142 EXPERIMENTS AND INVESTIGATIONS 



the two bent pencils, and v' r' the divergence of the inflected 

 pencil, equal also to d, because we may take the different 

 inflexibility to be as the different deflexibility. B acts on the 



T V 



red of A r v as ; on the violet as ; and so on A v' as 



a m (a + d) m 



V T 



on Ar' as . It is evident that 



(a + d+c)' (a+2d+c) 



the action in bending A r, A , or the fringe made by that 



action, is to the fringe made by the action on Ar', Av', as 



r_ __v _ r v 



a "" (a -f- d) m ' (a + 2d + c) m " (a + d + c) m ' 



mately the two actions (or sets of fringes) are (supposing 



a = 1 and d also = 1, for simplifying the expression) as 



2 m X r (3 + c) m (2 + c) m - v (3 + c) m (2 + c) m to 2 m r (2 + c) m 



- 2 m v (3 + c) m . 



Now the former of these expressions must always be greater 

 than the latter, because (3 + c) m > 1, and also (3 -f- c) m 

 1 > (2 + c ) m ~ 1 5 an< ^ this whatever be the value of m 

 and of c, and whatever proportion we allow of r to v, the 

 flexibilities. But it is also manifest that the excess of the 

 first expression above the second will be greater if the flexi- 

 bility of the red exceed that of the violet, or if r is greater 

 than v, as 2 v. Hence we conclude ; first, that in mixed or 

 white light the fringes inflected by B after deflexion by A 

 are greater than those deflected by B after inflexion by A ; 

 secondly, that they are also greater in homogeneous light ; 

 thirdly, that the excess of the inflected fringes over the 

 deflected is greater in mixed than in homogeneous light. 



The action of flexion after disposition is so much greater 

 than that of simple flexion, that I have only taken into the 

 calculation the compound flexion. But the most accurate 

 analysis is -that which makes the two fringes as 



r v r v 



D + -= - 7-7-77= to D + 



(a + d) m (a -f 2 d + c) m (a + d + c) m 



D being the breadth of the fringes on the chart by simple 

 flexion in case the rays had passed on without disposition 



