A. J. Loika — Mode of Growth of Material Aggregates. 203 



England and Wales 1871-1880 (Mean). 



Observed* Calculated 

 Birth-rate per head b -03546 -0352 



Death-rate per head d -02139 -0211 



Excess (b—d) = r -01407 (-0141) 



Age Scale. 



L,000/ 



c(a) da 



a-i. 



1,000 individuals, in age- o — 5 136 138 



groups of 5 and 10 years : 5 — 10 120 116 



10 — 15 107 106 



15 — 20 97 97 



20 — 25 89 87 



25 — 35 147 148 



35 — 45 113 116 



45 — 55 86 87 



55 — 65 59 59 



65 — 75 33 33 



75 — go 13 13 



Special Cases 

 B. Let B be constant. 



dp (a) 



^-tf-T* by(5) 



Then 



= B 



dt ' 



i.e., N also is constant, and we have a " stationary condition " 

 or "kinetic equilibrium." 



(19f) 



(20) 



Here evidently 



b = d 



and 



c(a) — bp(a). 



Furthermore, 





b = 



1 1 



= 7 sa y : 





p(a)da 



'o 

 and c(a) = ^-. (21) 



*Mean b and cl from 46th Ann. Rep. Reg. Gen. Births, etc., England and 

 Wales, p. xxxi ; p(a) from Supplt. to 45th Ann. Rep. Reg. Gen. Births, etc. , 

 England and Wales, pp. vii and viii. 



male births A n . 



assuming ratio : = 1 "04. 



female births 

 f Compare Farr, Roy. Soc. Trans.. 1859, p. 837. 



