406 Note 19: determination of law of electric attraction 



But it appears from the mathematical theory that if the law of repulsion 

 had been as r~ (2+9) f the potential of the globe when tested would have been 

 by equation (25), p. 425, 0-1478 x ? F. 



Hence q cannot differ from zero by more than jr . 



Now, even in a rough experiment, D was certainly more than 300^. In 

 fact no sensible value of d was ever observed. We may therefore conclude 

 that q, the excess of the true index above 2, must either be zero, or must differ 

 from zero by less than j 



Theory of the Experiment. 



Let the repulsion between two charges e and e' at a distance r be 



f=ee'^(r), ...... (i) 



where <f> (r) denotes any function of the distance which vanishes at an infinite 

 distance. 



The potential at a distance r from a charge e is 



V = er^>(r)df. ...... (2) 



.'r 



Let us write this in the form 



V=c l -f(r), ...... (3) 



where /*W-^p. ...... (4) 



and/(r) is a function of r equal to if I I <f> (r) dr\ dr. 



We have in the first place to find the potential at a given point B due to 

 an uniform spherical shell. 



Let A be the centre of the shell, a its radius, a its whole charge, and a its 



surface-density, then 



a = 47r 2 o-. ...... (5) 



Take A for the centre of spherical co-ordinates and AB for axis, and let 

 AB = b. 



Let P be a point on the sphere whose spherical co-ordinates are 6 and tf>, 



and let BP = r, then 



r z = a 2 lab cos 6 + b z . ...... (6) 



The charge of an element of the shell at P is 



aa a sin8d8d<f>= - a 

 The potential at P due to this element is 



aa a sin8d8d<f>= - asm9d6d</>. ...... (7) 



r 



(8) 



