566 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5 1 



elementary masses and therefore by making use of the equation 

 (a) § 13 we have 



a v dpl a r dp2 



dm. — — B. — — am 2 = — B 2 — ~ 



g g 



Substituting hereafter only approximate values we obtain 



f , k B,B 2 C Vm Po" ~ Pi 



f , k B X B 2 r p ° 2 p 2 - p h 



We may remark that although in the development of the binomials 



we previously retained only the terms of the first degree in — h 



Ph 

 yet on account of the limits of these definite integrals, they are 

 accurate to terms of the second degree. 

 From equation (a) there results 



J »»ft dp ' = J *»A dp < = J. R dz= H 



If we introduce the average temperatures T* and T 2 * of the 

 masses i and 2 as determined by the equations 



T t * (P01 " Ph) = J p r » d ^> T * &» - ^) = J p ^ 2 dp, 



we thus obtain for the above integrals 



J ( r - 25 dm, - - • y J r* ( Po -p h ) - R P M ] 



r , x B , B , ! g h 1 



J ( r t - 15 dm^-.^y [t* (*;.-« - -r A ) 



These expressions may be still further simplified if we introduce 

 other average temperatures Q l and 2 which for distinction we will 



