30 C. V. L. Cbarlier. 



We suppose c to be the abscissa of the discontinuous end of the frequency 

 curve. It is then 0 = F{c — (o) = F(c — 2o>) = . . . . Put .9 = 0. 



The area — Y — between the frequency curve and tlie line of the abscisses 

 may approximately be written 



r= 0. [l-F{c) + F{c + CO) + F{c + 2co) + . . .] 



or also 



Y= ^F{c) + J^(c + 1) + i^(c + 2) + . . . 



Using the abbreviation 



l., = i^(c) + i^(c+l) + F(c+2) + ..., 



which is adequate when integral variâtes are concerned, we thus have 



« S F{xi» + c) = (Xo + 1 F(c) {o> - 1), 



whereas in the preceding investigation the term multiplied by F{c) was omitted. 



Using only this correction the equations of condition in case 4:o take the form 



l\, + -hF{c){^'^-'^) = ^'^ßo> 

 (32) i,,'=c.'B,K 



which equations may be exactly solved. 

 Putting 



we obtain w from the equation 



h 2 2 " 2i 



(33) «2 + 2(0 



then X from 



1 1 U 0^ 



^ 0 ■ 



^(1 



TVh 



(33*) (oX 



l + |/.(a)- 1)' 



and from 



(33**) i?, = i^(l+i/Kco-l)). 



When F[c) is small, we may conveniently develop the solution of (32) into 

 powers of F(c). In the first approximation we then obtain the solution (25), which 

 solution will suffice when F{c) is very small. Compare in this respect the pro- 

 blem 8 below. 



