594 Prof. R. C. Tolman on the Relativity Theory : 

 particles which impinge per second will be 



1 



V-^-l I I ae d^d^d^ 



V J+x Jo Jo 



and their change in momentum, allowing for the effect of 

 the rebound, will be 



f+ x +d* x r» n* _ h jv +m 2 

 NrfSt It ae ^^ ° ^ x obd^ x d^ y d^r z . 



J^x Jo Jo 



Finally, the total change in momentum per second for all 

 particles can be found by integrating for all possible values 

 of y]r x . Equating this to the total force pd& we have 



Jo «^o Jo 

 Cancelling <:ZS, multiplying both sides of the equation by the 



volume V and substituting - for -\jr x we have 



Vl + v 2 



/'too /-ioo n* 

 V = NVl i ae :2Z— d+ m d^ 9 d+ M . 



Jo Jo *^o 



— h V^ 2 +«»o 2 w o^' 2 



But this by equation (12) reduces to 



■ 'i 



or since 



1 L/l- W SJav. 



m v 2 m x 2 m y 2 m z 2 



VT^T 2 = y/T=?. + x/l^^ 2 + a/1^ 2 



we have from symmetry, 



Since at a given temperature we have seen that the term in 

 parenthesis is independent of the volume and the nature of 

 the particles, we see that the laws of Boyle and Avogadro 

 hold also in relativity mechanics for a system of particles *. 

 For slow velocities equation (16) reduces to the familiar 



N 

 expression pY= ^(m Q v 2 ) &x . 



* Compare Jiittner, loc. cit. 



