240 Prof. Karl Pearson. Note on Regression and [June 20, 



have been unsuccessful. It is a hard, pale yellow, brittle resin, 

 nearly insoluble in water, light petroleum, and benzene, but readily 

 dissolved by alcohol, ether, and chloroform. When heated it gradu- 

 ally softens, and is quite fluid at 90 C. Croton-resin has neither 

 basic nor acidic properties ; it may be boiled with a mixture of lead 

 oxide and water without being appreciably affected. Ebullition with 

 aqueous potash or soda gradually decomposes it, destroying its vesi- 

 cating power. The products of this action are several acids, some of 

 which are members of the acetic series. By oxidation of the resin 

 with nitric acid a mixture of acids is obtained. The constitution of 

 croton-resin is therefore complicated, and its molecular formula 

 would appear to be at least (C 13 Hi 8 4 ) 2 or C 2 6H 36 08. Since it is not 

 saponified by a mixture of lead oxide and water, and as no glycerol 

 could be detected among the products of its decomposition by alkalis, 

 it is not a glyceride, and as it does not react with hydroxylamine or 

 phenylhydrazine or sodium bisulphite, it is probably neither a 

 ketone nor an aldehyde. The evidence so far obtained points to 

 the conclusion that the constitution of the vesicating constituent 

 of croton oil is that of a lactone or anhydride of complicated 

 structure. 



VII. " Note on Regression and Inheritance in the Case of Two 

 Parents." By KARL PEARSON, University College, London. 

 Communicated by FRANCIS GALTON, F.R.S. Received 

 June 5, 3895. 



Consider a population in which sexual selection and natural selec- 

 tion may or may not be taking place. Assume only that the 

 deviations from the mean in the case of any organ of any generation 

 follow exactly or closely the normal law of frequency, then the 

 following expressions may be shown to give the law of inheritance of 

 the population. 



Let H 2 = deviation of the father from mean of the total popula- 

 tion of fathers, and let <r 2 = the standard deviation of the total 

 population of fathers. 



Let H 3 and <r 3 be the corresponding quantities for the mother for 

 the same (or any other) organ. Let HI be the mean deviation of the 

 offspring (fraternity) due to fathers H 2 and mothers H 3 with regard 

 to the same (or any other) organ, and let a be the standard deviation 

 of the whole offspring population. If we are dealing with offspring 

 of one sex, both the mean and the standard deviation of the offspring 

 may differ, owing to natural selection, by any amount from those of 

 parents of the same sex. 



