402 MATHEMATICAL APPENDICES 23* 



Hence, in addition to the former equations of condition given 

 in 21*, we have six new ones of which the first three 



= 

 = 



agree with those already established in 17* for monatomic 

 molecules. The three others we can write only in the unsimplified 

 form 



= S s.m 



du 

 = SS.ra 



I dn d$ dm 



= ss.m 



L cZu 



since we do not know in what way the position given by x, 9, , 

 which an atom has inside the molecule, depends on the components 

 tl, t>, tt) of its velocity. 



In order to take account of these conditions we have again to 

 multiply each by a coefficient and then add it to the principal 

 equation, whereupon the resulting equation may be broken up into 

 a number of formulae. In this way we obtain the equations found 

 already in 17* for monatomic molecules, viz. 



= 



= + Mm(v -p + zt-xQ 



JJ av 



= 1 ? + 2km(w - 7 + xrj- yf), 



in which k, a, (3, y, g, -rj, are constants, and also the new 

 equations 



