298 M. L. Lorenz on the Identity of the 



from the point w 1 y' z'. The equations thus altered will hold 



good, provided the differentiation indicated on the left side be 



considered partial in such a manner that it is not effected as re- 



dor du dz 

 gards r. Both sides are afterwards multiplied by > and 



the equations are integrated over the entire space of the body. 

 By partial integration, for instance, the first member of the first 

 equation with the previous notation becomes 



C CCdx'dy'dzi 8V V~ a) Cds< 8u '('-I) 



JJJ— — ~w— =-jT^r- C0S ' t 



-b 



d CCCdx'dy'dz' V a J 



W 



dyJJJ r 81/ 



in which the last member by repeated partial integration passes 

 into 



— r 1 — u ( t jcos/^4- -jrs* 



dyj r \ a J dy* 



If now all the members on the left side of the equation in 

 question be treated in the same manner, it will be found that, if 

 all integrals are to vanish in reference to the surface of a body, 

 we must have 



(du 1 dv'\ (dw ] du!\ _ 



^>-d^) C0Sfl -{d?-di') C0SV=0 ' 



U 1 COS fl — V f cos X ;= 0, u' cos v — IV 1 COS X — 0, 

 in which equations we suppose / again introduced instead of 



T ..... . 



t ) which is permissible, since the equations are valid for all 



values of /, and the differentiation is not to be effected in refer- 

 ence to r. 



For an element at right angles to the .r-axis (that is, for 



COS fJL = 0, cos v = 0), 

 these equations give 



v' = and w/ = 0, 



and the corresponding equations, which are obtained from the 

 two other equations (B), and can be deduced from the above 

 equations by changing the letters, give 



du 1 dv' _ , dw l __ dvJ _ 



dy' dx* ~ dx l dz 1 ~~ 



Hence, if the integrals in reference to the surface of the body 

 are to disappear, they must for an element at right angles to the 



