64 Mr Pochlington, On the Symbolic Integration of 



In the first integral substitute u = q{—% + \f% 2 + p 2 ), and in 

 the second u = q(£ + V£ 2 + p 2 ), then 



Hence, 



•q (a;+Va; 2 +p2) Q - a u fl u rq (-x+ ^a; 2 +p2) e -a>u flu 



q (-h+^hi+pt) 



!. 



qdi+slW+p*) 



f(x, \p)-f(x, p) = 



2q _ 



e <*qx 



/; 



q (a+Va;2+x2p2) g-ww ^ w 



q («+Vx2+p2) 



p—(aqx 



2 (-aH-Vajs+AV) e -»>u flu 



rq (-a:+Va; 2 +A. 

 ^ 9 (-an- VxHp 2 ) 



+ e»9» 



/, 



ap s/2ft e-Mdu 



qpWjZh U 



when A is put = oo . 



The last term, since u is very small within the limits of inte- 

 gration, reduces to - e™* 35 log \ 2 , and thus is independent of p. On 



d 

 operating by -y- this term disappears, and may therefore be 

 ay 



left out. 



Substituting their values for the various quantities involved, 

 and writing 



Ei (— cou) = 



ow e~ u du 



e-" w du 



we have 



= FjV 



e -o>pr 



+ 



S£™[*{--*(7. + *)-»-*(7. + ')} 



It is easy to verify that this expression represents a diverging 

 wave at infinity, that it gives finite forces everywhere except at 

 the origin, and that there the forces have the correct form for an 

 oscillator. 



The case of a vibrator, neither parallel nor perpendicular to i, 

 can be solved by combining the results already obtained. 



The electric force can be found immediately from FVt = coper. 



The method can be applied to the case of a medium, the 

 principal specific inductive capacities of which are all unequal, but 



