388 Mh AIRV, on the INTENSITY OF LIGHT 



I*. To proceed now with the intensity of light at the iUuininated 

 point. I shall omit entirely the integration for the ordinate perpendicular 

 to the plane of x, y, because it would only introduce a factor common 

 to every part, and therefore would not modify the proportion of 

 intensity at different points. The great wave of light being supposed 

 to be divided into indefinitely small parts, each of which is the origin 

 of a small wave spreading in all directions: the disturbance of ether 

 at the illuminated point produced by this small wave, on the 

 Undulatory Theory, will be estimated by 



portion of surface of small wave x sin — (vt — whole path) 



A 



which in the first case becomes 



W X sin ^ \vt-E--^,{^'- ^-^ hp.z)\, 

 and in the second case 



1.5. In the first case therefore, the expression for the whole 

 disturbance is 



The limits through which the integration is to be performed are from 

 z a sensible quantity negative to »' a sensible quantity positive, and on 

 account of the minuteness of the divisor \, and the inefficiency of the 

 rays whose paths differ from E by many multiples of X, this will be 

 the same as taking it between the limits — infinity, + infinity. Now 

 the integral is the same as 



sm — {vt-E) J.COS — . gp„ 3 (,S5^ ■ .Ip.x) 



- cos — {vt-E) /,• sm — . «^^ («' : — . Sp.%'). 



\ ' ' ■" X 6PX' 



P 



But between — infinity and + infinity it is evident that 



. . 2,r p ,3 6.PX' , ,, „ 



