ON FARADAYS LINES OF FORCE. 



If there be two shells, one giving out fluid at a rate 4irPa', and the 

 other absorbing at the rate of 4irP'a' t , then the expression for the pressure will 

 be, outside the shells, 



D a* , y a? 



p = 4nP 47r/ x > . 



r r 



where / and r are the distances from the centres of the two shells. Equating 

 this expression to zero we have, as the surface of no pressure, that for which 



r' _ PV 

 r " TV' 



Now the surface, for which the distances to two fixed points have a given 

 i-atio, is a sphere of which the centre O is in the line joining the centres of 

 the shells CC* produced, so that 



and its radius 



Pa* 



' 



If at the centre of this sphere we place another source of the fluid, then 

 the pressure due to this source must be added to that due to the other two ; 

 and since this additional pressure depends only on the distance from the centre, 

 it will be constant at the surface of the sphere, where the pressure due to 

 the two other sources is zero. 



We have now the means of arranging a system of sources within a given 

 sphere, so that when combined with a given system of sources outside the 

 .sphere, they shall produce a given constant pressure at the surface of the sphere. 



Let a be the radius of the sphere, and p the given pressure, and let the 

 given sources be at distances 6,, 6 3 , &c. from the centre, and let their rates of 

 production be 47r/ J ,, 47rP s , &c. 



a* a* 

 Then if at distances .- , , , &c. (measured in the same direction as 6,, b t , &c. 



from the centre) we place negative sources whose rates are 



, - , <fec., 



