and the Partition of Thermal Energy. 681 



Compressibility 0=^=^ x j^aj. 



' 19x19x^2 19 /*0 ... 



■*• ^=- 16UN ^ ° r ^T^VCM' • (4) 

 Taking C = '74x 10- 12 and (9 = 17° C, 



we get /3 = '76 xl0~ 16 for Cu. 



Substituting this value of /3, we have for Ou 

 F=l'lxlO- 5 and a = 4'4xl()- 10 . 



The value of ft for the different metals has been calculated 

 and shown in the second table. The values of B are 

 obtained by difference. 



10. The calculation of Young's modulus gives good 

 support to the previous work. Suppose that the bod}' is 

 stretched so that I increases by x. 



.'. Bl=Sa = x, where l = a + 2r. 



Putting a-\- x instead of a in art. 8, the half-period of 

 vibration 



t 1 = 2s/3(a + x)/V. 



The change of momentum per sec. is, therefore, 

 MV 2 == MV 2 / 1 x\ 



6(a + #) ~" 6a \ a)' 



The force of repulsion due to impacts is diminished by 

 MV 8 * 

 6a 2 ' 

 The force of attraction 



=/G + '*)-/(o+.«r<o, 



f" (I) being of course negative. 



The total change in the force of attraction per molecule 



-•{£♦«*}■ 



and the total change per unit area 



Now the extension is x/l. Young's modulus is, therefore, 



