AGGREGATE EFFECT OF INTERFERENCE. 163 



Hence the intensity is 



He r*dx R= _ Z**Zi e -^ i+«. + *-»=i+!>. «.... + me -*« 

 4 J & *« 



+ (m - 1) e-<- Sr - 2)a + (m - 2)<r (4r - 2)s + ... + e -^^-*" 



- 2 [<?-*<"-»* + g e -*<»-»)<. + ... + ( m _ i)^-^™] 



— m\ 



7v He 



4a 



{1 + 2 + + m + (m - 1) + ... + 1 



- 2(1 + 2 + ... + m - 1) - m} 



7T 



i?e 



+ —7— .{l.(2r.m- I + 2) + 2(2rm - 2 + 2) + 3{2rm-3 + 2) 



+ ... + (*» - 1) (2r -f- 2) + m . 2 

 + (m - \)(2r - 2) + (m - 2) (4/*- 2)+ ... + 2r(m - 1) - 2 



- 2 \_2r .m — l + 2.2r(m—2) + ... + (m - 1) 2r~]\ 



Ti e 



— — — . \4>r(m — 1) + 2 . 4r (m — 2)+ ... + (m — 1) 4r 



+ 2m — 4r (m — 1) - 2 . 4r («» — 2) — ... - (m — 1) 4r| 

 ■n-Hem ttII 



2 2 



x space left uncovered. 



Thus it appears that the whole quantity of light is not at all affected by 

 the diminution of interference. For we obtain, whole quantity of light on 

 the screen : that which falls on the object-glass :: area of the uncovered part 

 of the glass : whole area of the glass. 



It is unnecessary to dwell on this result. That it is a strong confirmation 

 of the undulatory theory, as far as regards two hypotheses respecting the 

 intensity, and the vibrations in different directions, cannot be doubted. 



x 2 



