362 LORD RAYLEIGH ON THE COMPRESSIBILITY OF GASF.S 



Our equations expressing that the quantities of gas are the same at the single and 

 at the doubled pressures accordingly take the form 



H 2 f V, V s V 5 1 . . E(H } +H. 2 )j jVi _, V 3 +V 4 1 



l+mT,ll+00, 1+0T, l+0i/ ' l+mT 2 U+00 2 1+0T.J' 



H 2 f V 3 . V' s 1 



l+mT 3 U+0T 3 ~ l ~l+0 3 j" l+mr 4 1+0T 4 ' 



where B is the numerical quantity to be determined according to BOYLE'S law 

 identical with unity. 



By subtraction and neglect in the small terms of the squares of the small 

 temperature differences, we obtain 



1 B(H,+H 2 ) 



v i 



v i 



The first three terms on the right, viz., those in V 8 , V 4 , V 6 , vanish if T! = T S , 

 T 2 = T 4 , Tj = T 3 , T 2 = T 4 , t = t & . If in general R denote the sum of the five terms, 

 we may write with sufficient approximation for the actual experiments 



B = 



It may be well to exhibit further the steps of the reduction in the case of hydrogen 

 above detailed. The five terms composing R are 



Term in V 8 = '000038 



V 4 =- '000009 



V 6 =+ '000026 



Term in V 4 -V 4 = -'000775 



V 5 -V' 5 = +'001027 



R= +-000231 



