Mathematical Contributions to the Theory of Evolution. 417 



practical importance to the plant. I am inclined to believe, from 

 Sachs'* experiments on the depletion of leaves, that all saving of 

 heat must be valuable, by preventing the checking of translocation 

 which he observed on cold nights. 



The mechanism of the stoma is another subject which does not 

 lend itself to condensed treatment. I have tried to point out that 

 the stoma has been neglected in the modern reorganisation of plant 

 physiology from the point of view of irritability. Some observers 

 insist on the preponderant influence of the guard cells, while Leitgeb 

 in the same way exaggerated the importance of epidermic pressure, 

 whereas the two factors should, as far as possible, be considered as 

 parts of a whole and as correlated rather than opposed in action. I 

 have also attempted to show how the stoma, like other parts of the 

 plant, may be supposed to react adaptively to those signals, which we 

 usually call stimuli. The attempt which I have made to rank the 

 problem among the phenomena of irritability, is very tentative in 

 character. I have ventured to put it forth because I am convinced 

 that it is in this direction that advances will be made. 



" Mathematical Contributions to the Theory of Evolution. Y. 

 On the Reconstruction of the Stature of Prehistoric Races." 

 By KARL PEARSON, F.R.S,, University College, London. 

 Received June 6, Read June 16, 1898. 



(Abstract). 



1. The object of this memoir is to illustrate the general theory by 

 which we may reconstruct from the knowledge of one organ in a fossil 

 or prehistoric race, the dimensions of other organs, when the correla- 

 tion between organs in existing races of the same species has been 

 ascertained. The particular illustration chosen is the reconstruction 

 of probable stature from a measurement of the long bones. 



Up till quite recently this subject remained in great obscurity, 

 partly on account of absence of theory, and partly for want of trust- 

 worthy data. 



2. The estimated statures as obtained by Orh'la, Topinard or Beddoe, 

 or by use of their methods, differ widely, and those methods have 

 no satisfactory theoretical basis. It was usual to suppose that there 

 was some mean or average ratio of stature to long bone, and even 

 when it was recognised that this ratio varied with the length of the 

 long bone, it was thought sufficient to determine it for two or three 

 separate ranges of stature, and determine its mean value for these 

 ranges by a very limited number of cases. 



* ' Arbeiten,' 1884. 



