110 Mr. H. Tomliiison. The Influence of [June 19, 



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 examined, but also 

 in the case of a great many substances for which the values of C r 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 elasticity 

 were substituted. Denoting the bulk-modulus by e t , it was found 

 that, within the wide limits of error to which determinations of the 

 value of the bulk-modulus are liable to be affected 



___=a constant. 



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

 inasmuch as whilst the value of e, diminishes with rise of temperature, 

 that of C P increases, but at ordinary temperatures it seems that the 

 bulk-modulus of elasticity in grammes per square centimetre can be 

 calculated from the thermal capacity per unit volume by the formula 



e r =2071 x 10C r 5 



The thermal capacity per unit volume increases with the tempera- 

 ture, and the researches of Matthiessen, Fizeau, and others on the 

 one hand, and of Kohlrausch on the other, have shown that there is a 

 like increment in the thermal expansibility and torsionability* 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 expansibility with rise of temperature to 

 corresponding value in the case of torsionabilityf is, within 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 expansibility 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. 



The 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. If 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 designated the "variable 



* Tho inverse of " simple rigidity." 



t Iron and copper are the onlj two metals for which the increase of torsionabilit v 

 with rise of temperature" has been examined. 



