144 TliAXSACTlONS AND PUOCKEDINGS OF THE [Sess. Lxvi, 



ment ; ^ but it is their destiny to go through tlie process of 

 reduction of chromosomes, with the ensuing formation of 

 " sexual products " (or gametes), eggs, and spermatozoa. 

 Here, as is of course now generally recognised, unlikeness 

 enters. Although the egg, or sperm, traces its long 

 ancestry to one of a certain set of primary germ-cells, of 

 which one also gave rise to the " embryo," or form, whose 

 " offspring " — according to social and commonly accepted 

 ideas — the egg or sperm itself was, this said egg or sperm 

 unites with another sperm or egg, the offspring of a 

 different individual, which in its turn, with its repro- 

 ductive elements, traces a similar origin and ancestry from 

 another set of primary germ-cells. With the union the 

 new cycle begins. 



It is thus, that the formation of primary germ-cells 

 underlies the fundamental facts of heredity, and explains 

 these. And it is thus, without their knowing it, that the 

 formation of primary germ-cells at a certain epoch of the 

 development, prior to the production of the embryo, is 

 the real basis of Weismann's finds in heredity, and, to a 

 still greater degree, of those associated with the name of 

 Galton. 



The application in detail of the results to the phenomena 

 of heredity is beyond the scope of my researches. To 

 indicate the way may suffice. 



Galton has been led by his studies and researches on 

 inheritance to what is known as Galton's law." According 

 to this law, " the two parents between them contribute on 

 the average one-half of each inherited faculty, each of 

 them contributing one-quarter of it. The four grand- 

 parents contribute between them one-quarter, or each of 

 them one-sixteenth, and so on ; the sum of the series — 

 2 + i + i+TV+ 6tc., being equal to 1, as it should be, 

 It is a property of this infinite series that each term is 

 equal to the sum of all those that follow, thus — h = I + i 

 -f yV + etc. ; } = I -1- Jg- 4- etc., and so on. The pre- 

 potencies or subpotencies of particular ancestors, in any 



^ In the Vertebrata. 



- Francis Galton : " The average Contribution of each several 

 Ancestor to the total Heritage of the Offspring." — " Proc. Roy. Soc, 

 Lond.," vol. 61, pp. 401-408, 1897. 



