Kinetic Theory of Solids. 541 



Let M stand for the molecular weight of a molecule re- 

 ferred in the ordinary way to that of hydrogen, and let H 

 denote the real mass of a molecule of hydrogen, then the 

 swing of a molecule is. 



7(MH/» i 044/M\ 

 But its translatory kinetic energy is 



pfflr^JcMHT, 

 v=V2JcMT/M, 

 and accordingly the period of a complete vibration is 



M 3 2 x 7 x '044H* 

 p^T' \/2J6M ' 

 For comparative values we can drop the whole numerical 

 factor and take W/p*& as measuring the relative periods. 

 In the subjoined table I replace the erroneously copied values 

 for the beryllium family, given in my former paper, by the 

 correct ones. 



Relative Periods, M*/p* T *. 



Li. Na. K. Eb. Cs. Cu. Ag. Au. 



•205 -43 '66 -96 1-22 -21 -29 '35 



Be. Mg. Ca. Sr. Ba. Zn. Cd. Hg. 



•107 -22 -34 -51 -63 -32 -47 *94 



Al. La. Ga. In. Tl. 



•20 -55 -54 -57 -65 



Fe. 



Co. 



Ni. 



Ru. 



Rh. 



Pd. 



Os. 



Ir. 



Pt. 



•16 



•16 



•17 



•21 



•20 



•24 



•23 



•25 



•27 



In the Li family the periods run as 1, 2, 3, 4*5, 6 with 

 the copper sub-family connected ; in the Be family the 

 periods run as 1, 2, 3, 4*5, 6, with the zinc sub-family re- 

 lated in somewhat the same way as the copper to the lithium, 

 but not exactly. Al and La have periods nearly as 2 to 6. 

 The other periods do not call for comment at present ; but it 

 is worth noting that the periods of the Be family are half 

 those of the Li family. These beautiful harmonic relations 

 almost amount to a proof that the expansion of the metals is 

 a true measure of the amplitude of vibration of their mole- 

 cules. It will be interesting to try to get an absolute value 

 of one of these periods, and compare it with known periods 

 of light- and heat-vibrations. Sir W. Thomson estimates that 



