1 Phil. Mag. xxxix. pp. 477506. 1895. 
 
64 Measurement of Energy 
 
 determination of the water-equivalent of the calorimeter, 
 whose value had, in consequence, been underestimated by 
 nearly 1 part in 1000. The corrected result is given by 
 Schuster as follows : the specific heat of water at 16'5 C. 
 Paris nitrogen scale is 4'173 x 10 7 ergs. 
 
 This value differs by 1 part in 400 from determi- 
 nations made by Rowland and others. In fact the thirty- 
 five observations from which Joule calculated his final 
 value give results which differ by more than 1 per cent, 
 from each other, and his thermometer did not permit the 
 most accurate reading of temperature. The cause of these 
 discrepancies is to be found in three conditions of the 
 experiment : irregularity of the stirring, which was done 
 by hand, incomplete correction for loss of heat by radiation, 
 and insufficient knowledge of the variations in the readings 
 of mercury-in-glass thermometers caused by variations 
 in the conditions under which they are used and 
 standardised. 
 
 Let us now on account of its intrinsic interest consider 
 briefly the work of HiRN 1 . I may say at once that it is 
 impossible to attach any importance to his numerical 
 results. His thermometry was far too vague and his 
 energy-measurements were also not of the highest ac- 
 curacy. Nevertheless, his work is important; because, 
 not only was his method of degrading energy entirely 
 different from that of Joule but he also endeavoured to 
 obtain the value of the equivalent by the reverse process, 
 that is by measuring the disappearance of heat from a 
 1 Theorie Mecanique de la Chaleur. 
 
Lecture III 65 
 
 system performing work ; a feat, I believe, only seriously 
 attempted by Hirn. The method he adopted in the 
 degradation process was as follows : 
 
 Fig. 7. 
 
 A cylinder of iron AA (Fig. 7), weighing 350 kilos, 
 was suspended by two pairs of cords which compelled 
 it to move in a vertical plane with its axis always 
 horizontal. This cylinder was used as the hammer or 
 instrument of percussion. The anvil MB was a large 
 prismatic mass of stone weighing 941 kilos, and sus- 
 pended in the same way as the hammer. The mass of 
 lead D to be operated on was suspended between the two, 
 and the face B of the anvil adjacent to the lead was cased 
 with iron to receive the blow. In making an experiment 
 the hammer was drawn back by a tackle, and the height 
 to which it was raised was accurately measured. It was 
 then let fall upon the lead, and the recoil of the anvil was 
 registered by a sliding indicator which was pushed back 
 and then remained in situ. An observer also noted the 
 advance or recoil of the hammer after the blow, and from 
 G. 5 
 
66 Measurement of Energy 
 
 these data the work spent in percussion could easily be 
 calculated, as the difference between the kinetic energy of 
 the system before and after impact was known. Before the 
 blow was delivered, the temperature of the lead was taken 
 by inserting a thermometer t into a cylindrical cavity 
 made in the mass, and immediately after the blow the 
 mass of lead was removed and hung up by two strings 
 provided for the purpose, so that the axis of the cavity 
 was vertical. This cavity was immediately filled with 
 ice-cold water, which was stirred and the rise of tempera- 
 ture noted. The value 425 kgs. was obtained by Hirn in 
 this manner, which is remarkably good considering the 
 nature of the experiment. 
 
 His more interesting enquiry, however, was an attempt 
 to determine the difference between the heat conveyed 
 from the boiler to the condenser of an ordinary steam- 
 engine when running first with a heavy, and afterwards 
 with a light load. 
 
 After making allowance for the heat lost by radiation, 
 conduction, etc. he proved that the difference was much 
 greater when the engine was performing heavy external 
 work than when it was running with no load. 
 
 " Hirn also pushed the experimental enquiry further, 
 and actually deduced a fair estimate of the dynamical 
 equivalent of heat from the observations of the work 
 done by the engine, and the quantity of heat used up in 
 performing it. The work performed in any time can be 
 deduced from the area of the Watt's indicator diagram, 
 and the number of strokes of the piston. To determine 
 the quantity of heat converted into work, the weight of 
 
Lecture III 67 
 
 water that passes from the boiler to the condenser must 
 be estimated. Knowing the latent heat of vaporisation 
 at the temperature of the boiler, the quantity of heat Q 
 drawn from the boiler in any time becomes known. But 
 this quantity is not all converted into work. Part of it 
 q is carried into the condenser, and a part R is lost by 
 radiation in the transit. Hence the quantity of heat 
 converted into work is Q q R, and the value of J is 
 found from the equation 
 
 W = J(Q-q-R). 
 
 " By this means Hirn obtained the numbers 413 and 
 420'4 (gramme-metres), which, considering the difficulty 
 of the investigation, must be regarded as exceedingly 
 good approximations 1 ." 
 
 These results are extremely interesting ; but, as I said 
 before, I do not propose to include the actual numerical 
 values in our final table. 
 
 I now pass to what is undoubtedly the most important 
 determination of all, namely, ROWLAND'S 2 . 
 
 In the years 1878 and 1879 Professor Rowland of the 
 Johns Hopkins University, Baltimore, performed a series 
 of experiments for the determination of the specific heat 
 of water at different temperatures. His method was in 
 principle the same as that of Joule, although devised 
 independently. 
 
 By means of a petroleum engine, a specially designed 
 paddle-wheel was turned at a rapid rate (200 to 250 
 
 1 Preston's Theory of Heat, p. 47. 
 
 2 Proc. American Academy, No. 188081. 
 
 52 
 
68 
 
 Measurement of Energy 
 
 Fig. 8. a, 6 is a vertical shaft supporting calorimeter and suspended by 
 a torsion wire. 
 
 Axis of paddle passed through base of calorimeter and was 
 connected with shaft e, /, which was kept in uniform rotation by the 
 driving engine. 
 
 o andp, weights attached to silk tapes passing round wheel k, I, 
 the couple acting on calorimeter being thus measured (corrections 
 being applied for the torsion of the suspending wire). The moment of 
 inertia could be varied by means of the weights q and r. A water- 
 jacket, u, t, surrounded the calorimeter and was used for the estima- 
 tion of the radiation. 
 
Lecture III 69 
 
 revolutions per minute) in a calorimeter which was 
 suspended by a wire and which was prevented from 
 turning, when the paddle was revolving, by means of a 
 moment applied by weights. The water equivalent of 
 the calorimeter was 347 grammes, and the rise in 
 temperature was about 0'6 C. per minute, and was 
 observed on different m ere ury-in-g lass thermometers. 
 These thermometers had all been compared with a 
 constant volume air-thermometer, and the readings were 
 all finally reduced to the "absolute scale"; the results 
 of Thomson and Joule's experiments on the expansion 
 of air through a porous plug being used to make the 
 necessary corrections to the air-thermometer temperatures. 
 While the temperature was rising through any range, 
 e.g. from 8 to 30 C., readings were made on all the 
 instruments for each degree or half degree, and in 
 this way any one experiment gave a great number of 
 determinations of the capacity for heat. The work was 
 calculated for 10 intervals, and one-tenth of that re- 
 quired to raise the temperature of one gramme of water 
 from (t 5) to (t + 5) was called the specific heat at t C. 
 All corrections for losses due to radiation, variations in 
 speed of paddle, &c., were carefully considered and made. 
 
 Rowland's method of using his mercury thermometers 
 was different from that which has been universally adopted 
 within the past few years owing to the efforts of Prof. 
 Fernet of Zurich, and of MM. Chappuis and Guillaume 
 of the Bureau International, and the scale of his air- 
 thermometer in terms of other thermometers used by later 
 observers was not known. In 1897, therefore, a series 
 
70 
 
 Measurement of Energy 
 
 of comparisons was undertaken at the Johns Hopkins 
 University between Rowland's thermometers, three Ton- 
 nelot mercury thermometers standardised at the Bureau 
 International, and a Callendar-Griffiths platinum thermo- 
 
 Fig. 9. Section of Eowland's Calorimeter and sketch of Paddle. 
 
 meter. The result has been a recalculation of Rowland's 
 figures. In the following table the values for the specific 
 heat are given as Rowland first published them, and as 
 recalculated by Day 1 , and by Waidner and Mallory 2 . 
 
 Professor Fernet has also endeavoured to recalculate 
 Rowland's values from a careful study of Baudin ther- 
 mometers of the same glass and construction as those 
 of Rowland. His figures are almost exactly 1 part in 
 400 less than those determined by Day and by Waidner 
 and Mallory, and in such a case as this, one must have 
 the greater confidence in the direct comparisons. 
 
 1 Phil. Mag. XLVI. 129, 1898. 
 
 2 Physical Review, vin. 193236, 1899. 
 
Lecture III 
 TABLE III. 
 
 71 
 
 Tempera- 
 ture 
 
 Rowland's 
 original values, 
 absolute scale 
 
 Recalculated 
 by Day, 
 Paris hydrogen 
 scale 
 
 Same 
 reduced to 
 Paris nitrogen 
 scale 
 
 Recalculated by 
 Waidner and 
 Mallory, Paris 
 nitrogen scale 
 
 5C. 
 10 
 
 4-212 x 10 7 ergs 
 4-200 
 
 4-196 xlO 7 
 
 4-194 XlO 7 
 
 4-195 x 10 7 
 
 15 
 
 4-189 
 
 4-188 
 
 4-186 
 
 4-187 
 
 20 
 
 4-179 
 
 4-181 
 
 4-180 
 
 4-181 
 
 25 
 
 4-173 
 
 4-176 
 
 4-176 
 
 4-176 
 
 30 
 
 4-171 
 
 4-174 
 
 4-174 
 
 4-175 
 
 35 
 
 4-173 
 
 4-175 
 
 4-175 
 
 4-177 
 
 Rowland took pains to vary all the conditions of his 
 experiments as much as possible, running his engines at 
 different speeds, using different thermometers, carrying 
 his observations over different ranges and making in all 
 thirty series of observations. Therefore great weight 
 must be given to his determinations. The only criticisms 
 that can be made are that the range of 10 degrees is 
 too large if the specific heat at the mean temperature is 
 desired, and that the radiation correction is uncertain at 
 and above 30. As Rowland himself says : " The error 
 due to radiation is nearly neutralized, at least between 
 and 30, by using the jacket at different temperatures. 
 There may be an error of a small amount at that point 
 (30) in the direction of making the mechanical equivalent 
 too great, and the specific heat may keep on decreasing 
 to even 40." 
 
 Professor Ames's criticism on this work is as follows : 
 "Rowland estimates his possible error at less than 
 two parts in 1000; and, now that his thermometric 
 readings have been recalculated, the possible error is 
 
72 Measurement of Energy 
 
 probably reduced to less than one part in 1000, unless 
 there was a constant or systematic error, which is most 
 improbable. Rowland's method of making thermometric 
 readings is one which is liable to serious error, and it is 
 possible that in the recalculations made by Day, and by 
 Waidner and Mallory, the thermometers were not used 
 in identically the same manner as they were originally. 
 There is no obvious reason, however, for believing, as 
 Fernet does, that there is a systematic error in Rowland's 
 research." 
 
 The experiments of REYNOLDS and MooRBY 1 are also 
 examples of physical work of the highest order. In 1897 
 they published an account of their determinations of the 
 mean specific heat of water between and 100 C. 
 The apparatus used was of such a nature that I do not 
 think it possible to convey, in a brief description, any 
 clear idea of the machinery and its connections ; therefore, 
 I will only call your attention to the manner in which the 
 work was controlled and estimated. The general idea is 
 that of a hydraulic brake attached to the shaft of a triple 
 expansion 100 horse-power engine making 300 revolutions 
 per minute. 
 
 The water enters the brake at, or near, C. and runs 
 through it at such a rate that it issues at, or near, 100 C., 
 the work expended on the water being estimated by 
 means of a dynamometer consisting of a lever and weights 
 fastened to the brake. The whole of the work done being 
 
 1 Phil. Trans. A. 1897. 
 
Lecture III 
 
 73 
 
 absorbed by the agitation of the water in the brake, the 
 moment of resistance of the brake at any speed is a 
 definite function of the quantity of water in it. Except 
 for this moment the unloaded brake is balanced on the 
 shaft, the load being suspended on the brake lever at a 
 distance of 4 ft. from the axis of the shaft. If the 
 moment of resistance of the brake exceeds the moment 
 
 Fig. 10. This figure shows the hydraulic brake, lagged with cotton-wool 
 covered by flannel, the brake lever projecting from it towards the 
 left. The load carried by the lever can be seen at the bottom 
 left-hand corner. 
 
 of this load, the lever rises and vice versd. By making 
 this lever actuate the valve which regulates the discharge 
 from the brake, the quantity of water is continually 
 regulated to that which is just required to support the 
 
74 Measurement of Energy 
 
 load with the lever horizontal, and thus a constant moment 
 of resistance is maintained whatever the speed of the 
 engines. 
 
 In order to eliminate as many errors as possible, three 
 " heavy trials " were made in succession, followed by three 
 " light trials," each trial lasting 60 minutes, and the 
 difference in the two cases, " heavy " and " light," of the 
 'mean work per trial' and the difference of the 'mean 
 heat per trial ' were taken as equivalent. 
 
 In a " heavy trial," the dynamometer was adjusted to 
 a moment of 1200 foot-pounds, and the quantity of water 
 run through in the 60 minutes was about 960 pounds ; 
 in a " light trial " the moment was generally 600 foot- 
 pounds, and the quantity of water run through in the 
 60 minutes was about 475 pounds, although six trials 
 were made with the moment at 400 foot-pounds. As it 
 was only necessary to determine temperatures in the 
 neighbourhood of and 100 Q, the results are almost 
 independent of the nature of the temperature scale, as all 
 temperature scales must be in agreement at the two 
 standardising points, while the temperature range was so 
 great that an error in actual elevation at either end of it 
 would have but a small effect. Again, the large scale on 
 which the experiments were conducted would tend to 
 diminish the effect of inaccuracies in the measurements of 
 the thermal loss by radiation, etc. The most minute 
 attention was paid to all possible causes of inaccuracy, and 
 there is no apparent constant source of error in the final 
 results. 
 
 When their value is expressed in ergs, it becomes 
 
Lecture III 75 
 
 4'1833 x 10 7 ; that is, the mean capacity for heat of unit 
 mass of water between O c and 100 C. is 4'1833 x 10 7 . 
 
 Unfortunately the work of Reynolds and Moorby does 
 not afford us much assistance in our efforts to determine 
 the actual value of the heat equivalent. Assuming the 
 validity of their conclusions, we know how many ergs 
 (or primary units) are required to raise the temperature 
 of 1 gramme of water from to 100; but we are unable 
 to compare their results with the values obtained by 
 Joule and Rowland, unless we know the relation of the 
 mean thermal unit over the range to 100 to the 
 thermal unit at the temperatures covered by the ex- 
 periments of those observers. It is quite certain that the 
 number of primary units required to raise 1 gramme of 
 water through 1 at different temperatures is not the 
 same ; hence it is impossible in the present state of our 
 knowledge to ascertain if Reynolds and Moorby's results 
 are coincident with those obtained by other investigators. 
 
 On the other hand, if we assume the validity of the 
 result obtained by Reynolds and Moorby, and compare it 
 with the numbers given by Rowland, we can find the 
 value of the mean thermal unit in terms of a thermal 
 unit at some definite temperature ; a piece of informa- 
 tion of great value when we remember that no use can 
 be made of the Bunsen's calorimeter methods in the 
 absence of such knowledge. 
 
 I now pass to the consideration of indirect methods, 
 many of which were first employed by Joule. At various 
 times he estimated the heat developed by electro-magnetic 
 
76 Measurement of Energy 
 
 currents, the decrease of heat in a voltaic cell when the 
 current does work, compression and expansion of air, &c. 
 
 I have already called your attention to the great 
 variety of experiments performed by Joule, and it would 
 be difficult to overestimate the importance of this variety 
 as evidence that all forms of. energy can be expressed as 
 heat. For the purpose of our present enquiry, however, 
 viz. the exact determination of the equivalent, his indirect 
 determinations are of little use. 
 
 Next, in chronological order, I come to my own ex- 
 periments during the years 1888 to 1893 1 . 
 
 It is difficult, of course, for a parent to speak dis- 
 passionately concerning one of his own children and, 
 therefore, I propose to quote the remarks of Prof. Ames, 
 of Baltimore, in his Report addressed to the International 
 Congress of Paris in 1900. I should, however, like to 
 make two preliminary statements. 
 
 Firstly, my chief object in embarking on this in- 
 vestigation was to ascertain the validity of our system of 
 electrical units. 
 
 If all the measurements were correct by means of 
 which the practical values of the volt, the ohm, and the 
 ampere had been determined, then we know that if the 
 ends of a conductor, whose resistance is 1 ohm, are 
 maintained at a potential difference of 1 volt, the work 
 done by the current per second must be 1() 7 ergs, and 
 if this work is wholly expended as heat, then if J be 
 
 1 Phil. Trans. Roy. Soc. A. 1893; Proc. Roy. Soc. LV. 1894; Phil. 
 Mag. XL. 1895. 
 
Lecture III 77 
 
 the ratio of the secondary to the primary heat unit, 
 
 10 7 
 
 the heat liberated should be =- secondary heat units per 
 
 J 
 
 second, where J is the ratio of the secondary to the 
 primary heat unit. 
 
 Of course if we start by assuming the validity of our 
 electrical measurements, we can thus obtain the value 
 of /; but, I repeat, my object was to proceed in the 
 opposite direction. 
 
 Secondly, I was anxious to throw some light on the 
 changes in the capacity for heat of water, for, at that time 
 the only information of importance that we possessed in 
 this matter was that due to Regnault and Rowland, and, 
 while results deduced from the work of the former in- 
 dicated a steady increase from upwards, Rowland had 
 found a decrease over the range 5 to 30 C. 
 
 I may add that of the three or four years I expended 
 on this work the greater portion was employed in the 
 standardisation of the thermometers. 
 
 Prof. Ames writes as follows : 
 
 " Mr E. H. GRIFFITHS, of Cambridge, England, devised 
 a method for the determination of the specific heat of 
 water by the use .of the heating effect of an electric 
 current, which is, to a large extent, free from the errors 
 connected with the previous methods in which electric 
 currents were used. 
 
 " If a coil of wire carrying a current is immersed in 
 water any one of the three following methods may be used 
 to determine the energy spent in raising the temperature 
 of the water : 
 
78 Measurement of Energy 
 
 (1) measure E, C and t. 
 
 (2) measure C, R and t 
 
 (3) measure E, R and t. 
 
 " Griffiths used the third method, although for many 
 reasons it is the most difficult. The obvious difficulty 
 lies in the measurement of R ; because, unless measured 
 actually during the progress of the heating experiment, it 
 is necessary to know the temperature of the wire and 
 the temperature coefficient of its resistance ; and its tem- 
 perature is not that of the surrounding water. Griffiths 
 thought to obviate this difficulty by making a series of 
 subsidiary experiments which were designed to give the 
 difference in temperature between the water and the 
 wire when the former was at a known temperature and 
 an E.M.F. of known strength was applied to the latter. 
 The resistance of the wire was then measured at a known 
 temperature and its temperature coefficient was also 
 measured ; therefore, when in the course of a heating 
 experiment the temperature of the water was read, the 
 resistance of the wire could be calculated. Griffiths found 
 also that most rapid and thorough stirring of the water 
 was necessary in order to secure consistent or satisfactory 
 results. He designed a most efficient stirrer which made 
 about 2000 revolutions per minute, the rise in temperature 
 produced by the stirrer alone being in some cases equi- 
 valent to 10 per cent, of the whole work spent in raising 
 the temperature. The necessary correction, owing to this, 
 was ascertained by a series of preliminary experiments. 
 
 " Griffiths' apparatus consisted of a platinum wire 
 (diameter 0'004 in. (O'OIO cm.), length 13 in. (33 cm.), 
 
Lecture III 
 
 79 
 
 resistance about 9 ohms) coiled inside a cylindrical calori- 
 meter, 8 cm. in height and 8 cm. diameter, whose water 
 equivalent was 85. This wire was heated by means of 
 a current from storage cells. The terminals of the wire 
 
 Fig. 11. Section of constant temperature chamber in which the calori- 
 meter was suspended by glass tubes. ABC is a large steel vessel with 
 double walls, the annular space (printed black in figure) being filled 
 with mercury which is connected with a gas regulator by the tube D. 
 The steel vessel stood in a large tank filled with water, which was 
 rapidly stirred by the paddle Q, A small stream of water flowed 
 continuously into the tank, the excess passing away at W. The 
 temperature of the incoming water was controlled by the regulator 
 which was governed by the mass of mercury (exceeding 70 Ibs.) 
 within the walls ABC. A. very constant temperature could thus be 
 maintained within the steel vessel. The space between the calori- 
 meter and the steel walls was thoroughly dried and the pressure 
 reduced to less than 1 mm. 
 
 were maintained at a constant difference of potential by 
 balancing against sets of Clark cells; and, while the 
 temperature of the water contained in the calorimeter 
 was raised from 14 to 25 C., the time varying from forty 
 
80 Measurement of Energy 
 
 to eighty minutes, observations of the temperature and 
 time were made every degree. The E.M.F. used varied 
 from that of three to six Clark cells. Experiments 
 were made using different quantities of water ; and by 
 taking differences in the energy and the heat produced 
 in the different sets, many errors were eliminated, 
 and the water-equivalent of the calorimeter disappeared 
 from the equation. In the end, therefore, the method 
 depended on the introduction of 120 grams of water into 
 the calorimeter, this being the difference between the 
 quantities used in two trials. 
 
 "Griffiths measured his E.M.F. in terms of the Cavendish 
 standard Clark cell; his resistance in terms of the "B. A. 
 ohm of 1892," which is the " International Ohm " as 
 defined in 1893 ; his time by a "rated" chronometer; and 
 his temperature by a Hicks mercury thermometer which 
 had been compared with a Callendar-Griffiths platinum 
 thermometer and also with a Tonnelot thermometer 
 standardised at the Bureau International. In accordance 
 with the work of Glazebrook and Skinner he assumed the 
 E.M.F. of the Clark cell at 15 C. to be 1'4344 volts, and 
 its temperature coefficient to be 1 + 0'00077 (15 t). 
 
 "Later, Schuster called attention to an error of one 
 part in four thousand due to the capacity for heat of the 
 displaced air 1 ; but this was neutralized by the fact that 
 there was a slight probable error discovered in the 
 estimation of the E.M.F. of the Clark cells used by 
 Griffiths 2 , reducing the value to 1*4342 volts at 15 C. 
 
 1 Phil. Trans. Roy. Soc. A. 1895. 
 
 2 Phil. Mag. XL. 1895. 
 
Lecture III 
 
 81 
 
 
 Fig. 12. Section of calorimeter showing the stirring arrangements at D 
 by which the water was drawn through the bottom of the cylinder AB, 
 and thrown against the roof of the calorimeter. The platinum coil 
 is not shown in this section, as it was wound in a horizontal circle 
 placed near the base of the vessel, the rack on which it was wound 
 being supported by the rod indicated by the dotted lines to the right 
 of the thermometer bulb. At the top of the stirrer-shaft is shown 
 the counter which recorded the number of revolutions. 
 
 G. 6 
 
82 Measurement of Energy 
 
 "Hence Griffiths' final values are : 
 
 15 C. nitrogen scale, 4'198 x 10 7 ergs. 
 20 4192 xlO 7 
 
 25 4'187xl0 7 
 
 " In criticism of the method, it may be said that using 
 as small quantities of water as Griffiths did, always 
 practically under the same external conditions, there is 
 more opportunity than should be for systematic errors 
 and for errors due to radiation corrections. In this con- 
 nection reference must be made to criticisms by Schuster 1 
 and to the reply by Griffiths 2 ." 
 
 It will be seen from this summary by Professor Ames 
 that the results of my work lead to the conclusion 
 that (assuming the value of J obtained from Rowland's 
 revised experiments) there is at all events no error 
 exceeding 1 in 1000 in the value of our electrical 
 units ; but that there is an indication of a possible error 
 of some such magnitude in the electro- chemical equivalent 
 of silver, an indication which (as we shall see later) is 
 strengthened by the work of Schuster and Gannon, Kahle, 
 Patterson and Guthe. 
 
 A comparison of the curves resulting from Rowland's 
 work and my own proved that we could not both be 
 correct in our thermometry, and this of course excited 
 suspicion as to any conclusions regarding the value of the 
 electrical units. The revision of Rowland's thermometry 
 was, I believe, partly due to this discrepancy, and the 
 double restandardisations by different methods were, as 
 
 1 Phil. Tram. CLXXXVI. A. 1895. 
 
 2 Phil. Mag. 1895. pp. 431454. 
 
Lecture III 83 
 
 we have seen, Table III. supra, in agreement with each 
 other, while the resulting corrections caused Rowland's 
 curve of the changes in capacity for heat to be almost 
 parallel with rny own over the range of my experiments. 
 This parallelism did not mean that the value of J, ob- 
 tained by the assumption of the validity of the electrical 
 units, was coincident with Rowland's, but that our 
 remaining differences were probably due to the nature 
 of the calorimetric determinations, or to some hitherto 
 undiscovered error in our system of electrical measure- 
 ments. 
 
 The results obtained by Professor SCHUSTER and 
 Mr GANNON were published in 1895 1 . 
 
 They also measured the heat developed by an electric 
 current when overcoming resistance ; but in this case, the 
 work was estimated by observation of E and G, the latter 
 by the use of a silver voltameter. (See Fig. 13.) 
 
 The rise in temperature was determined by a Baudin 
 mercury thermometer, which was compared directly with 
 a Tonnelot thermometer standardised at the Bureau 
 International. The calorimeter had a water equivalent of 
 27 and the mass of water used was about 1514 grammes. 
 The heated wire was of platinoid, 760 cm. long and of 
 about 31 ohms resistance. The E.M.F. was produced by 
 storage cells, and was constantly balanced against twenty 
 Clark cells. The resulting current was in the neighbour- 
 hood of 0*9 ampere, and passed in series through a silver 
 voltameber consisting of a silver plate and a platinum bowl 
 
 1 Phil. Trans. Roy. Soc. CLXXXVI. A. 1895. 
 
 62 
 
84 
 
 Measurement of Energy 
 
 S M 
 
 J 1 I 
 
 -. s' I i 
 
 a is ^ g 
 
 ^ h-S -2 'a I 
 
 
 3 
 
 O e6 
 . 
 
 I P' S 1 IMJJ 
 
 wltllftlS 
 
 I fe 
 
 s 
 
 s : S b -s & 
 
 ii H ii ii Uli 
 
 S 2 |.2 II ft-Jl "9 
 
 J-5 .^1 
 
 i'T> S 
 
 8.2. 
 
Lecture III 85 
 
 9 cm. in diameter and 4 cm. deep, whose weight was 
 approximately 64 grammes. An experiment lasted ten 
 minutes, during which about 0'56 grammes of silver were 
 deposited, and the temperature of the water was raised 
 about 2'2 C. All experiments were performed in the 
 neighbourhood of 19'6. The final result is the mean 
 of six experiments which agree closely with each other. 
 
 The result of their investigation gives 
 
 Capacity for heat of water at 19'1C. on nitrogen 
 scale = 4'1905 x 10 7 ergs. 
 
 These experiments were conducted with the skill and 
 accuracy which we necessarily associate with the name 
 of Prof. Schuster; "Nevertheless," (I here again quote 
 Prof. Ames) " there are several criticisms which may be 
 offered to this research. There was only one voltameter 
 used throughout, and none of the conditions were varied. 
 The radiation corrections were most carefully considered, 
 but no details are given of the stirring or of any correction 
 for it. Griffiths in his investigation insists strongly on the 
 need of thorough, not to say violent, stirring. 
 
 "These facts make the final result uncertain to an 
 extent which it is difficult to estimate, but which probably 
 is not large. If, as seems probable from the work of Kahle 
 and Patterson and Guthe, the electro-equivalent of silver 
 is 0-001119 instead of O'OOlllS, Schuster and Gannon's 
 value for the specific heat at 191 becomes 4'189 x 10 7 ; 
 and, if a consequent error of one part in a thousand is 
 made in the assumed value of the E.M.F. of their Clark 
 cell, the corrected result is 4185 x 10 7 ." 
 
 It is also necessary to remember that Schuster and 
 
86 Measurement of Energy 
 
 Gannon did not trace the value of the secondary unit 
 over any appreciable range of temperature, all their 
 observations being confined to a rise of about 2' 2 C. in 
 the neighbourhood of 19 C. 
 
 I now wish to call your attention to the most 
 recent enquiry of all, viz. that of Prof. CALLENDAR and 
 Dr BARNES. 
 
 The main object of the investigation was not to 
 determine the capacity for heat of water at any particular 
 temperature; but to trace the variations in the capacity for 
 heat with the temperature. A brief summary of the work 
 was published in 1899, and in 1900 Dr Barnes presented 
 to the Royal Society a full Report (not yet published) 1 , 
 together with an account of the revision of the work 
 conducted by him, in which certain corrections were made 
 for the eddies in the water and the effects of contained air. 
 
 I extract the following description of the apparatus 
 from the summary by Prof. Callendar 2 : 
 
 "The general principle of the method, and the 
 construction of the apparatus, will be readily understood 
 by reference to the diagram of the Steady-flow Electric 
 Calorimeter given in Fig. 14. A steady current of water 
 flowing through a fine tube, is heated by a steady 
 electric current through a central conductor of platinum. 
 The steady difference of temperature between the inflowing 
 and outflowing water is observed by means of a differential 
 pair of platinum thermometers at either end. The bulbs 
 
 1 An abstract will be found in Proc. Roy. Soc. 1900. 
 
 2 B.A. Report, Dover, 1899. 
 
Lecture III 87 
 
 of these thermometers are surrounded by thick copper 
 tubes, which by their conductivity serve at once to 
 equalise the temperature, and to prevent the generation 
 of heat by the current in the immediate neighbourhood 
 
 >f LOW TUBE AMD CENTRAL CONDUCTOR^- 
 
 __ [ 
 ^] |[c 
 
 j INFLOW. GLASS VACUUM JACKET. OUTFLOW 
 
 Fig. 14. Diagram of Steady-flow Electric Calorimeter. 
 
 of the bulbs of the thermometers. The leads CO serve 
 for the introduction of the current, and the leads PP> 
 which are carefully insulated, for the measurement of the 
 difference of potential on the central conductor. The 
 flow tube is constructed of glass, and is sealed at either 
 end, at some distance beyond the bulbs of the thermo- 
 meters, into a glass vacuum jacket, the function of which 
 is to diminish as much as possible the external loss of 
 heat. The whole is enclosed in an external copper jacket 
 (not shown in the figure), containing water in rapid 
 circulation at a constant temperature maintained by 
 means of a very delicate electric regulator. 
 
 " Neglecting small corrections, the general equation of 
 the method may be stated in the following form : 
 
 ECt = JMdO + H. 
 
 " The difference of potential E on the central conductor 
 is measured in terms of the Clark cell by means of a very 
 accurately calibrated potentiometer, which serves also to 
 measure the current C by the observation of the difference 
 of potential on a standard resistance R included in the 
 circuit. 
 
88 
 
 Measurement of Energy 
 
 " The Clark cells chiefly employed in this work were of 
 the hermetically sealed type described by the authors in 
 the Proc. Roy. Soc. October 1897. They were kept 
 immersed in a regulated water-bath at 15 C., and have 
 maintained their relative differences constant to one or 
 two parts in 100,000 for the last two years. 
 
 "The standard resistance R consists of four bare 
 platinum silver wires in parallel wound on mica frames 
 and immersed in oil at a constant temperature. The coils 
 were annealed at a red heat after winding on the mica, 
 and are not appreciably heated by the passage of the 
 currents employed in the work. 
 
 CUrk ceils. 
 
 r 
 
 E 
 
 torn 
 1epc 
 
 -\y 
 
 n 
 
 1 
 
 
 p^i*/ ? ^fen 
 
 
 
 il 
 
 f ( 
 
 
 Stendssd 
 
 sonVd.rley 
 tentiomeCer. 
 
 CaLori meter. 
 
 lililili 
 
 resistance. 
 
 Accumulators. ffheosCa. 
 
 Fig. 15. Diagram of the electrical connections. 
 
 " The time of flow t of the mass of water, M, was 
 generally about fifteen to twenty minutes, and was 
 recorded automatically on an electric chronograph reading 
 
Lecture III 89 
 
 to '01 seconds, on which the seconds were marked by a 
 standard clock. 
 
 " The letter / stands for the number of joules in one 
 calorie at a temperature which is the mean of the range, 
 dO, through which the water is heated. 
 
 " The mass of water, M, was generally a quantity of the 
 order of 500 grammes. After passing through a cooler, 
 it was collected and weighed in a tared flask in such a 
 manner as to obviate all possible loss by evaporation. 
 
 "The range of temperature, dO, was generally from 
 8 to 10 in the series of experiments on the variation of 
 J, but other ranges were tried for the purpose of testing 
 the theory of the method and the application of small 
 corrections. The thermometers were read to the ten- 
 thousandth part of a degree, and the difference was 
 probably in all cases accurate to *001 C. This order 
 of accuracy could not possibly have been attained with 
 mercury thermometers under the conditions of the 
 experiment. 
 
 "The external loss of heat, H, was very small and 
 regular, owing to the perfection and constancy of the 
 vacuum attainable in the sealed glass jacket. It was 
 determined and eliminated by adjusting the electric 
 current so as to secure the same rise of temperature 
 dO, for widely different values of the water-flow. 
 
 " The great advantage of the steady-flow method as 
 compared with the more common method in which a 
 constant mass of water at a uniform temperature is 
 heated in a calorimeter, the temperature of which is 
 changing continuously, is that in the steady-flow method 
 
90 
 
 Measurement of Energy 
 
 there is practically no change of temperature in any 
 part of the apparatus during the experiment. There is 
 no correction required for the thermal capacity of the 
 calorimeter ; the external heat loss is more regular and 
 certain, and there is no question of lag of the thermometers. 
 Another incidental advantage of great importance is that 
 the steadiness of the conditions permits the attainment 
 of the highest degree 'of accuracy in the instrumental 
 readings. 
 
 Fig. 16. Diagram of the arrangements for controlling the rate of 
 flow of water. 
 
 " In work of this nature it is recognised as being of the 
 utmost importance to be able to detect and eliminate 
 constant errors by varying the conditions of the experiment 
 through as wide a range as possible. In addition to 
 varying the electric current, the water-flow, and the range 
 of temperature, it was possible, with comparatively little 
 trouble, to alter the form and resistance of the central 
 conductor, and to change the glass calorimeter for one 
 with a different degree of vacuum, or a different bore for 
 the flow tube. In all six different calorimeters were 
 employed, and the agreement of the results on reduction 
 
Lecture III 91 
 
 afforded a very satisfactory test of the accuracy of the 
 method." 
 
 I am conscious of one difficulty regarding the expression 
 of the results obtained by Callendar and Barnes, viz. the 
 reduction of their numbers to the hydrogen scale, for, 
 until the publication of the full paper, I am unable to 
 give details regarding the standardisation of their pla- 
 tinum thermometers. As the method adopted was that 
 published by Callendar and Griffiths in 1891 \ the 
 thermometric scale is that of the constant pressure air- 
 thermometer. Now, it is probable that over the range 
 to 100 C., this scale closely corresponds with that 
 of the nitrogen thermometer, a conclusion verified to a 
 certain extent by experiment. 
 
 In Table IV. (infra) the numbers under Col. 1 are the 
 values of /, as given by Dr Barnes in the abstract 2 in 
 which he gives an account of the further experiments 
 conducted by him subsequently to the joint work by 
 Professor Callendar and himself. 
 
 Under Col. 2 will be found the numbers I obtain by 
 the conversion of Dr Barnes' values from the nitrogen to 
 the hydrogen scale. For the purposes of this reduction 
 I have used the Tables given by M. Chappuis 3 , our 
 leading authority on this matter. 
 
 1 Phil. Trans. Roy. Soc. A. 1891. 
 
 2 Proc. Roy. Soc. Nov. 1900. 
 
 3 M6moires du Bureau International. Etudes sur le Thermometre 
 a Gat, p. 119. 
 
92 
 
 Measurement of Energy 
 
 TABLE IY. 
 
 
 Col. I 
 
 Col. II 
 
 Temperature 
 
 (Air scale) 
 
 (H scale) 
 
 5 
 
 4-2105 x 10 7 
 
 4-2130 x 10 7 
 
 10 
 
 4-1979 
 
 4-1999 
 
 15 
 
 4-1895 
 
 4-1912 
 
 20 
 
 4-1838 
 
 4-1851 
 
 25 
 
 4-1801 
 
 4-1805 
 
 30 
 
 4-1780 
 
 4-1780 
 
 35 
 
 4-1773 
 
 4-1774 
 
 40 
 
 4-1773 
 
 4-1769 
 
 45 
 
 4-1782 
 
 41776 
 
 50 
 
 4-1798 
 
 4-1785 
 
 55 
 
 4-1819 
 
 4-1806 
 
 60 
 
 4-1845 
 
 4-1828 
 
 65 
 
 4-1870 
 
 41854 
 
 70 
 
 4-1898 
 
 4-1881 
 
 75 
 
 4-1925 
 
 4-1912 
 
 80 
 
 4-1954 
 
 4-1946 
 
 85 
 
 4-1982 
 
 4-1979 
 
 90 
 
 4-2010 
 
 4-2014 
 
 95 
 
 4-2036 
 
 4-2050 
 
 Mean 4-1888 
 
 4-1887 
 
 On a later occasion I shall have to make further use 
 of this Table. At present, for the purposes of comparison, 
 we only require Callendar and Barnes' value on the 
 nitrogen scale at 20, i.e. 4184 x 10 7 ergs. 
 
 A summary of the results obtained by those observers, 
 whose experiments we have examined, is given in the 
 following Table. 
 
Lecture III 
 
 93 
 
 TABLE V. 
 
 Capacity Jor Heat of Water per 1 of the N thermometer. 
 
 Name 
 
 Method 
 
 Standards 
 
 Kesults 
 
 Temperature 
 
 Joule ... 
 
 Mechanical 
 
 
 4-173 xlO 7 
 
 16-5 
 
 Eowland 
 
 - 
 
 
 /4-194 
 
 J4-186 
 J4-180 
 <4-176 
 
 10 
 15 
 20 
 25 
 
 Reynolds ^ 
 
 
 
 
 
 and [ 
 
 5) 
 
 
 4-1833 
 
 mean calorie 
 
 Moorby J 
 
 
 
 
 
 Griffiths 
 
 Electrical 
 
 Clark cell x 
 
 (4-198 
 
 15 
 
 
 5' 1 
 
 = 1-4342 1 
 International | 
 ohm 
 
 4-192 
 
 4-187 
 
 20 
 25 
 
 Schuster 
 
 E. C. t 
 
 Clark cell v 
 
 
 
 and 
 Gannon 
 
 
 = 1-4340 1 
 El. Ch. E of f 
 
 4-1905 
 
 19-1 
 
 
 
 Ag. = 0-001118) 
 
 
 
 Callendar 
 
 E. C. t 
 
 Clark cell 
 
 /4-198 
 
 10 
 
 and 
 
 
 = 1-4342 
 
 J4-190 
 
 15 
 
 Barnes 
 
 
 Ag. = 0-001 118 
 
 14-184 
 
 U-181 
 
 20 
 25 
 
 The discrepancy between the values given in the above 
 Table is, in reality, much less than would appear from a 
 casual inspection. Before any real comparisons can be 
 made, we must come to some conclusion regarding the 
 variation in the capacity for heat of water, and when 
 arriving at a decision on this matter we must also consider 
 some evidence we possess which is independent of any 
 determinations based upon the transformation of energy. 
 
94 Measurement of Energy 
 
 To-day I have devoted the greater portion of the time 
 at our disposal to the consideration of experimental 
 details and numerical values. In justification I will 
 confess to holding the opinion that some teachers, in 
 their anxiety to impart results, pay too little attention to 
 the methods by which those results are obtained. A 
 healthy scepticism, rather than a habit of comfortable 
 belief, should, it appears to me, be cultivated by the 
 seeker after natural knowledge. Text-books are not in- 
 spired, and teachers, above all, should learn to weigh the 
 evidence and arrive at independent conclusions. We 
 cannot rightly appreciate the authority of any natural 
 law unless we have studied the experimental evidence 
 upon which that law is based. 
 
LECTURE IV. 
 
 Distinction between Capacity for Heat and Specific Heat of Water. 
 Changes in <r t consequent on changes in t as deduced from the 
 experiments of Regnault, Rowland, Bartoli and Stracciati, 
 Griffiths, Ludin, and Callendar and Barnes. 
 
 Reduction of the results, given in Lecture III., to a common 
 temperature. Possible errors in Electrical Units. Values of 
 C t from to 100. Final Conclusions regarding the Secondary 
 Thermal Unit. The First Law of Thermodynamics and 
 Perpetual Motion. The Second Law. Illustrations of its 
 Application. The Dissipation of Energy. 
 
 IN my last Lecture, I placed before you the numerical 
 values of the mechanical equivalent resulting from those 
 determinations which seemed to me the most trustworthy. 
 It is not possible, however, to compare these results and 
 arrive at a final decision unless we are able to trace those 
 changes in the value of the secondary thermal unit which 
 are due to the apparently capricious behaviour of water. 
 
 I wish here to make a distinction between two phrases 
 which are often employed (wrongly in my opinion) as 
 though they had the same meaning, viz., the capacity for 
 heat of water and the specific heat of water. I propose 
 to define the meaning of these terms as follows : 
 
 By " capacity for heat of unit mass of water at t " 
 
96 Measurement of Energy 
 
 or, more shortly, "the capacity for heat of water at t" 
 I indicate the number of ergs required to raise 1 gramme 
 of water through 1 of the hydrogen scale at the tempera- 
 ture t on that scale. 
 
 By the specific heat of water, I denote " the ratio of 
 the quantity of heat required to raise any mass of water 
 through 1 at t, to the quantity required to raise an 
 equal mass of water through 1 at a standard temperature 
 0, all temperatures being measured on the hydrogen 
 scale." 
 
 Thus the capacity for heat, i.e. the value of C t , is 
 dependent on energy measurements, whereas the specific 
 heat o- t can be obtained by comparison of quantities of 
 heat only. True, if we know the capacity for heat of 
 water at different temperatures, we can deduce the 
 
 C 
 
 specific heat without further measurements since ~=o- t) 
 
 ^e 
 
 and there is little doubt that this method is the 
 best, although the most laborious, way of finding cr t . 
 Nevertheless determinations of a, not involving (7, are 
 of importance. 
 
 I would call your attention to the fact that the ratio 
 
 C 
 
 of -^- is not affected either by inaccuracies in the magni- 
 ^o 
 
 tude of our electrical units, or by experimental errors in 
 the determination of the value of the standards used 
 by the observer, whereas the absolute value of C t is 
 dependent upon the accuracy of all the quantities involved. 
 Thus, although electrical methods may be of secondary 
 importance when our object is the determination of the 
 
Lecture IV 97 
 
 numerical values of C t , they are, for many reasons, of 
 primary importance in the attempt to trace the changes 
 
 G 
 
 in the value of -^ consequent on changes in temperature. 
 ^o 
 
 I have already referred to the conservative nature of 
 text-books. Take almost any one you please, and you will 
 find tables of the specific heat of various bodies written 
 to four or five places of decimals. Not content with this, 
 the changes in its value are generally given by an equation 
 of the form a + (3t + <yt 2 , and occasionally even the third 
 power is used. Now, I confess that I am sceptical as to 
 the third significant figure of these specific values at a 
 given temperature, and I refuse to give any credit at all 
 to the fourth. Let us, however, assume that, at some 
 temperature, the values given in these tables are correct, 
 say to three significant figures ; what importance can we 
 attach to the values at other temperatures obtained from 
 these equations ? If you examine into the matter you 
 will find that they are, in nearly all cases, dependent 
 upon the assumed changes in the specific heat of water 
 resulting from the extrapolation of Regnault's formula, 
 or on Bosscha's reduction of Regnault's experiments 1 . 
 At first sight this seems good enough, for it would be 
 difficult to quote any higher authority where questions 
 of accuracy are concerned. Regnault's experimental skill 
 is admitted by all physicists and, therefore, the text-book 
 writer goes ahead in all confidence, and peace and con- 
 
 1 Usually given as 1 + -00004 t + '0000009 1 2 (Eegnault, Mtmoires de 
 VAcad. xxi. p. 729, 1847) or 1+ -00022* (Bosscha, Pogg. Ann. Jah. 
 p. 549, 1876). 
 
 G. 7 
 
98 Measurement of Energy 
 
 tentment prevail in the land. Let us enquire a little 
 more curiously, however, and go back to Regnault's 
 original papers. We find that with two exceptions 
 Regnault performed no experiments concerning the 
 specific heat of water below 107 C., and as these two 
 were only made with a view of testing the working of the 
 apparatus, he himself attached no importance to them. 
 This really appears almost incredible; at all events it did 
 so to me when I first enquired into the matter. The real 
 facts are, I believe, as follows : Regnault performed a 
 series of determinations of the changes in the specific 
 heat of water over the range 107 to 190 C. After 
 discussing the results, he states what the nature of the 
 variation between and 100 would be if deduced by 
 extrapolation of the experimental curve obtained at the 
 higher range. Bosscha discussed Regnault's experiments, 
 made several small corrections, found an equation which, 
 in his opinion, more closely represented the experimental 
 results over the range 107 to 190, and then assumed 
 that a similar expression held good down to 0. Both 
 Regnault's and Bosscha's equations are quoted by the 
 text-books, and when once that has happened there is no 
 escape. 
 
 Observe the consequences. Investigators who have 
 performed experiments with the object of finding the 
 specific heat of bodies at a certain temperature, and also 
 the variation with temperature, have as a rule reduced 
 the results to a standard temperature by these extrapolated 
 values. Hence nearly all their conclusions require the 
 revision which is rendered necessary by our knowledge 
 
Lecture IV 99 
 
 that the changes in the specific heat of water between 
 and 100 differ both in magnitude and in direction 
 from the changes which take place at higher temperatures. 
 
 No one who has not actually tried it can form any 
 conception of the labour involved in attempting such 
 revisions. In the majority of cases the process is at the 
 best unsatisfactory, as the required data are not usually 
 given ; for they are not of the nature which, owing to his 
 confidence in Regnault's supposed values, the writer of 
 the paper has considered necessary. It is painful to 
 contemplate the amount of good experimental work which 
 has in consequence to be laid aside as useless. 
 
 Until 1879 Regnault's assumed values were universally 
 accepted as Rowland was the first to supply sufficient data 
 to justify the conclusion that, so far from increasing, the 
 capacity for heat of water decreased with rise of tem- 
 perature, at all events up to 30. This result has, as 
 we saw in my last Lecture, been confirmed by the work of 
 Griffiths (range 13 to 27), and Gallendar and Barnes 
 (range 1 to 99). 
 
 The changes in the specific heat have been determined 
 by Bartoli and Stracciati, and Ludin. In both cases the 
 conclusions were arrived at by the method of mixtures, 
 and are, therefore, independent of all energy measurements. 
 Bartoli and Stracciati devoted nearly nine years to their 
 investigation ; they not only mixed water with water, but 
 also with mercury and several metals. Their thermometry 
 was based on the standards supplied by the Bureau 
 International and their results are given in a formula 
 containing the third power of t. They find a minimum 
 
 72 
 
100 Measurement of Einergy 
 
 about 20. The difficulties of this method are consider- 
 able, and a careful examination of their experimental 
 numbers leads to the conclusion that the discrepancies 
 between individual experiments are too great to allow 
 of our attaching much authority to their final values. 
 
 A very fine series of determinations by the same 
 method was made by Ludin in 1890. This investigator 
 was able to take advantage of many of the recent advances 
 in thermometric measurements, and his work is of a very 
 high order. Fernet has written a very full criticism of 
 this work and Ludin in his reply introduces a few cor- 
 rections. 
 
 I now give a table which summarises the results of 
 the observers I have named. I have assumed 15 as the 
 standard temperature and in the case of the energy deter- 
 minations (Rowland revised, Griffiths, and Callendar and 
 
 C 
 Barnes 1 ) I have given the value of ~ where is 15. In 
 
 ^0 
 
 the cases of Bartoli and Stracciati and Ludin I have 
 expressed a t in terms of a l5 throughout. 
 
 This table is a very important one. I would first of 
 all call your attention to the comparatively close agree- 
 ment between the values obtained by Rowland, Griffiths, 
 and Callendar and Barnes. 
 
 Now, remember how entirely different the methods 
 of experiment were in these three cases. In Rowland's, 
 
 1 The numbers given in the last column of this table are deduced 
 from Col. II. Table IV. as it was necessary to express Barnes' results 
 in terms of the hydrogen scale before making a comparison with the 
 values obtained by the other observers. 
 
Lecture JV 
 
 101 
 
 TABLE VI. 
 
 Values of the Specific Heat of Water referred to that at 
 15 C. as unity. 
 
 Temperature by 
 the hydrogen 
 thermometer 
 
 Rowland 
 (Day) 
 
 Bartoli and 
 Stracciatij 
 (Fernet) 
 
 Griffiths 
 
 Ludin 
 
 Callendar 
 and 
 Barnes 
 
 
 
 
 
 (1-0080) 
 
 
 
 (1-0051) 
 
 (] -0084) 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 
 
 1-0059 
 
 
 
 1-0035 
 
 
 
 4 
 
 
 
 52 
 
 
 
 31 
 
 
 
 5 
 
 (1-0042) 
 
 46 
 
 
 
 27 
 
 1-0052 
 
 6 
 
 1-0036 
 
 40 
 
 
 
 23 
 
 45 
 
 7 
 
 31 
 
 34 
 
 
 
 19 
 
 38 
 
 8 
 
 26 
 
 28 
 
 
 
 16 
 
 32 
 
 9 
 
 23 
 
 23 
 
 
 
 13 
 
 26 
 
 10 
 
 19 
 
 18 
 
 
 
 10 
 
 21 
 
 11 
 
 14 
 
 13 
 
 
 
 8 
 
 16 
 
 12 
 
 10 
 
 09 
 
 
 
 6 
 
 11 
 
 13 
 
 07 
 
 05 
 
 1-0006 
 
 4 
 
 07 
 
 14 
 
 03 
 
 02 
 
 03 
 
 2 
 
 03 
 
 15 
 
 1-0000 
 
 1-0000 
 
 1-0000 
 
 1-0000 
 
 1-0000 
 
 16 
 
 0-9996 
 
 0-9998 
 
 0-9997 
 
 0-9998 
 
 0-9997 
 
 17 
 
 93 
 
 97 ' 
 
 94 
 
 97 
 
 94 
 
 18 
 
 90 
 
 96 
 
 91 
 
 96 
 
 90 
 
 19 
 
 86 
 
 95 
 
 88 
 
 95 
 
 88 
 
 20 
 
 83 
 
 94 
 
 85 
 
 94 
 
 85 
 
 21 
 
 81 
 
 93 
 
 82 
 
 93 
 
 83 
 
 22 
 
 79 
 
 93 
 
 79 
 
 93 
 
 80 
 
 23 
 
 76 
 
 94 
 
 76 
 
 92 
 
 77 
 
 24 
 
 74 
 
 95 
 
 73 
 
 92 
 
 75 
 
 25 
 
 72 
 
 97 
 
 70 
 
 93 
 
 74 
 
 26 
 
 71 
 
 98 
 
 0-9968 
 
 93 
 
 73 
 
 27 
 
 69 
 
 1-0000 
 
 
 
 94 
 
 72 
 
 28 
 
 69 
 
 02 
 
 
 
 94 
 
 71 
 
 29 
 
 68 
 
 05 
 
 
 
 95 
 
 70 
 
 30 
 
 67 
 
 10 
 
 
 
 96 
 
 69 
 
 31 
 
 67 
 
 1-0011 
 
 
 
 97 
 
 69 
 
 32 
 
 67 
 
 
 
 
 
 98 
 
 68 
 
 33 
 
 67 
 
 
 
 
 
 99 
 
 68 
 
 34 
 
 67 
 
 
 
 
 
 1-0001 
 
 67 
 
 35 
 
 0-9969 
 
 . 
 
 
 
 1-0003 
 
 0-9967 
 
 Values in brackets obtained by extrapolation. 
 
102 Measurement of Energy 
 
 the mechanical work was done against friction of water, the 
 results as revised being dependent on the thermometry of 
 the Bureau International. In Griffiths', the work done 
 was measured by an electric current, the data being E and 
 R, the thermometers mercury-in-glass instruments stan- 
 dardised by platinum thermometers and also by the 
 standards of the Bureau International. In Callendar and 
 Barnes', a very different method of estimating the heat 
 developed by an electric current was adopted, viz. the use 
 of a steady flow of water, the data being E and G, and the 
 thermometry the differential platinum method. 
 
 We have seen that the values of C e are somewhat 
 different in the three cases; but, on the other hand, 
 
 Q 
 
 this table shows that the values of ~ are wonderfully 
 
 ^0 
 
 concordant. 
 
 Now, observe the results of Bartoli and Stracciati 
 and Ludin. The methods they adopted were similar in 
 principle, although differing in detail ; hence, one would 
 have expected, a priori, that their results would have 
 been in closer agreement than those obtained by the 
 other observers. You see, however, that this is not the 
 case; the differences between them are very marked 
 (almost 3 in 1000 near 0, and 1-4 in 1000 at 30). 
 
 As it is unlikely that the skill and patience shown 
 by Messrs Bartoli and Stracciati, and also by Ludin, can 
 be exceeded, it is probable that the method of mixtures 
 presents peculiar difficulties and uncertainties, which are 
 absent in the energy determinations. Therefore, I think 
 you will agree that if we take the mean value resulting 
 
Lecture IV 103 
 
 from the observations of Rowland, Bartoli and Stracciati, 
 and Griffiths over the range 13 to 26, we shall be very 
 near the truth. It is noticeable, by the way, that 
 throughout the whole of this range the resulting values 
 approximate most closely to Rowland's corrected results. 
 
 Before leaving this table it is interesting to notice 
 how it illustrates the cosmopolitan character of scientific 
 investigation and the importance attached to this matter 
 by physicists of all nationalities. 
 
 The first column comes from Baltimore, the second 
 from Pisa, the third from Cambridge, England, the fourth 
 from Zurich, and the last from Montreal. 
 
 We are now, I think, in a position to reduce to some 
 standard temperature the absolute values of G t which 
 were given in Table V. 
 
 Let us, by means of the curve representing our con- 
 clusions as to the changes in the specific heat over the 
 range covered by these experiments, reduce them all to 
 20 C. on the N. scale. We get, 
 
 Joule 4169 x 10 7 . 
 
 Rowland 4180 
 
 Griffiths 4192 
 
 Schuster and Gannon 4189 
 
 Callendar and Barnes 4184 
 
 I am afraid that in our search for the most probable 
 value we must omit the number due to Joule. The doubt 
 as to the exact conditions under which his thermometers 
 were used renders the rejection advisable. (See p. 59, 
 supra.) 
 
104 Measurement of Energy 
 
 As previously indicated, there is a considerable amount 
 of evidence that the value assumed for the potential 
 difference of a Clark cell is somewhat too high. 
 
 The value used in the electrical experiments was that 
 found by Lord Rayleigh in 1884 as 1*4344 at 15 and 
 redetermined by Messrs Glazebrook and Skinner in 1891, 
 when they obtained 1-4342 at 15. My own cells were 
 compared with Lord Rayleigh's in a prolonged series of 
 observations in 1892, and six of those cells were taken 
 to Owens College and compared with Professor Schuster's 
 in 1894 ; it would appear, therefore, that the comparative 
 values of those cells are known with sufficient accuracy. 
 The absolute values were obtained on the assumption 
 that the electro-chemical-equivalent of silver is O'OlllS. 
 
 On this point, I will again quote from the Report by 
 Prof. Ames : 
 
 " In regard to the electrical standards, it must be 
 observed that no meaning can be attached to the 'electro- 
 chemical-equivalent ' of silver, unless the construction and 
 use of the voltameter are most carefully specified, and 
 even then there is considerable doubt unless several 
 instruments are used in series. This fact is well shown 
 in the recent work of Richards, Collins and Heimrod at 
 Harvard University, and of Merrill at Johns Hopkins 
 University. The former deduce from a comparison of 
 their porous-jar voltameter with other forms of instru- 
 ments that the electro-chemical-equivalent with their 
 instrument is 0'0011172 grams per sec. per ampere; 
 while Patterson and Guthe with their instrument find 
 0'0011193. If, however, the same voltameter and the 
 
Lecture IV 105 
 
 same method of use are adopted in the experiments on the 
 electro-chemical-equivalent and in those on the E.M.F. of a 
 Clark cell, the value of the latter is independent of the value 
 assigned to the former. For this reason Kahle's value of 
 the E.M.F. of the standard Clark cells of the Reichsanstalt 
 (T4325 volts at 15 C.) is probably correct. The Caven- 
 dish standard cell has been compared with the German 
 ones; its resulting value is 1*4329 at 15 C. and the 
 later investigations of Patterson and Guthe would reduce 
 this to 1-4327. As Griffiths used the value 1-4342 and 
 as the E.M.F. enters into the equation to the second power, 
 the necessary correction would be almost exactly two 
 parts in one thousand. 
 
 "For the method used by Schuster and Gannon, where 
 both the E.M.F. and the current are measured, a correction 
 may be accurately applied to the E.M.F., but not to the 
 current, as it is not known what amount of silver one 
 ampere should deposit in their voltameter ; but if we 
 assume that the correction in both cases is 1 in 1000, 
 these results also would be reduced by 2 parts in 1000. 
 The correction assigned is probably in the right direction. 
 
 " The cells used by Callendar and Barnes have not 
 been compared with those of the Reichsanstalt, and no 
 'correction' can be applied with certainty 1 . The figures 
 used above 2 are probably in excess." 
 
 77f 
 
 1 Here the value of the current was obtained by measurement of , 
 
 jK 
 
 where R was a standard resistance, and it is somewhat difficult to estimate 
 the probable effect of the change in the equivalent of silver in the absence 
 of certain knowledge concerning the comparative value of Callendar and 
 Barnes cells, in terms of the Kayleigh cell. 
 
 2 i.e. a correction of 2 parts in 1000. 
 
106 Measurement of Energy 
 
 Assuming, therefore, the values of the E.M.F. of a 
 Clark cell, and the electro-chemical-equivaleiit of silver 
 deduced from the work of Kahle, Patterson and Guthe, 
 we obtain the following table : 
 
 Rowland 1 4180 x 10 7 
 
 Griffiths 4184 
 
 Schuster and Gannon 4*181 
 
 Callendar and Barnes 4176 
 
 Mean 41802 at 20 N. 
 
 This close agreement between the mean and Rowland's 
 number may be fortuitous, but, at the same time, the 
 resulting coincidence between the values obtained by the 
 mechanical and electrical methods renders it very probable 
 that T4328 is more nearly the true potential difference of 
 a Clark cell than the values 1'4340 to 1'4342 used in the 
 original calculations 2 . 
 
 Anyhow, cceteris paribus, we ought to attach far the 
 greatest weight to the direct mechanical transformation, 
 and, therefore, we can with confidence adopt the number 
 4180 x 10 7 as very near to the truth. This converted to the 
 hydrogen scale at 20 = 4181 x 10 7 . If we assume as our 
 standard change in temperature the rise from 17 to 18 
 (and I will presently explain the reason for this selection), 
 we get (from Table VI.) the number 4184 x 10 7 ergs. 
 
 1 4-181 according to Waidner and Mallory (see Table V. supra) ; but 
 as Day directly obtained the value 4-181 on the hydrogen scale, the proba- 
 bility is that 4-180 is the closer approximation on the nitrogen scale. 
 
 2 For a further discussion of this matter see the Eeport of the 
 Electrical Standards Committee, 1897. 
 
Lecture IV 107 
 
 In order to obtain the most probable values of C t over 
 the range to 100 C. I propose to proceed as follows : 
 From Table VI. we can obtain the mean values of 
 
 C 
 
 - given by Cols. I. III. and V. over the range to 35. 
 
 kji 
 
 From 35 to 100 we must be guided by the observations 
 of Calleridar and Barnes (Table IV. Col. II.), and we can 
 
 G 
 
 thus deduce the values of -^- over the whole range. The 
 
 ^17-5 
 
 results of this reduction are given in Col. I. Table VII. 
 (infra). Let us then assume the value (7 17 . 5 = 4'184 and 
 deduce the value of C t at other temperatures. The 
 results are shown in Col. II. (infra). 
 
 Now, we have one test which we can apply to these 
 numbers. 
 
 The result obtained by Reynolds and Moorby for " the 
 mean thermal unit" was 41833 (supra, p. 75). A study 
 of the tables given in their papers shows that the actual 
 range was, on the average, from about 1 2 or 1*4 C. to 100. 
 An inspection of Table VII. will show that the rate of 
 
 C 
 variation of -^- is very rapid near 0C., and that the 
 
 G 
 
 probable value of -~ is about 1*008. 
 &vs 
 
 It is possible to make an approximate correction 
 which, however, only raises Reynolds and Moorby's 
 value to 4* 1836. This result differs from the mean of the 
 numbers in Col. II. Table VII. by less than 1 part in 
 2000. The correspondence is remarkable, and greatly 
 increases the probability of the conclusions at which we 
 have arrived. 
 
108 
 
 Measurement of Energy 
 
 Temperature 
 on H. scale 
 
 
 
 5 
 
 10 
 15 
 20 
 25 
 30 
 35 
 40 
 45 
 50 
 55 
 60 
 65 
 70 
 75 
 80 
 85 
 90 
 95 
 100 
 
 Mean 
 
 TABLE VII. 
 Col. I. 
 
 1-00033 
 
 Col. II. 
 
 (1-0083) 
 
 (4-219) x 10 7 
 
 54 
 
 206 
 
 27 
 
 195 
 
 7 
 
 187 
 
 9992 
 
 181 
 
 78 
 
 176 
 
 75 
 
 174 
 
 74 
 
 173 
 
 73 
 
 173 
 
 74 
 
 173 
 
 77 
 
 174 
 
 81 
 
 176 
 
 87 
 
 178 
 
 93 
 
 181 
 
 1-0000 
 
 184 
 
 7 
 
 187 
 
 15 
 
 190 
 
 23 
 
 193 
 
 31 
 
 197 
 
 40 
 
 201 
 
 (1-0051) 
 
 (4-205) 
 
 41854 
 
 It is possible that the methods of reduction may 
 appear somewhat artificial. Kemember, however, that 
 even if we apply no correction for the possible errors in 
 the electrical standards, we should probably have come to 
 the same conclusion regarding the value of (7 17 . 5 ; for we 
 should, in every case, have attached greater importance 
 to Rowland's direct determinations than to any results 
 obtained by indirect methods. Again, if when tracing 
 
Lecture IV 109 
 
 the changes in C t we had used Dr Barnes' original figures 
 (without reduction to the hydrogen scale), the discrepancy 
 between the values of the "mean unit" resulting from 
 the work of Reynolds and Moorby, and Callendar and 
 Barnes would not have been increased to as much as 
 
 1 in 1000. There is also a certain amount of indirect 
 evidence, with which I will not trouble you, although it 
 lends some support to our conclusions 1 . 
 
 You will now understand the motives which dictated 
 the proposal to regard the value of C\ 7 . 5 as the standard 
 secondary unit, for it is almost coincident with the most 
 probable value of the " mean thermal unit " over the 
 range to 100. 
 
 This coincidence is a convenience, but not a necessity. 
 Had the temperature 17 to 18 been in other respects 
 unsuitable, I do not think it would have been wise to 
 attach too much importance to this point. As it is, we 
 are enabled to express the value of thermal measurements 
 obtained by Bunsen's calorimeter in terms of the standard 
 unit, and the accuracy is sufficient, for Prof. Nicholls has 
 recently shown that the density of ice depends upon its 
 rate of formation ; the variations sometimes amounting to 
 
 2 parts in 1000 2 . Hence the experimental errors of such 
 determinations are probably greater than those arising 
 from the assumption that the secondary thermal unit at 
 17*5 C. is the same as the mean unit over the range 
 to 100. 
 
 1 See Griffiths, Phil. Trans. A. 1895, p. 321; Joly, ibid. p. 323; 
 Griffiths, Phil. Mag. Nov. 1895. 
 
 2 Physical Review, 1899. 
 
110 Measurement of Energy 
 
 The following is a summary of the conclusions to which 
 our enquiry has led us : 
 
 1. The standard (secondary) thermal unit is the 
 energy required to raise 1 gramme of water from 17 to 
 18 C. on the Paris hydrogen scale, or one-fifth the amount 
 required to raise it from 15 to 20 C. on the same scale. 
 
 2. The value of this standard secondary unit 
 
 = 4-184 x 10 7 ergs. 
 = 426'5 kil. met. at Paris. 
 = 1400-0 ft.-lbs. at Greenwich. 
 
 This unit expressed in terms of the F. scale at 63'5 F. 
 = 7777 ft.-lbs. at Greenwich. 
 
 3. The value of the secondary unit at other tempera- 
 tures over the range to 100 approximates closely to 
 that given in Col. II. Table VII. 
 
 4. The mean thermal unit over the range to 100 C. 
 may be taken as identical with the standard unit as defined 
 in (1) supra. 
 
 The above conclusions are practically the same as those 
 presented by me in a Report to the Paris Congress in 
 1900 ; although, as Dr Barnes had not then published the 
 results of his revision of his own and Callendar's work, 
 some small modifications have now been made, but they 
 nowhere amount to more than 1 in 2000. 
 
 If, as I hope, thermal quantities are in future expressed 
 in terms of the values given in Table VII., we shall at all 
 events get rid of many of the difficulties which have 
 hitherto hampered and perplexed all students of thermal 
 measurements \ 
 
 1 See Appendix in. 
 
Lecture IV 111 
 
 The first law of thermodynamics is usually enunciated 
 as follows. " When work is expended in producing heat 
 the quantity of heat generated is proportional to the work 
 done," and the evidence at our disposal is not only sufficient 
 to establish the existence of such a proportion but also 
 enables us to assign to it a definite numerical value. 
 
 The enunciation of this law was an event not only 
 important in itself but far-reaching in its consequences. 
 You remember that from the time of Newton to that 
 of Joule the one thing wanting to justify a belief in the 
 indestructibility of energy was experimental proof of a 
 definite relation between work done in producing heat 
 and the heat developed. The discovery of this missing 
 link completed the chain of evidence, and the truth of the 
 principle of the Conservation of Energy at once became 
 apparent. The effects of a general recognition of this 
 truth were soon evident in every branch of science, for 
 it was found that phenomena hitherto regarded as isolated 
 or disconnected were in many cases related as closely as 
 cause and effect. To-day the validity of that principle is 
 acknowledged alike by the physicist, the chemist, the 
 biologist and the engineer, and one and all reject such 
 explanations of natural phenomena as can be shown to 
 conflict with this, the greatest and most fruitful genera- 
 lization of modern physics. 
 
 It is possible that when speaking of " different forms 
 of energy " we are but emphasizing unnecessary dis- 
 tinctions. If so we may state the principle as follows : 
 " the energy of motion is indestructible," in other words, 
 all transmutations of energy are really but the presen- 
 
112 Measurement of Energy 
 
 tation of motion under differing circumstances. The 
 existence of potential energy may appear a difficulty. 
 Suppose a body shot upwards and caught at its highest 
 point; what has become of its energy of motion? The 
 supposition that we have transferred its initial motional 
 energy to the ether naturally presents itself. If a body 
 when accelerated receives energy of motion from the 
 ether, and if when retarded it communicates energy of 
 motion to the ether, then by potential energy we mean 
 energy of motion of ether external to the body; by kinetic 
 energy, motion of the body, or in the body, itself. 
 
 Perpetual motion (not, as Prof. Tait well remarks, "the 
 perpetual motion") is a law of nature, and it is possible 
 that the doctrine of the indestructibility of motion may be 
 regarded as of equal validity to that of the indestructi- 
 bility of matter; or again, the two statements may after 
 all be but different aspects of one and the same propo- 
 sition. 
 
 Although the second law involves no numerical 
 determinations, we should remember that it, like the 
 first, is a purely experimental one. 
 
 " That it is impossible to derive mechanical effect 
 by means of heat obtained from any portion of matter 
 by cooling it below the temperature of the coldest 
 of the surrounding bodies " is a conclusion dependent 
 simply upon experience, like all other natural laws. 
 It should always be borne in mind, however, that this 
 law when thus enunciated, is only applicable in those 
 cases in which the working substance has been taken 
 
Lecture IV 113 
 
 through a complete cycle, and has therefore been restored 
 to its initial condition. For example (as previously pointed 
 out, p. 17) we can derive mechanical effect by allowing a 
 gas to expand against pressure, and, as a consequence, its 
 temperature may fall below that of surrounding bodies. 
 This operation, however, is not a complete cycle, for work 
 has been done at the expense of the internal energy of the 
 working substance. We cannot draw any legitimate con- 
 clusion, concerning the relation between the heat supplied 
 to the system and the work obtained from it until the 
 working substance has been restored to its initial state. 
 
 I have an impression that students rarely appreciate 
 the importance, alike to the physicist and the chemist, 
 of this second law. By means of it we can not only 
 test the validity of our conclusions regarding operations 
 involving transference of energy, but we can also predict 
 phenomena and verify by experiment the truth of our 
 predictions. One beautiful application is, of course, 
 known to you all, viz. J. Thomson's calculation of the 
 effect of increase in pressure upon the melting-point of 
 ice. The usual proof is of a mathematical nature ; but, 
 if you will permit me, I should like to show that we can 
 arrive at the same conclusion by going through a series of 
 operations somewhat similar to those already performed 
 by means of Carnot's engine. 
 
 Let the hot and cold bodies X and T in Fig. 2, p. 35, 
 be replaced by two equal vessels R and Q (Fig. 17) similar 
 in form to V, their walls being made of an adiabatic 
 substance except where they come in contact with the 
 sides of V at the shutters L and K, which you remember 
 G. 8 
 
114 
 
 Measurement of Energy 
 
 can be changed at will from adiabatic to perfectly con- 
 ducting faces, and thus, when open, permit the transference 
 of heat from one vessel to another, although the system as 
 a whole is thermally isolated. 
 
 Let Q contain ice and water, then if the pressure on p 2 
 is that of one atmosphere, the temperature within Q will 
 be C. 
 
 Fill R also with ice and water, and let a heavy weight 
 W be supported by its piston p 3 , so that the pressure in 
 R always exceeds that in Q. 
 
 Fig. 17. 
 
 Open K so that the substance in V assumes the 
 temperature of Q (i.e. C.), and let its piston (pi) stand 
 at A. Now force p^ downwards, say to B; the heat 
 produced by the work thus done will pass into Q, melting 
 some ice, but not altering its temperature. This will 
 cause the contents of Q to diminish in volume and the 
 piston p z will descend through some distance GH. Now 
 
Lecture IV 115 
 
 close K and open L and allow p l to rise until it is again 
 at A. Heat will be taken from R during this operation 
 and some ice must be formed in R. The piston p s must 
 therefore rise, lifting the weight W. 
 
 Now, if we assume that the temperature of R during 
 the formation of ice remained at C., then the working 
 substance in F must have remained at the same tempera- 
 ture throughout the cycle, and therefore, as its piston has 
 returned to its original position at A, no external work 
 has been done by its contents. 
 
 Again, since the pressure on p 3 is greater than that 
 on p 2 , the work done on Q could only equal that done 
 by R if the piston p 2 had descended through a greater 
 distance than that ascended by p 3 . This is not, however, 
 possible ; for, if so, a greater volume of ice must have been 
 melted in Q than was formed in R and thus the system 
 would have received heat without disappearance of other 
 forms of energy. Hence (on the above hypothesis that R 
 remained at C.) the system has done work by the 
 transference of heat from one body to another at the 
 same temperature. This, as the second law tells us, is 
 contrary to all experimental evidence. 
 
 We are thus forced to the conclusion that during the 
 cycle sufficient work must have been done on V to restore 
 the balance of energy. Therefore, the work done by the 
 substance in V during an upward, was less than that done 
 on it during a downward, stroke. That is, the pressure, 
 and therefore the temperature, of V was diminished by 
 shutting K and opening L ; hence the temperature of the 
 mixture in R was lower than that in Q, i.e. below C. 
 
 82 
 
116 Measurement of Energy 
 
 The same method of reasoning shows that if a body 
 contracts on solidification, its freezing-point must be 
 raised by pressure. 
 
 Many other similar applications suggest themselves. 
 For example, the volume of a saturated solution of 
 ammonium chloride in water exceeds that of the water 
 and salt when separate. Hence the application of great 
 pressure would cause the formation of crystals. On the 
 other hand, the volume of a saturated solution of copper 
 sulphate in water is less than the volume of its constituents. 
 Hence the effect of greater pressure must be the disappear- 
 ance of crystals. I presume, therefore (although I do not 
 know of any experimental evidence), that if we took two 
 long columns of these solutions we should perceive the 
 crystals of ammonium chloride form at the bottom, while 
 those of copper sulphate would form near the top. 
 
 In estimating the importance of this second law, we 
 must remember that by means of it we were able to 
 complete the demonstration of the truth of the statement 
 that a reversible engine is the best possible engine, and 
 that, therefore, all reversible engines are equally efficient, 
 and it is upon this conclusion that our true conception of 
 anabsolute temperature scale depends. 
 
 Our scientific knowledge of to-day is a great building 
 containing many chambers. The whole edifice has been 
 erected upon certain fundamental piers of which not the 
 least important is this conception of an absolute tempera- 
 ture scale, and if this pillar were removed it would be 
 difficult to set any limit to the effect upon the stability of 
 the whole structure. 
 
Lecture IV 117 
 
 Reflect for a moment on one of the consequences 
 which results from our definition of an absolute scale, 
 viz. that if a source is at an absolute temperature 6 and 
 our sink, or condenser, at temperature t, then the efficiency 
 
 of a perfect engine working between these temperatures is 
 r\ j. 
 
 -. That statement alone not only gives the engineer 
 u 
 
 complete knowledge of the limitations under which he 
 works, but also the ideal limit towards which he should 
 ever struggle, although he can never attain to it. 
 
 " Never " may appear to be a dangerous word to use ; 
 but in this case it is allowable. So long as the conditions 
 of the universe remain as we now find them, the word 
 is not only allowable but necessary. Let us consider the 
 matter more fully. You remember that when we traced 
 the various steps of the Carnot cycle, we saw that the 
 area representing the work done during that cycle was 
 bounded by isothermal and adiabatic lines. Now, we 
 have not as yet discovered either a perfect conductor or 
 an adiabatic substance ; thus during a downward stroke the 
 contents must always be at a higher temperature than the 
 walls and, therefore, the pressure must exceed that shown 
 by the isothermal until we have come to rest at the end 
 of the stroke. Conversely, during an upward movement 
 the contents must be cooler and hence the pressure less. 
 During a forward cycle, therefore, the area of the work- 
 space is diminished and during a reverse cycle it is 
 increased 1 . 
 
 1 The dotted lines in Fig. 3 (p. 38, supra) indicate the effect upon the 
 area of the work- space during a forward cycle. 
 
1 18 Measurement of Energy 
 
 The only way of meeting this difficulty would be for 
 the movement of our piston during the isothermal strokes 
 to be infinitely slow. Again, during the so-called adiabatic 
 strokes some heat must enter or leave the cylinder in any 
 given interval of time, as we do not possess any adiabatic 
 substance. These strokes would, therefore, have to be 
 made with infinite rapidity. Hence, when the valves 
 communicating with either the source or the condenser 
 are open, our engine must move with infinite slowness; and 
 when those valves are closed, with infinite rapidity. Also 
 all movements must be frictionless if it is to play the part of 
 a reversible engine. Here, I think, are enough impossi- 
 bilities to justify the use of the word "never." 
 
 We know that under the best possible conditions, the 
 elevation of heat to other forms of energy can never 
 be more than partial ; whereas the complete degradation 
 of the mechanical to the heat form of motion is constantly 
 taking place. Again, such partial restoration as we have 
 is only feasible where differences of temperature exist and 
 where, by its very occurrence, it tends to destroy those 
 differences of temperature, and thus the available or free 
 energy of a system always tends to become a minimum. 
 The conclusion is inevitable. All energy must ultimately 
 be degraded to the heat form and become so distributed 
 that all matter is at one temperature. 
 
 It is not possible at the close of such a course of 
 lectures as this to give proper consideration to the grand 
 generalisation known as the Dissipation of Energy a 
 generalisation perhaps as important as that of con- 
 servation. 
 
Lecture IV 119 
 
 Even as the Conservation of Energy recalls the name 
 of Joule, so does the Dissipation of Energy suggest the 
 name of William Thomson, and I cannot more fitly 
 summarise this portion of our subject than by the follow- 
 ing quotation from the writings of Lord Kelvin : 
 
 " Exhaustive consideration of all that is known of the 
 natural history of the properties of matter, and of all 
 conceivable methods for obtaining mechanical work from 
 natural sources of energy, whether by heat-engines, or by 
 electric engines, or water-wheels, or tide-mills or any other 
 conceivable kind of engine, proves to us that the most 
 perfectly designed engine can only be an approach to the 
 perfect engine ; and that the irreversibility of actions 
 connected with its working is only part of a physical 
 law of irreversibility according to which there is a uni- 
 versal tendency in nature to the dissipation of mechanical 
 energy ; and any partial restoration of mechanical energy 
 is impossible in inanimate material processes and is 
 probably never effected by means of organised matter, 
 either endowed with vegetable life, or subject to the 
 will of an animal. 
 
 " The doctrine of the ' Dissipation of Energy ' forces 
 upon us the conclusion that within a finite period of 
 time past, the earth must have been, and within a finite 
 period of time to come must again be, unfit for the 
 habitation of man as at present constituted, unless opera- 
 tions have been, and are to be, performed, which are 
 impossible under the laws governing the known operations 
 going on at present in the material world 1 ." 
 
 1 Lectures and Addresses, Lord Kelvin, Vol. n. p. 469. 
 
120 Measurement of Energy 
 
 In this necessarily brief survey, I have endeavoured to 
 set before you, as fully as time permitted, the extent of 
 our present knowledge regarding one of the leading 
 principles of natural science. I will now venture to 
 recall to your memories the following quotation from 
 my first Lecture : 
 
 " The recent history of the establishment and develop- 
 ment of the Conservation of Energy is a steady record of 
 progress ; but that progress partakes rather of the nature 
 of an accurate survey of country whose main outlines 
 are already familiar, than of any advance into unknown 
 territory. 
 
 "It is not on that account, however, of less consequence; 
 for settlement is often as true an indication of progress as 
 discovery itself." 
 
 This statement has, I hope, been justified by the facts 
 to which I have called your attention during these lectures. 
 
 I have only been able to give you faint outlines, 
 even of the works selected for consideration ; the 
 details must be filled in by direct study of the original 
 papers. Enough has been said, however, to indicate the 
 strength of the evidence that has been gradually collected 
 by many observers in different lands. 
 
 I doubt if so much time, thought, and experimental 
 skill have been devoted to the determination of any other 
 physical quantity. Such labours, however, have not been 
 in vain, for at the commencement of this new century 
 we are in a position to speak with some confidence re- 
 garding the value of what I do not hesitate to call the 
 most important of all natural constants. 
 
APPENDIX I. 
 
 THE THERMAL UNIT. 
 
 IN December, 1895, I received from Professor Rowland a 
 letter regarding the question of the selection of a secondary 
 unit. In answer to a request, he then gave me permission to 
 publish that letter, in whole or in part, and the portion here 
 given will be found in the Reports of the Electrical Standards 
 Committee 1 . 
 
 I now reproduce it, not only on account of the importance 
 of the opinions therein expressed, but also because it possesses 
 at the present time a sad interest, as a record of the great 
 physicist who has so recently passed away. 
 
 "JOHNS HOPKINS UNIVERSITY, 
 
 December 15, 1895. 
 
 "As to the standard for heat measurement, it is to be 
 considered from both a theoretical as well as a practical 
 standpoint. 
 
 The ideal theoretical unit would be that quantity of heat 
 necessary to melt one gramme of ice. This is independent of 
 any system of thermometry, and presents to our minds the 
 idea of quantity of heat independent of temperature. 
 
 Thus the system of thermometry would have no connection 
 
 1 B.A. Report, Liverpool, 1896. 
 
122 Measurement of Energy 
 
 whatever with the heat unit, and the first law of thermo- 
 dynamics would stand, as it should, entirely independent of 
 the second. 
 
 The idea of a quantity of heat at a high temperature being 
 very different from the same quantity at a low temperature, 
 would then be easy and simple. Likewise we could treat 
 thermo-dynamics without any reference to temperature until 
 we came to the second law, which would then introduce 
 temperature and the way of measuring it. 
 
 From a practical standpoint, however, the unit depending 
 on the specific heat of water is at present certainly the most 
 convenient. It has been the one mostly used, and its value is 
 well known in terms of energy. Furthermore, the establish- 
 ment of institutions where It is said thermometers can be 
 compared with a standard, renders the unit very available 
 in practice. In other words, this unit is a better practical 
 one at present. I am very sorry this is so, because it is 
 a very poor theoretical one indeed. 
 
 But as we can write our text-books as we please, I suppose 
 that it is best to accept the most practical unit. This I con- 
 ceive to be the heat required to raise a gramme of water 1 C., 
 on the hydrogen thermometer at 20 C. 
 
 I take 20 because in ordinary thermometry the room is 
 usually about this temperature, and no reduction will be 
 necessary. However, 15 would not be inconvenient, or 
 10 to 20. 
 
 As I write these words I have a feeling that I may be 
 wrong. / Why should we continue to teach in our text-books 
 that heat has anything to do with temperature? It is decidedly 
 wrong, and if I ever write a text-book I shall probably use the 
 ice unit. ' But if I ever write a scientific paper of an experi- 
 mental nature, I shall probably use the other unit." 
 
APPENDIX II. 
 
 APPROXIMATE METHODS OF DETERMINING THE 
 MECHANICAL EQUIVALENT. 
 
 As stated at the close of the second Lecture, I give the following 
 notes in the hope that they may be found useful by teachers. 
 
 Experiment I. A very thin-walled brass tube, diameter 
 about 9 cm., length 110 cm., was surrounded by wrappings of 
 asbestos and then firmly fixed within a strong iron cylinder 1 . 
 The ends of the tube were closed by brass plates and those of 
 the cylinder by iron plates, the end spaces being also filled 
 with asbestos. 
 
 A quantity of lead shot was placed within the brass tube, 
 the distance from the surface of this shot to the opposite end 
 of the tube being 102 cm. when the tube was vertical. 
 
 A small thin-walled re-entering tube, whose diameter was 
 just sufficient to contain the bulb of a thermometer, was so 
 fixed that its closed end was in the middle of the shot, while 
 its open end was in the flat surface at the base of the iron 
 cylinder. The temperature of the shot was determined by 
 inserting the thermometer in this tube at the beginning 
 and end of an experiment. 
 
 The iron cylinder was clasped at its centre by a band fixed 
 to the end of a horizontal axis, and at the further end of that 
 axis was placed a cross-bar terminating in handles. The 
 bearings of the axis were supported on a firm stand. If the 
 
 1 This apparatus is merely a more elaborate (and therefore probably 
 inferior) form of that described in Edser's Heat, p. 272. 
 
124 Measurement of Energy 
 
 cylinder was rotated with sufficient rapidity the shot did not 
 fall, even when the loaded end was uppermost; but if the 
 motion was then arrested, the shot fell through 102 cm. on to 
 the flat plate at the lower end of the brass tube. 
 
 A projecting bar, controlled by springs, was fitted on to 
 the stand in such a manner as to arrest the motion of the 
 cylinder whenever it assumed a vertical position. The energy 
 due to the motion of the cylinder was chiefly expended in 
 warming the surfaces rubbed by these springs. 
 
 If h is the distance through which the shot falls in each 
 stroke, then its kinetic energy when reaching the lower end 
 is ^rav 2 , i.e. mgh. Thus the work done in n strokes is n . mgh. 
 Let the rise in temperature of the shot be 6 and o- the specific 
 heat of the lead. Then heat developed = crmO. 
 
 n . mgh ngh 
 
 6<r 
 
 In the actual experiment performed at the close of the 
 lecture, 50 strokes were given and h =102 cm. 
 
 .'. ngh - 5,000,000 approximately. 
 
 The observed rise in temperature was 3 -4 C. and we may 
 take a-= -033. 
 Therefore 
 
 In this case it would be difficult to estimate the loss of 
 heat by radiation, etc., or to allow for the thermal capacity 
 of the tube. Even if such corrections were possible they 
 would have little significance, and their insertion would 
 impart a false appearance of accuracy to the results. 
 
 The experiment is useful educationally if regarded rather 
 as an illustration of the conversion of kinetic energy into 
 heat, rather than as an attempt to obtain a numerical value 
 of the equivalent. 
 
Appendix II 
 
 125 
 
 Experiment II. In all essential points the following 
 method is similar to that adopted by Joule (in his later 
 experiments) and by Rowland. 
 
 Although results obtained by this apparatus cannot of 
 course (in the absence of elaborate precautions) lay claim 
 to a high order of accuracy, yet, in the hands of a capable 
 student, the probable error should not exceed 1 to 2 per cent. 
 A higher order of accuracy would be useless, for the errors in 
 thermometry would, under ordinary circumstances, be of the 
 same order. In the example given (infra) I have reason to 
 believe that the error of the thermometer is probably of the 
 order of 1 per cent, over the range 10 to 35 C. 
 
 Fig. 18. 
 1. Description of the apparatus 1 . In the machine 
 
 1 This account of the apparatus has, by the kind permission of 
 Mr G. F. C. Searle, been copied from the note-book prepared by him for the 
 
126 
 
 Measurement of Energy 
 
 used for this experiment, a vertical spindle carries at its upper 
 end a brass cup A (Fig. 18). Into an ebonite ring concentric 
 with A there fits tightly one of a pair of hollow truncated 
 cones. The second cone C (Fig. 19) fits into the first one and 
 is provided at its upper edge with a pair of steel pins which 
 correspond to the two holes in a grooved wooden disc B 
 (Fig. 18). In the experiment, the disc B prevents the inner 
 cone from revolving when the spindle and the outer cone 
 revolve, and the friction between the two cones gives rise to 
 heat. A cast-iron ring, resting on the disc and fixed by two 
 pins, serves to give a suitable pressure between the cones. 
 
 A 
 
 Fig. 19. 
 
 A brass wheel is fixed to the spindle (Fig. 18), and by a 
 string passing round this wheel, and also round a handwheel, 
 motion is imparted to the spindle. A pair of guide pulleys 
 prevents the string from running off the wheel. Above the 
 wheel is a screw cut upon the spindle which moves a 
 cogwheel of 100 teeth, which makes one revolution for each 
 100 revolutions of the spindle. 
 
 To the base of the apparatus one end of a cranked steel 
 
 use of students at the Cavendish Laboratory. A few trivial alterations 
 have been made therein in consequence of certain slight modifications 
 introduced into the apparatus used by me at Leeds. 
 
Appendix II 127 
 
 rod is attached and the rod can be fixed in any position by a 
 nut beneath the base. The other end of the rod carries a 
 cradle in which runs a small guide pulley, this pulley being on 
 the same level as the disc. The cradle turns freely about a 
 vertical axis. 
 
 A fine string (plaited silk fishing line) is fastened to the 
 disc and passes along the groove in its edge ; it then passes 
 over the pulley and is fastened to M, a mass of 200 or 
 300 grammes. On turning the handwheel it is easy to 
 regulate the speed so that the friction between the cones 
 just causes M to be supported at a nearly constant level. 
 
 Through unskilful driving of the handwheel, the string 
 may slip off the guide pulley, and in consequence off the disc ; 
 the mass M may also be wound up over the guide pulley. To 
 prevent the string from running off the guide pulley, a stiff 
 wire with an eye is fixed to the cradle, in such a manner that 
 the eye is on the same level as the groove of the pulley and 
 about 5 cm. from the axle of the pulley towards the disc. If 
 the string is passed through this eye it will always turn the 
 cradle so that the string runs fairly over the pulley. In order 
 to prevent the mass M from being wound up over the pulley 
 an eye is fixed to the steel rod, and the string supporting M 
 passes through this eye. With these arrangements it is 
 impossible either to throw the string off the guide pulley or 
 to wind M up over the pulley. 
 
 2. Setting up the apparatus. Two tables wilj, 
 generally be required. The frictional machine is firmly 
 clamped to one table, and the handwheel is clamped to 
 the other table at a distance of 10 or more feet. Care 
 must be taken that the driving string runs properly, without 
 any risk of slipping off the handwheel. The steel rod is also 
 fixed in a convenient position. 
 
 A thermometer is hung from a support so that it passes 
 through the central aperture in the disc, and almost touches 
 
128 Measurement of Etiergy 
 
 the bottom of the inner cone. The thermometer should also 
 pass through the hole in the stirrer. 
 
 The string supporting M should be of such a length, that 
 when as much as possible has been unwound from the disc, 
 M is not quite in contact with the floor. 
 
 Before putting the cones together the rubbing surfaces 
 must be carefully cleaned, and then four or five drops of oil 
 must be put between them ; the bearings of the spindle and 
 guide pulleys should also be oiled. 
 
 3. Method of experimenting. The cones, cleaned and 
 oiled, are weighed, together with the stirrer. The inner cone 
 is then filled with water up to about 1 cm. from its edge, and 
 the system is again weighed. The water should be at the tem- 
 perature of the room. The apparatus is now put into working 
 order, the counting wheel having previously been brought to 
 its zero position. One observer, X t takes his place at the 
 hand wheel, and a second observer, Y, at the machine. After 
 the initial temperature of the water has been carefully 
 observed, the operator X turns the handwheel at such a rate, 
 that the mass M is raised so far from the floor that the string 
 supporting M is a tangent to the edge of the disc. If the 
 string is not a tangent to the disc the moment of the tension 
 about the axis of revolution is seriously diminished. The 
 observer Y stirs the water and notes the temperature at the 
 end of each 100 revolutions of the spindle. He gives a signal 
 as each 100 revolutions is completed, and X notes the time 
 upon a watch. After 'Y has recorded the temperature upon a 
 sheet of paper previously ruled for the purpose he also records 
 the time observed by X. Very accurate readings of these 
 temperatures and times are difficult to make and are not 
 necessary. When M is 200 grammes the temperature will 
 rise about 0'8 C. for each 100 revolutions of the spindle in 
 the case of apparatus similar to that used in the lecture. 
 It will be found that the time occupied by 100 revolutions of 
 
 
Appendix II 129 
 
 the spindle diminishes as the temperature rises ; this effect is 
 due to the diminution of the viscosity of the oil between the 
 cones, consequent upon the rise of temperature. 
 
 After about 1000 revolutions have been made by the 
 spindle the motion is stopped, and the highest temperature 
 shown by the thermometer is carefully read. The index of 
 the counting wheel is also observed, and from this reading 
 and the number of complete revolutions made by the counting 
 wheel the exact number of revolutions made by the spindle is 
 ascertained. 
 
 Without disturbing the apparatus the water is allowed to 
 cool, and observations of the temperature are taken at the end 
 of each one or two minutes till the water is only slightly 
 (2 degrees or so) above the temperature of the room. 
 
 4. Calculation of the correction for cooling. If 
 there had been no loss of heat during the time that the 
 apparatus was in action, the difference between the final and 
 initial temperatures of the water could be used in the calcula- 
 tion, without any correction. The correction necessary to 
 allow for the loss of heat in the actual case is ascertained in 
 the following manner. From the observations taken, a curve 
 is plotted, (the abscissae denoting time, the ordinates tempera- 
 ture) showing how the temperature increased with the time. 
 On account of the increase of speed, due to the diminution in 
 the viscosity of the oil, the curve is concave upwards. 
 
 From the observations on the cooling of the water a second 
 curve is drawn with time as abscissa, and temperature as 
 ordiiiate ; and from it the rate of cooling in degrees per minute 
 at any particular temperature is determined by the slope 
 of the tangent to the curve. It is best not to actually draw 
 the tangent. If a triangular "drawing square" ABC be 
 adjusted so that one of its edges AB touches the curve at 
 the desired point, and if one of the other sides, as A, be 
 
 G. 9 
 
130 Measurement of Energy 
 
 made to slide along a straight edge, AB can be moved parallel 
 to itself until it passes through an intersection of the lines 
 ruled on the squared paper. It is now easy to read off along 
 the edge of the square the number of degrees lost in 10 
 minutes. Dividing this number by 10, the rate of cooling, in 
 degrees per minute, is obtained for the particular temperature 
 at which the tangent was taken. 
 
 A third curve is now constructed. From the first curve 
 the temperatures of the water at the end of 1, 2, 3... minutes 
 are determined, and by the second curve the rates of cooling 
 at these temperatures are determined. The third curve is 
 drawn with the time as abscissa and the corresponding rate 
 of cooling as ordinate. The origin is one point on the curve, 
 since the water was initially at the temperature of the room. 
 The area included between the line of times, the curve and 
 the ordinate corresponding to the time when the highest 
 temperature was noted, represents the total loss of temperature 
 during the- experiment. If 1 inch (or cm.) on the squared 
 paper corresponds to p minutes, and 1 inch (or cm.) corre- 
 sponds to q degrees per minute, then each square inch (or 
 square cm.) represents^ degrees. 
 
 (If the original temperature was below that of the room 
 experiments must be made to determine the rate of heating 
 for the lower temperatures. In this case part of the curve 
 will lie below the axis of time, and the area of that part is to 
 be taken as negative.) 
 
 5. Calculation of the Mechanical Equivalent of 
 Heat. When the spindle has made n turns, the work which 
 has been spent in overcoming the friction between the two 
 cones is the same as if the outer cone had been fixed and the 
 inner one had been made to revolve by the mass M grammes. 
 In the latter case M would have fallen through 2irnr cm., 
 where r centimetres is the radius of the groove of the wooden 
 
Appendix II 131 
 
 disc. Hence the total work spent upon overcoming friction 
 is 2irnrMg ergs. 
 
 Let W be the mass of the water in grammes. 
 w ,, cones and stirrer. 
 
 The specific heat of the brass, if not previously determined, 
 may be taken as '095, and thus the system of cones, stirrer 
 and water is thermally equivalent to (TT+'095w) grammes 
 of water. 
 
 (If the thermometer has a large bulb it is necessary to 
 take account of its water equivalent. Its water equivalent 
 is found by heating the thermometer and plunging it while 
 hot into a small vessel containing a known quantity of water 
 at a known temperature. From the rise of temperature the 
 water equivalent is calculated. Its value must be added to 
 JF+-095 in the equation for J.) 
 
 Let be the observed rise of temperature, and < the 
 calculated total loss of temperature during the time for which 
 the experiment was in progress. Then the total number of 
 thermal units produced is (JF+'095w;) (6 + <) water gramme 
 degrees. 
 
 If J denote the number of ergs of work which must be 
 spent to produce one thermal unit, we have 
 
 = 
 
 As an example I give the details of the following experi- 
 ment, which was performed before the lecture ; as it would 
 have been impossible to obtain the cooling curve in the time 
 available during, or after, its close. The working of the 
 apparatus was however exhibited, and the experimental num- 
 bers previously obtained were given ; with a request that 
 the results should be worked out before the following meeting. 
 
132 
 
 Measurement of Energy 
 
 DETAILS OF AN EXPERIMENT PERFORMED 
 MARCH QTH, 1901. 
 
 Weight of the two brass cones and stirrer = 164'1 grms. 
 
 ,, ,, contained water =21 '35 
 
 Suspended mass =300 
 
 Circumference of wheel =78-40 cm. 
 
 Specific heat of brass cones and stirrer ='095 
 Capacity for heat of thermometer =0'1 
 
 During experiment the external temp, rose from 10-2 to 10'6 C. 
 TABLE A. TABLE B. 
 
 Rate of rise during rotation. Observations on rate of cooling 
 
 after experiment. 
 
 Ti 
 
 Minutes 
 
 me 
 Seconds 
 
 Temperature C. 
 
 
 
 
 
 10-4 
 
 
 
 50 
 
 no 
 
 2 
 
 25 
 
 12-0 
 
 3 
 
 57 
 
 13-0 
 
 5 
 
 23 
 
 14-0 
 
 6 
 
 45 
 
 15-0 
 
 7 
 
 58 
 
 16-0 
 
 9 
 
 12 
 
 17-0 
 
 10 
 
 15 
 
 18-0 
 
 11 
 
 8 
 
 19-0 
 
 12 
 
 
 
 20-0 
 
 12 
 
 45 
 
 21-0 
 
 13 
 
 28 
 
 22-0 
 
 14 
 
 8 
 
 23-0 
 
 14 
 
 46 
 
 24-0 
 
 15 
 
 22 
 
 25-0 
 
 15 
 
 50 
 
 26-0 
 
 16 
 
 11 
 
 27-0 
 
 16 
 
 37 
 
 28-0 
 
 17 
 
 2 
 
 29-0 
 
 17 
 
 23 
 
 30-0 
 
 
 
 
 
 31-0 
 
 18 
 
 
 
 32-0 
 
 18 
 
 13 
 
 33 -O 1 
 
 18 
 
 20 
 
 331 2 
 
 Ti 
 
 Minutes 
 
 me 
 Seconds 
 
 Temperature C. 
 
 18 
 
 13 
 
 33 -O 1 
 
 18 
 
 20 
 
 33-1 
 
 18 
 
 50 
 
 32-6 
 
 19 
 
 32 
 
 32-0 
 
 20 
 
 39 
 
 31-0 
 
 21 
 
 57 
 
 30-0 
 
 23 
 
 20 
 
 29-0 
 
 25 
 
 2 
 
 28-0 
 
 26 
 
 43 
 
 27-0 
 
 28 
 
 42 
 
 26-0 
 
 30 
 
 44 
 
 25-0 
 
 32 
 
 59 
 
 24-0 
 
 35 
 
 56 
 
 23-0 
 
 39 
 
 10 
 
 220 
 
 42 
 
 42 
 
 21-0 
 
 46 
 
 10 
 
 20-0 
 
 50 
 
 42 
 
 19-0 
 
 55 42 
 
 18-0 
 
 61 
 
 15 
 
 17-0 
 
 1 Eotation stopped. 
 
 1 Eotation stopped. 
 
 2 Highest temperature reached. 
 
 Total number of re volutions = 1854. 
 
Appendix II 133 
 
 REDUCTION OF THE RESULTS. 
 
 Capacity for heat of cones, thermometer and water =37 '05. 
 Observed rise in temperature = 22'7C. 
 
 Loss of temperature by radiation, etc. =4-52. 
 
 Hence total heat evolved = 37 '05 x 27 '22 thermal units. 
 Work done = 1854 x 78'4 x 300 x 981 = 4277 x 10 7 ergs. 
 4277 x TO 7 
 
 This is the mean value over the range 10 to 33 C. by a mercury- 
 in-glass thermometer. The value would probably be raised by 
 reduction to the H scale. 
 
APPENDIX III. 
 
 COPY OF RESOLUTIONS PASSED BY THE ELECTRICAL 
 STANDARDS COMMITTEE OF THE BRITISH ASSOCIA- 
 TION IN 1896. 
 
 Propositions. 
 
 " I. The fundamental thermodynamic unit of heat is 
 10 7 ergs, to which unit the name joule has already 
 been given by the Electrical Standards Committee 
 of the British Association. 
 
 For many practical purposes heat will continue to be 
 measured in terms of the heat required to raise a measured 
 mass of water through a definite range of temperature. If 
 the mass of water be 1 gramme, and the range 1 C. in the 
 neighbourhood of 10 C., then the number of joules required 
 will be approximately 4-2. It will be convenient to fix upon 
 this number of joules as a thermometric unit of heat, and to 
 state 
 
 "jll. The thermometric unit of heat is 4-2 joules. 
 
 According to the best of the existing determinations (see 
 Mr Griffiths' paper already quoted), this is the amount of heat 
 required to raise 1 gramme of water from 9 '5 C. of the scale 
 of the hydrogen thermometer to 10 '5 of that scale. 
 
Appendix III 135 
 
 Accordingly for the present [or until the year 1905?] a 
 third proposition would be 
 
 " III. The amount of heat requisite to raise the tempera- 
 ture of 1 gramme of water 1 C. of the scale of the 
 hydrogen thermometer from 9 '5 to 10 '5 C. of 
 that thermometer, is equivalent to one thermo- 
 metric unit of heat. 
 
 In case further research should show that this statement is 
 not exact, the definition could be adjusted by a small alteration 
 in the mean temperature at which the rise of 1 takes place. 
 The definitions in I. and II. would remain unaltered." 
 
 As the conclusion given in Proposition III. of this Report 
 differs considerably from that given on page 110, I take this 
 opportunity of calling attention to the following points : 
 
 (1) The revision of Rowland's results, the determinations 
 of Reynolds and Moorby, and of Callendar and Barnes had 
 not been accomplished at the time the Committee presented 
 the above Report. 
 
 (2) It will be seen (supra) that Proposition III. was 
 regarded by the Committee as a provisional statement. 
 
 (3) The effect of the subsequent increase in our knowledge 
 is to shift the probable temperature at which the capacity for 
 heat of water is 4-2 joules to about 7'5 C. This temperature 
 is certainly inconveniently low and therefore it is desirable 
 that a change should now be made in Proposition III. 
 
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