Kinetic Theory of Solids. 225 



These give us the following mean values of Young's 

 modulus at 15° C. : — 







Table VII. 











io- 6 



imes Young's Modulus at 15° C. 





Cu. 



Ag- 



Aii. 



Mg. 



Zn. 



Od. 



Al. 



1220 



740 



760 



390 



930 



480 



680 



Sn. 



Pb. 



Fe. 



Ni. 



Co. 



Pd. 



Pt. 



420 



190 



2000 



2240 



1820 



1050 



1600 



In most cases these values must be close to the truth. 



3. Law of Variation of Young's Modulus with Temperature. 

 — By the light of the result for rigidity this law is easily 

 found ; temperature must only occur in the ratio 0/T, where 

 T is the melting-point ; and as a general survey of the values 

 of Young's modulus for different metals at different tempera- 

 tures shows that the modulus within our experimental range 

 is a linear function of the temperature, it was easy to test 

 whether the empirical equation q/Q,= l — ad/T would apply to 

 all the metals, Q being the rigidity at absolute zero, and a a 

 constant the same for all metals. The result was to find that 

 g/Q = l — , 823t/T represents with considerable accuracy all the 

 foregoing experimental results. But it is important to notice 

 that this can only rank as an approximate empirical relation 

 covering the range of temperature of my experiments, and 

 cannot rank as a natural law in the same way as the rigidity 

 relation n/N=l— (#/T) 2 , because it does not cover the range 

 of temperature right down to the melting-point ; the relation 

 gives a finite value for Young's modulus at the melting-point, 

 whereas it ought to give a zero value. The relation then does 

 not give the general law sought, and is only mentioned here 

 on account of its simplicity and the facilities it gives for 

 getting approximate values of Q, the Young's modulus at 

 absolute zero. 



As a theoretical relation between Young's modulus and 

 temperature will be investigated in the theoretical part of this 

 paper, and the values of Young's modulus at absolute zero 

 will be given there, there is no need to consider any further 

 the empirical relation. 



[To be continued..] 

 Phil. Mag. S. 5. Vol. 32. No. 195. August 1891. Q 



