540 Mr. W. Sutherland on a 



According to the kinetic theory of solids now under dis- 

 cussion, it is necessary, if the molecules of different metals are 

 not much different in shape, that the ratio of the domain of 

 the molecule at the melting-point to the volume of the mole- 

 cule should be the same for all, because melting is merely 

 the result of the domain reaching a size at which the molecule 

 escapes from it. Hence (1 + 6T)(1 + 6'T) is to be the same 

 for all, that is bT + b'T is to be constant; but b' — 6b, hence 

 bT is to be constant. Now in a previous paper (Phil. Mag. 



Oct. 1890) I mentioned that 6Tm G is nearly constant for the 

 metals, and used the result to calculate the periods of vibra- 

 tion of the molecules of solids at their melting-points with 



satisfactory results. But the range in the value of m for the 

 metals is not great, and it will be worth while tabulating side 



by side the values of bT and bTm* -. Fizeau's values of b are 

 used. 



Cu. Ag. Au. Mg. Zn. Cd. Al. 



1000 bT 22 24 19 27 20 18 26 



1000 6Tm*... 45 52 45 47 40 40 45 



In. Tl. Sn. Pb. Fe. Co. Ni. 



1000 bT 19 17 11 18 25 26 24 



lOOO&Twi*... 41 41 25 43 49 51 47 



Eu. Eh. Pd. Os. Ir. Pt. 



1000 bT 20 19 21 18 16 18 



1000 6Tm V ... 43 42 45 44 37 44 



This comparison shows that the requirement of theory that 

 bT should be constant is approximately satisfied, bT having a 



mean value *021 when tin is excluded; but as bTm* is more 

 nearly constant, having a mean value *044, it is evident that 

 the power of a molecule to break away from its domain de- 

 pends slightly on its mass, that dependence being expressed 

 in the empirical relation bTm e = constant. 



5. Periods of Vibration of the Molecules of Metals. — As the 

 vibrational motion of the molecules is fundamental to the 

 kinetic theory of solids here unfolded, it will be well at this 

 stage to secure such support for the theory as is given by the 

 harmonic relations I have shown to exist among the periods 

 of vibration of the molecules of metals at their melting-points 

 (Phil. Mag. Oct. 1890). The full swing of a molecule in one 

 direction is 



«-E = E (6T + &'T)=7E &T. 



