hersey: derivatives of physical quantities 623 



Comparing (10) and (11) 



u dcf> _ QiH / 1 5Qp a \ (12) 



du~ a \Q dQ 1 QJ K 



Similarly 



u d<f> _ Q 2 U / 1 dQo j3 \ , . 



du" p \Q bQ 2 QJ ) 



Comparing (12) and (13) 



<>Qo _ foe \ Q a Q 2 bQ Q n .. 



Hence the desired relation (2) has the linear form 



^=a + b^ (15) 



in which the coefficients 



.-(=*-«.)§ (16) 



and 



b = «9l (17) 



involve none of the N quantities save Q , Q lf and Q 2 . 

 Evidently (14) can be written also 



dlogQo (<* R \ adlogQo nQ N 



___^ - ao j + ___ (18) 



in which the coefficients are independent of the coordinates. 

 Thus the relation connecting the logarithmic derivatives is the 

 same all over the generalized surface. , 



Extension to higher derivatives. Differentiating (14) with re- 

 spect to Qi and using the identity (3) gives 



^=A+B^ +C ^-° (19) 



cQl dQ 2 dQl 



in which the coefficients are 



■ A -Sfe fc — )&*— '- 1 ) (2P) 



