64 STATIC ELECTRICITY 



by calculating it on the supposition that it is due to the din-ct 

 action of the charged surfaces, each little bit of charge ij acting 

 directly at its distance d without regard to the nature, conduct 

 or insulating, of the intervening matter, and producing sti 



? always from or towards itself according as it is posit h 



^_,x72 * 



negative, all the strains due to the various elements being com- 

 pounded as vectors. For with this law of action, as we proved 

 in Chapter III, the charge on B will have on the whole no effect 

 on a point within its surface, while the charge on A will 1 



the same effect as if collected at its centre, giving therefore ^^3 



as the resultant. Within A and without B there ix no xtrnin, a 

 result again agreeing with that obtained on the supposition <>t 

 direct action. For within A the point is within both -ph i 

 surfaces, and neither will on the whole have any effect . Without 

 B each charge will have the same effect as if collected at the centre 

 of the sphere on which it lies. Being equal and 0] tin- 



two charges will evidently produce equal and opp> 

 neutralising each other. These resiil t s suggest tin 1 a w t hat 



The strain at anif point of any f/ntrinil .w/v d homo- 



geneous insulator may be calculated In f ntppoitaftkot it i\t/n- n. \nltant 

 of the strains due to w/>arutf clumnt* <>f fin' chargf. 

 according to the law charge -f 4-U//.v///mv)-, these elemcn 

 being compounded according to the irriur /< 



Assuming this, we may pass to the general case in which \u 

 have any assigned arrangement of conducting elect ri lit 1 lx>dics of 

 known shape possessing Known charges, a: it.d 1>\ a homo- 



geneous insulator. Whatever the distribution, we know (1) t 

 there is no strain within the conductors, and (2) that th- 

 just outside each surface is at every point perpendicular to tin- 

 surface. Assuming that the strain is e\er\ where, both in 

 conductors and in the medium, the same as if each element a 

 separately according to the inverse square law, it is possible to fit: 

 general mathematical expression for a distribution which will 

 satisfy the conditions stated above, and it may be shown that 

 there is in each case only one possible distribution. The mathe- 

 matical expression can be interpreted numerically onlv in a few- 

 cases. Among these cases are an ellipsoid with a given charge, 

 a sphere acted on inductively by a charged point, and two charged 

 spheres in contact. In some cases the results of calculation 1. 

 been verified by experiment, and we may therefore consider that 

 the employment of the inverse square law i> justified.* 



* A proof of the inverse square law is frequently jrivL-n which <ir|-inl.- onl\ <>n 

 the fact that there is no strain within a i Hnlm-tin. 



It is usually assigned to Cavendish, but it appears to have been given firv 

 Priestley in his " Electricity," 1st ed. 1 7r>7. l>. 7 II be 



found in the Report of the Hritish A**uctatiuH. l^ 



