Mathematical Contributions to the Theory of Evolution. 343 



rises in the gutta-percha tube, the pressure on the valves increases, 

 and the sound becomes more marked ; when the fluid on the other 

 hand diminishes, the sounds become less distinct. If the heart be 

 placed horizontally, the sounds become wobbly. The terminal piece 

 of small diameter of a binaural stethoscope gently placed over the 

 aorta at its commencement is most suitable for observing the cardiac 

 sounds in this experiment. 



The experiment here described, when first suggested by me, was 

 submitted, with the assistance of Dr. Sibbald, to my lamented friend 

 the late Dr. Sharpey, and to Sir James Paget, who were quite satisfied 

 that with the increase or diminution of the column the sounds closely 

 resembled those of the heart in man, and that they became more or 

 less distinct in proportion to the quantity of fluid contained in the 

 tube. 



In conclusion, I may say that I was moved to undertake and con- 

 tinue this inquiry by a desire to obtain a solution of what seemed to 

 be an insoluble problem, and also by a belief that a correct explana- 

 tion of the cause of the first sound of the heart would be of practical 

 value in the study of the clinical phenomena of diseases of this 

 organ. 



I would wish further to add that the explanation of the cause of 

 the first sound of the heart given in this communication, being so 

 different from that hitherto accepted, may seem calculated to create 

 difficulties in the diagnosis of valvular diseases of the heart. Closer 

 consideration will show, however, this not to be the case, but that, 

 like all accurate knowledge, it will be found to simplify, and not to 

 confuse. It will afford an explanation of the relations of certain 

 morbid phenomena which are at present unintelligible, such, for 

 example, as that a systolic murmur may be heard at the apex whilst 

 the first sound is audible at the base free from murmur ; and it will 

 serve to encourage a closer study of the relation between muscular 

 contraction of the walls of the heart and the tension of the vessels of 

 the system. 



" Mathematical Contributions to the Theory of Evolution. On 

 the Relative Variation and Correlation in Civilised and 

 Uncivilised Races." By Miss Alice Lee, Bedford College, 

 and Karl Pearson, M.A., F.R.S., Professor of Mathe- 

 matics and Mechanics, University College, London. Re- 

 ceived April 9, — Read June 3, 1897. 



1. The following numerical data were calculated in the hope of 

 reaching some general ideas on the comparative variation and com- 



