lotka: a natural population norm 



291 



TABLE V 

 Age-Distribution at Death (Males) 



IV. Average age at death. The average age at death is given by 



A^ = ac'{a)da (18) 



Jo 



In the case of the stable age distribution this becomes (see 15) 



A^= — -\ a e-^^p(a) da (19) 



dJo 



I, r • "1 "" ?i r* °° 



= — - ae-^^ p (a) + - (1 — ra) e-"'' p (a) da 

 dl Jo d Jo 



= + - \ c{a) da — - \ a c{a) da 

 d Jo d Jo 



^-^^■' 



(20) 



(21) 

 (22) 



if we denote by A^ the mean age of the living population. 



In a stationary population we have r == 0, d ^ do and hence 



1 f" 



A^ = -r = h where I is the mean length of life, viz., I = \ p{a) da. 

 do J" 



V. Third equation between b, d and r. We have so far considered 



b, d and r as connected by two relations, namely equation (2) (or 



