234 



NA TURE 



[July 3, 1884 



on the botanical discoveries of M. Roezl in America, and two 

 -fine coloured plates of Cypripedium Spiccrianum, and Aphelandra 



Marnirit.r. 



SOCIETIES AND ACADEMIES 

 London 

 Royal Society, June 10. — "The Influence of Stress and 

 Strain on the Physical Properties of Matter." l Part I. Moduli 

 of Elasticity — continued. Relations between Moduli of Elasti- 

 city, Thermal Capacity, and other Physical Constants. By 

 Herbert Tomlinson, P. A. Communicated by Prof. W. Grylls 

 Adams, M.A , F.R.S. 



The thermal capacity of each of the wires already used for the 

 experiments on moduli of elasticity and electrical conductivity 

 described in Parts I. and II. of this paper- was determined. 



Every precaution was taken both with regard to the instru- 

 ments themselves and the mode of using them to avoid error, 

 and the formula 1 given below may be received with great con- 

 fidence. 



It will be seen that the thermal capacity of all the metals 

 examined increased with die temperature, a result which we find 

 confirmed by the observations of other investigators. 



The thermal capacities of the alloys platinum-silver and 

 German-silver are, within the limits of error, exactly the same as 

 those calculated from the proportions of their components. Ther- 

 mal capacity is, therefore, a physical property which is not 

 likely to be altered to any appreciable extent by small impuri- 

 ties, so that the results obtained by different experimenters agree 

 very closely with each oilier. 



It has been proved 3 that if e be taken to denote "Young's 

 Modulus," and a the mean distance between the centres of two 

 adjacent molecules, c X a 7 is in the case of most metals ap- 

 proximately a constant. From this it would follow that the law 

 of force proved by Maxwell in his experiments on the viscosity 

 of gases 4 to exist between the molecules of a gas is approxi- 

 mately true for solids, accordingly the force between any two 

 adjacent molecules of a solid is approximately .is the fifth power 

 of the distance between their centres. Now if we denote the 

 atomic mass by A, the density by A, the thermal capacity per 

 unit mass by C„„ and the thermal capacity per unit volume by 

 •C r , we have the following relations : — 



( ' X A = a constant ; 



c, = a x < : ; 



• X a 7 = a constant ; 



A \' 



ay 



examined, but also in the case of a great many substances for 

 which the values of C ;/ and e have been determined by other 

 investigators. 



Still more approximately is it believed that this relation would 

 hold good if for " Young's Modulus " the bulk-modulus of elas- 

 ticity were substituted. Denoting the bulk-modulus by e w it 

 was found that, within the wide limits of error to which de- 

 terminations of the value of the bulk-modulus are liable to be 

 affected — 



1 



a constant. 



Neither of the above relations can be true for all temperatures, 

 inasmuch as, whilst the value of e- diminishes with rise of tem- 

 perature, that of C- increases, but at ordinary temperatures it 

 seems that the bulk-modulus of elasticity can be calculated from 

 the thermal capacity per unit volume by the formula — 

 e., = 2071 X io 6 C„5- 



The thermal capacity per unit volume increases with the tem- 

 perature, and the researches of Matthiessen, Fizeau, and others 

 on the one hand, and of Kohlrattsch on the other, have shown 

 thai there is a like increment in the thermal expansibility and 

 torsionability l of metals. A careful comparison was made of 

 the various increments above mentioned, and it is shown in the 

 paper that whilst the ratio of increase per unit of exparisil ility 

 with rise of temperature to corresponding value in the casi oi 

 torsionability - is, v ithin the limits of error of observation, unity, 

 that in which thermal expansibility and thermal capacity are 

 concerned is about two, so that the rate at which thermal expan- 

 sibility increases with the temperature is about twice the rate at 

 which thermal capacity increases. The rate of increase of both 

 thermal expansibility and thermal capacity varies with the nature 

 of the metal, being greatest for iron and least for platinum. 



'1 lie so-called "real thermal capacity" of a solid may be found 

 by dividing the thermal capacity of hydrogen per unit mass at 

 constant volume, namely, 2-417, by the atomic mass ; and this 

 part of the capacity will be independent of the temperature. It 

 the " real capacity " be subtracted from the total thermal capacity 

 we obtain that part of the capacity which does vary with the 

 temperature, and which has therefore in this paper been desig- 

 nated the "variable thermal capacity." The following table 

 shows that the rate of increase per unit of thermal expansibility 

 is at 0° C, and therefore at any temperature, equal to the increase 

 p. r unit oj Ike " variable capacity" : — 



From these 1 lations we obtain 



or that the cube of "Young's Modulus" varies as the seventh 

 power of the thermal capacity per unit volume. This relation 

 was found to hold approximately not merely for the metals here 



1 The original title of tin 

 nore exact in e 



5 Loc. at 



■ has been altered to the above, a- being 

 'Phil. Trans, part i .. i " p. i. 

 186 . v,,!. 1 xv,i. part i. 



It is shown in the paper that the thermal capacity "per unit 

 mass is nearly two and a half times the " real capacity," so that 

 only two-fifths of the whole thermal energy which we may im- 

 part to a mass of metal goes towards raising the temperature, 

 the remaining three-fifths being expended in internal and ex- 

 ternal work. The external work is practically insensible in 

 ordinary cases. Of the internal work, that expended against 

 bulk-elasticity amounts in the limiting cases from i/l, oooth to 

 i,'io,oooth of the whole, and, though greater than the external 

 work, is almost insensible; moreover, there seems to be no re- 

 lationship whatever between the whole thermal capacity per 

 unit volume and the work done against bulk-elasticity. 



Raoul Pictet has concluded 3 that the amplitude of the oscil- 

 lation of molecules around their positions of equilibrium may be 

 taken as corresponding to temperature, and in the case of several 

 ire 11I- Ins shown that 



T X /3 X a = a constant, 



■ 1 he imerse of "simple rigidity." 

 2 Iron and copper are the only two metals for v 

 ability u ith rise of temperature has been t 



*. X A I 1 RE, ' ';e. ]'. 356, 



