164 Mathematical Contrihitions to the TJieory of Evolution. 



(c) That the mean correlation of an nth. parent with the offspring is 

 one-half that of an (n - l)th parent also appears doubtful. (This would 

 follow if reversion were started from the parent.) 



(d) Testing theory by the case of Basset Hounds, we find much 

 difficulty, owing partly to the great prepotency of the dam, and partly 

 to the large amount of artificial selection which is evidenced at every 

 turn, and obscures what may be termed the natural laws of inheritance. 



{e) There is an urgent need to widely extend our knowledge of 

 heredity by new experiments and observations on other organs in 

 difi'erent races. Facts are of the first necessity at the present time, 

 and facts collected on a large scale for a wide range.* 



* It may be of service to indicate to would-be investigators what has already 

 been done or is now in hand : — 



In man : — 



(a) Stature (direct to first degree and collateral, fraternal). 



(J) Head index ( „ „ „ « )• 



(e) Span and forearm (direct to first degree and collateral, fraternal). 



{d) Eye-colour (direct to second degree, collateral, fraternal and avuncular). 



(e) Shape of bead, physique, intellectual capacities, tastes (collateral only). 



(/) Fertility (direct to second degree). 



{g) Longevity (direct and collateral, fraternal). 



In horses : — 



(Ji) Coat-colour (direct to second degree and collateral). 

 {%) Fecundity (direct to second degree and collateral, fraternal and avun- 

 cular). 



In hounds : — 



{j) Coat-colour (direct to third degree and collateral). 



In moths : — 



{Jc) Wing-markings (direct and collateral). 



In daphnia : — 



(Z) Shape of spine (direct and collateral) . 



In all these cases the coefficients of correlation have already been worked out, 

 or material is being collected to determine them, by Mr. Francis G-alton, Professor 

 W. F. !R. Weldon, Dr. Warren, or by my collaborators and myself at University 

 College. Hence I would impress upon others to take as far as possible widely 

 different characters in widely different races. Above all, cases in which artificial 

 selection plays a great part, i.e., dogs^ fancy pigeons, &c., ought to be avoided. 



