ACCORDING TO THE UNDULATORY THEORY. 



497 



S= <! 



—pi" ~" ) 



S = -1- Urn - 1) - (m - l)y' - (/J +ij2 +i9^ + . . +/ ■) 

 + 0.-1)/] 



= pr^j (/« - 1) - (m - «)/ - f£-^ J • 



It is now evident that n, or the number of the raj^s whicli have tra- 

 versed after the second reflection, must be equal to »* — 1, or amount 

 to one less than the number of the reflecting surfaces. Bearing this in 

 mind we have 



<5 _ (m-l) -(m-2)p +jp'" 

 (1 -pY 



Although we dare not here suppose m to be, properly, indefinitely 

 great, it must however be so great that we may consider jo™ in com- 

 parison with (m — 2)j9 as evanescent, and m — 1, as well as m — 2, 

 equal to ni. By this we have 



S = 



1-p 



If we now put this value of S in the formula (9), and instead of p 



2b 

 its value, and moreover represent 2 tt -— for shortness' sake by o, we 



have 



A' (cos i + \/ — 1 .sin i) 



_ a (1 — r)"' m r"- (cos y -f- -j/ ^ . sin y) 



