132 EXPERIMENTS AND INVESTIGATIONS 



C P = x, P M = y, the force acting on a ray at the distance 

 a = x from A and a x from B. Then if B is removed and 



only A acts, y = -. . If B also acts, y' = (- 



(a + a?)" (a + a?)- 1 



1 



(a x) m ' 



Now the loci of y and y' are different curves, one similar to 

 a conic hyperbola, the other similar to a cubic ; but of some 

 such form when t = 1, as S S' and T T'. It is evident that 

 the proportion of 'y : y' can never be the same at any two 

 points, and consequently that the breadths of the fringes 

 made by the action of one can never bear the same proportion 

 to the breadths of those made by the action of both, unless we 

 introduce some other power as an element in the equation, 

 some power whereby from both values, y and y', x may dis- 

 appear, else any given proportion of y : y' can only exist at 

 some one value of x. Thus suppose (which the fact is) 

 y : y' : : I : 5 or 1 : 6, say : : 1 : 6, this proportion could 

 only hold when 



(5" - l) a V4 - l) a 



x = 7 or = 7 , if y : y' : : 1 : 5. 



o m + 1 4 m + 1 



When m = 2, the force being inversely as the square of the 



distance, then x = and x = a, are the values at 



V5+ 1 



which alone y : y' : : I : 5 and 1 : 6 respectively. 



But this is wholly inconsistent with all the experiments ; 

 for all of these give nearly the same proportion of y : y' 

 without regard to the distance, consequently the new element 

 must be introduced to reconcile this fact. Thus we can 

 easily suppose the conditions, disposition and polarization (I use 

 the latter term merely because the effect of the first edge 

 resembles polarization, and I use it without giving any 

 opinion as to its identity), to satisfy the equation by intro- 

 ducing into the value of y some function of a x. But that 



