( '35 ) 



lying between the before mentioned tangent planes. Now the direc- 

 tions for which P lies inside these j)lanes are those excluded by a 

 certain cone A', which may be detined as the locus of all normals to 

 another cone, having its vertex in P and tangent to the boundary 

 of the element of space t. On the other hand, all directions of wave 

 normals, for which /'' lies outside the tangent planes are included 

 by the cone K. It is clear that tliis cone will differ infinitely little 

 from the plane passing through <) |)erpeiHlicularly to OP. 



We may tiierefore tind the total electric force by integrating the 

 right hand members of the equations (8) wiih respect to all direc- 

 tions lying within K and tlion adding to the result the quantity 

 obtained by integrating the expressions relating to the remaining 

 directions. In effecting the lirst integration we must replace z' by 

 — z' for negative values of z', according to the remark made at the 

 end of ^ 6. But we may as well Hunt the integration to half the 

 cone K multiplying the result by 2. Again, we may extend this 

 integration to the plane F ; indeed the right hand members of (8) 

 contain x as a factor, so that it does not matter, whether or no an 

 infinitely small solid angle is included in this integration. 



It remains to consider the expressions 



^x' ^= dot dio, 



22''F" 2?''F' 



^•--'1 = ^v- (l<^ + — -r^ dio ] — — ^y , 



8:x\ dz- ^ e„ dz- J f„ -^ ' 



which liave to be integrated over all directions outside the cone A'. 

 Now, from these expressions we get the components along the 

 axes of symmetry by multiplying them by finite factors. It is easily 

 seen that terms already containing tlie factor x may therefore be 

 omitted, so that we may write 



£t' =^ dio, 



2r'F' 



^ 8. We shall resolve this last vector into two other vectors, 

 the components of the first being 



^^ = 2 v> v^ ' ^'^'1 — ~ 7" ^'^' ' 

 and those of the second 



<^V = 0, 



1 /ö'iLv 6,,d-^aö;,.-\ 



