GENERAL EQUATIONS. 6ll 



On the other hand, we have by equations (12) of (572), 



and the equations (2) of (567) give 



fii- - J=i + -- + J -AF = AF, 



in which 



AF- ^ F 



~ + + ' 



Substituting this value in equation (13) we get 

 (14) 



Eliminating u' between equations (12) and (14) and repeating 

 the analogous operations for the other co-ordinates, we get finally 



Taking the partial differentials of these equations in reference 

 to x, y, and z respectively, and adding them, we get 



(16) 



\ 4 



R R 2 



