42tt TREMBLEY. 



these h^fl 1 die of other diseases, and subtract. Now the total 



number who die of other diseases during the x^^ year is 



_ A 



h 

 these die out of the number a^ ~ , HencO; by proportion, the 



number who die out of &^ f 1 — - ] is 



a^ — a, 



mn 



K \' ""~W- 



Therefore 5,^, = 5, 1 1 — — 



n Mill)/ ^ K\ 



a^ — a^^, 



'^' n n) h \-- --+1 r^nl 



% 



mn 



Ka,Jl-\ 



O^x-^- 



mn 



We can thus estabHsh our result by induction; for we may 

 shew in the manner just given that 



3.^ "-(^-^- 



1- — 



mn 



and then universally that 





m tn V nj 



785. We may put our result in the form 



, ma. 

 J. = ' 



i4.(^,_i)(i^ir 



