542 Mr. W. Sutherland on a 



there are between 3 x 10 24 and 10 26 molecules in a cubic 

 centimetre of ordinary liquids and solids. Now the limiting 

 volume of a gramme of hydrogen is about 4 cubic centi- 

 metres, so that if we take 10 25 as the number of molecules in 

 a cubic centimetre of hydrogen H = 2*5 x 10~ 26 gramme, and 

 the numerical factor dropped above becomes 8 X 10" 14 , which 

 makes the absolute period of the Lithium molecule 1*6 X 10~ 14 

 second; that is to say, there are 6 x 10 18 complete vibrations 

 of the molecule in a second. Now the A line of the spectrum 

 represents 3*945 x 10 14 vibrations, and the II 2 line 7'628 x 10 14 

 vibrations per second, while in the dark part of the spectrum 

 Langley has found a line of l'l X 10 14 , and in the radiation 

 of bodies below 100° C. a line of 2 x 10 13 vibrations in a 

 second. Accordingly, the periods of vibration of the mole- 

 cules of the metals at their melting-points fall within the 

 limits of actually measured periods of non-luminous vibra- 

 tions. This fact supplies good general verification to the 

 theory, and shows how interesting a bolometric study of the 

 radiation of solids just about to melt would be. 



6. Comparison of the Theoretical Variation of Young's Modu- 

 lus with Temperature with the Experimental. — The next subject 

 to apply the theory to with advantage is the theoretical law 

 of variation of Young's modulus with temperature for com- 

 parison with the experimental results given in the introduc- 

 tion. The metals, as will yet be shown, may be assumed to 

 be approximately isotropic. In isotropic solids the relation 

 between q, n, and k is q = 9kn/(3k-\-n). Now in the intro- 

 duction it was shown for all the metals that n/N=l — {0/T) 2 , 

 where N is rigidity at absolute zero, and from the theoretic 

 equation (11) we have the values of k at all temperatures, 

 and 



3N{l-(<9/T) 2 } 

 2~l + N{l-(0/T) 2 }/3F 



Now, according to (11), k is infinite at absolute zero, which 

 we will interpret to mean that it is very large, and hence Q 

 the value of Young's modulus q at absolute zero is 3N. 

 Accordingly we have 



Q{l-(0/T) 2 }(l/ ? -l/9F>=l . . . (13) 



as the definitely prescribed law of variation of Young's mo- 

 dulus with temperature. Because of this definite theoretic 

 relation I did not, in the introduction, dwell on the demon- 

 stration of any empiric relation, but the values given for 

 different temperatures and different metals will now furnish a 



