An Extension of the Method of treating Variations, 

 with Examples and certain Conclusions. 



By H. M. Kyle, M.A., B.Sc. (St. Andrews). 



It is proposed to give in this paper a short account of an extension of 

 the method at present used in the study of variations. Examples will 

 be shown in order to illustrate the working of this method, and a brief 

 discussion of the conclusions towards which the results already obtained 

 point will be added. 1 



It is unnecessary to enter into the details of the present method, 

 since they are now so well known, and only the underlying principles 

 will be mentioned in order to preserve the continuity of the subject 

 and display the exact point of the new departure. For the sake of 

 clearness the various stages will be denoted by propositions, three in 

 number: (1) the application of the laws of probability; (2) a law 

 which holds for all the individuals of a " group " ; (3) a formula for 

 determining to which of known groups any chosen individual belongs. 



1. The variations of any organ or part of an organ in a series of 

 individuals of the same race or species conform to the laws of prob- 

 ability. When arranged in order these variations form a curve which 

 may be expressed by one of several algebraic equations. The most 

 common of these equations is that known as the " Probability Integral." 

 Further, when the variations of one organ have been expressed, a con- 

 stant can be found showing the relation of these variations to those 

 of another organ ; in other words, the correlation of organs can be 

 expressed mathematically. 



With two great exceptions the examples hitherto given have been 

 concerned with the variations of particular organs and the correlation 

 of these variations. The conclusions have been restricted for the most 

 part to displaying the " fact " of variation and the importance of the 

 mathematical method. More recently an effort has been made to pass 

 beyond this stage and connect the observed change in a range of 

 variations at different times with a known change in the environmental 

 conditions. 



It is necessary here to enter into a slight criticism of this position 



1 For conclusions, see pp. 417 rt scq. 

 410 



