24 



NATURE 



[September 5, 1912 



of the probability of an arrangement. In a similar 

 way, some twent}' years ago the view was commonly 

 held that electric phenomena were due merely to strains 

 in the sether, and that the electric fluids had no exist- 

 ence except as a convenient means of mathematical 

 expression. Recent discoveries have enabled us to 

 form a more concrete conception of a charge of elec- 

 tricity, which has proved invaluable as a guide to 

 research. I'erhaps it is not too much to hope that it 

 may be possible to attach a similar conception with 

 advantage to caloric as the measure of a quantity of 

 heat. 



It has generally been admitted in recent years that 

 some independent measure of heat quantitj- as opposed 

 to heat energy is required, but opinions have differed 

 widely with regard to the adoption of entropy as the 

 quantity factor of heat. Many of these objections 

 have been felt rather than explicitly stated, and are 

 therefore the more difficult to answer satisfactorilv. 

 Others arise from the difficulty of attaching any con- 

 crete conception of a quantity of something to such a 

 vague and shadowy mathematical function as entropy. 

 The answer to the question "What is caloric?" must 

 necessarily be of a somewhat speculative nature. But 

 it is so necessary for the experimentalist to reason by 

 analogy from the seen to the unseen, that almost any 

 answer, however crude, is better than none at all. The 

 difficulties experienced in regarding entropy as a 

 measure of heat quantity are more of an academic 

 nature, but may be usefully considered as a pre- 

 liminary in attempting to answer the more funda- 

 mental question. 



The first difficulty felt by the student in regarding 

 caloric as the measure of heat quantitv is that when 

 two portions of the same substance, such as water, 

 at different temperatures are mixed, the quantitv of 

 caloric in the mixture is greater than the sum of the 

 quantities in the separate portions. The same diffi- 

 culty was encountered by Carnot from the opposite 

 point of view. The two portions at different tempera- 

 tures represented a possible source of motive-power. 

 The question which he asked himself may be put as 

 follows: — "If the total quantity of caloric remained 

 the same when the two portions at different tempera- 

 tures were simply mixed, what had become of the 

 motive-power wasted?" The answer is that caloric 

 is generated, and that the quantity generated is such 

 that its energy is the precise equivalent of the motive- 

 power which might have been obtained if the transfer 

 of heat had been effected by means of a perfect engine 

 working without generation of caloric. The caloric 

 generated in wasting a difference of temperature is the 

 necessary and appropriate measure of the quantitv of 

 heat obtained by the degradation of available motive- 

 power into the less available or transformable varietv 

 of heat energy. 



The processes by which caloric is generated in mixing 

 substances at different temperatures, or in other cases 

 where available motive-power is allowed to run to 

 waste, are generally of so turbulent a character that 

 the steps of the process cannot be followed, although 

 the final result can be predicted under given conditions 

 from the energy principle. Such processes could not 

 be expected a priori, to throw much light on the nature 

 of caloric. The familiar process of conduction of 

 heat through a body the parts of which are at different 

 temperatures, while equally leading to the generation 

 of a quantity of caloric equivalent to the motive-power 

 wasted, affords better promise of elucidating the nature 

 of caloric, owing to the comparative simplicitv and 

 regularity of the phenomena, which permit closer ex- 

 perimental study. The earliest measurements of the 

 relative conducting powers of the metals for heat and 

 electricity showed that the ratio of the thermal to the 

 electric conductivity was nearly the same for all the 

 NO. 2236, VOL. 90] 



pure metals, and suggested that, in this case, the 

 carriers of heat and electricity were the same. Later 

 and more accurate experiments showed that the ratio 

 of the conductivities was net constant, but varied 

 nearly as the absolute temperature. At first sight this 

 might appear to suggest a radical difference between 

 the two conductivities, but it results merely from the 

 fact that heat is measured as energy in the definition 

 of thermal conductivity, whereas electricity is measured 

 as a quantity of fluid. If thermal conductivity were 

 defined in terms of caloric or thermal fluid, the ratio 

 of the two conductivities would be constant with 

 respect to temperature almost, if not quite, within the 

 limits of error of experiment. On the hypothesis that 

 the carriers are the same for electricity and heat, and 

 that the kinetic energy of each carrier is the same as 

 that of a gas molecule at the same temperature, it 

 becomes possible, on the analogy of the kinetic theory 

 of gases, to calculate the actual value of the ratio of 

 the conductivities. The value thus found agrees closely 

 in magnitude with that given by experiment, and may 

 be regarded as confirming the view that the carriers 

 are the same, although the hypotheses and analogies 

 invoked are somewhat speculative. 



When the electrons or corpuscles of negative elec- 

 tricity were discovered it w^as a natural step to identify 

 them with the carriers of energy, and to imagine that 

 a metal contained a large number of such corpuscles, 

 moving in all directions, and colliding with each other 

 and with the metallic atoms, like the molecules of a 

 gas on the kinetic theory. If the mass of each carrier 

 were 1/1700 of that of an atom of hydrogen, the 

 velocity at 0° C. would be about sixty miles a second, 

 and would be of the right order of magnitude to 

 account for the observed values of the conductivities of 

 good conductors, on the assumption that the number 

 of negative corpuscles was the same as the number 

 of positive metallic atoms, and that the mean free path 

 of each corpuscle was of the same order as the dis- 

 tance between the atoms. The same hypothesis 

 served to give a qualitative account of thermo-electric 

 phenomena, such as the Peltier and Thomson effects, 

 and of radiation and absorption of heat, though in a 

 less satisfactory manner. When extended to give a 

 consistent account of nil the related phenomena, it 

 would appear that the number of free corpuscles re- 

 quired is too large to be reconciled, for instance, with 

 the observed values of the specific heat, on the assump- 

 tion that each corpuscle possesses energy of translation 

 equal to that of a gas molecule at the same tem- 

 perature. 



Sir J. J. Thomson has accordinglv proposed and 

 discussed another possible theory of metallic conduc- 

 tion, in which the neutral electric doublets present in 

 the metal are supposed to be continually interchanging 

 corpuscles at a very high rate. Under ordinary condi- 

 tion these interchanges take place indifferently in all 

 directions, but under the action of an electric field 

 the axes of the doublets are supposed to become more 

 or less oriented, as in the Grotthus-chain hypothesis 

 of electrolvtic conduction, producing a general drift 

 or current proportional to the field. This hypothesis, 

 though fundamentally different from the preceding or 

 more generally accepted view, appears to lead to prac- 

 ticallv the same relations, and is in some ways pre- 

 ferable, as suggesting possible explanations of diffi- 

 culties encountered by the first theory in postulating so 

 large a number of free negative corpuscles. On the 

 otlier hand, the second theory requires that each 

 neutral doublet should be continually ejecting cor- 

 puscles at the rate of about 10" per second. There 

 are probablv elements of truth in both theories, but, 

 without insisting too much on the exact details of the 

 process, we mav at least assert with some confidence 

 that the corpuscles of caloric which constitute a cur- 



