394 Mr Murphy on the Inverse Method of 



dP 

 Now for all the maximum values of P„ we have — ^ = 0, 



hence f t Pn vanishes from / = to /= any value which makes P„ 

 a maximum, and also between any two such values, from which 

 it is evident that the positive and negative parts of those in- 

 tegrals are exactly equal. 



33. Let us now suppose any law of external tension (vanish- 

 ing at infinite distances) as -% + -^ + -0- + &c. and seek the law 

 of electric accumulation, necessary to produce it. 



It is evident from what has preceded, that the corresponding 



law of internal tension will be — + — 7- + —3- + &c. Now the 



a a a 



laws of accumulation necessary to produce the tensions 



£-3. (5?-^. (f -©•- 



are respectively by Art. 30. 



A -B d C 5_ tf -JO _!__ d^ 3 



Inra" 



and if we suppose the electrical systems which correspond to 

 these laws of accumulation to be superposed into one system, 

 and the accumulation at each point estimated by the excess of 

 the positive sum above the sum of the negative electricity at 

 that point, it will be the arrangement which was required to 

 produce the given phenomenon. 

 The accumulation therefore is 



4 ir a 4 dt 1.2 dr 



and therefore at similar points in different spheres it is inversely 

 as the surface of the sphere. 



