3j30 Practical Comparison of 



18. In the quadratic hypothesis, s being 1 — £_, we have ds = 



cc 



2x 2x 



A- — d^, and d.r is the fluxion of the probabiHty that a 



cc kcc 



person of the supposed age will die at a certain time, which, for 



the age of the younger x — p, taking k' for A:, becomes 2 — ZX d^r, 



cck' 



to be multiplied by — , the probability that the elder will 

 k 



2 



is 



survive, that is, by — (1 — -^ j : the product i 



k \ cc / cckk' 



\ cc cc / kk' \ 2cc cc 



4- -=- — , which taken from x :rz to a; r=: cr, becomes 



4c4 3c4 ^ 



—{L - Z- - i_ + Z_ - Jl- + ?1 + .JL - 'Pf\' 

 M'\2 c 4 3c 2cc cc 40-* 3cV' 



that is, putting-^ = «, and-i- =. q, it ^ ( — — — «, 



c c M' \ 4 3 



- 4-9% + p> q. + T^'' -■F^'^O* 



H. Probabilities of survivorship, compared with the quadratic 

 hypothesis. 



Ages. IT. Carlisle. — '■ — C. North. 



2e' 



30,60 .172 .158 .209 (.230) 



40,80 .060 .074 .100 (.102) 



The ages are here assumed very distant, in order to compare 



