ON LIGHT AND COLOURS. 143 



and without a second flexion. If it be carefully kept in mind 



r T 



that D is much less than , or even , and that 



a m (a + 2 d + c) m 



d is still less than D, then it will always be certain that the 

 first quantity is larger than the second. 



Cor. It is a corollary to this proposition that the dif- 

 ference of the two sets of fringes is increased by the dis- 

 position communicated by the rays in passing by the first 

 body. For the excess of the value of r over that of v being 

 increased, the difference between the two expressions is 

 increased. 



PROPOSITION VII. 



When one body only acts upon the rays, it must, by 

 deflexion, form them into fringes or images decreasing as the 

 distance from the bending body increases. But when the 

 rays deflected and disposed by one body are afterwards in- 

 flected by a second body, the fringes will increase as they 

 recede from the direct rays. Also when the fringes made by 

 the inflexion of one body, and which increase with the 

 distance from the direct rays, are deflected by a second body, 

 the effect of the disposition and of the distances is such as to 

 correct the effect of the first flexion, and the fringes by de- 

 flection of the second body are made to decrease as they 

 recede from the direct rays. 



In fig. 15, A P is the pencil inflected by A and forming the 

 first and narrower fringe p ; A r 

 is the pencil inflected nearer to 

 A and forming the broader fringe 

 r. Such are the relative breadths, 

 because the} 7 are inversely as some 

 power of the distance at which A 

 acts on them. But if B afterwards 

 acts, it is shown by the same reasoning which was applied to 

 the last proposition that r will be less than p ; and so in like 

 manner will r' be made less than o', though o' was greater 

 than r' until B's action, and the effects of disposition with 



