1895.] 



On the Mathematical Theory of Evolution. 



69 



950 c.c. gave 4*5 c.c. This corresponds to about 0*4 per cent, of 

 indifferent gas. The first portion was unfortunately lost, but the 

 spectrum of the second portion was carefully compared with that of 

 argon, and the lines were all found to be coincident. No new lines 

 appeared, nor was any helium yellow visible. 



An incombustible gas from another well at the same place was also 

 tested, and was found to contain 0"5 per cent, of argon (Kellas). 



Some gas from a boiling spring near Reykjavik, Iceland, was col- 

 lected last autumn (Ramsay), and, on removing the combinable 

 constituents, 7*45 c.c. were obtained from 660 c.c. of the gas. This 

 is a greater proportion of argon than is present in air, being 1*14 per 

 cent. No helium could be detected in the gas, nor were there any 

 lines which could not be recognised as belonging to argon. 



It has been thought worth while to place on record these experi- 

 ments, although they show nothing remarkable. We have to express 

 our indebtedness to Mr. Noel Heaton for help kindly rendered. 



IV. " Contributions to the Mathematical Theory of Evolution. 

 III. Regression, Heredity, and Panmixia." By Karl 

 Pearson, University College, London. Communicated 

 by Professor Henrict, F.R.S. Received September 28, 

 1895. 



(Abstract.) 



The object of this paper is to develop the methods and generalise 

 the conclusions of Mr. Francis Gralton's work on ' Natural Inherit- 

 ance.' It endeayours to show the wide field which a purely statisti- 

 cal (as distinguished from a mechanical or physiological) theory of 

 heredity may be made to cover. In order to do this it is needful to 

 define certain biological terms in such a manner that they are capable 

 of quantitative measurement, the symbols in terms of which they 

 are expressed being the standard -deviations, correlation- coefficients, 

 and regression-coefficients already well known from the labours of 

 Mr. Galton. The fundamental assumption made is that the distribu- 

 tion of variation in any organ or characteristic follows the normal 

 law. It is pointed out that this distribution, although very general, 

 is not absolute, and that, especially in cases of disease and heredity, 

 we require the consideration of skew-variation and skew-correlation. 



The quantities mathematically defined are variation, correlation, 

 natural, sexual and reproductive selection, heredity, regression, and 

 panmixia. The definitions given agree in part with those already 

 adopted by Mr. Gralton or Professor Weldon. At some points they 

 extend or develop the ideas of those naturalists. In particular the 

 author finds it necessary to emphasise the distinction between two 



