An Extension of the Method of treating Variations, 
with Examples and certain Conclusions. 
By H. M. Ky1ez, M.A., B.Se. (St. Andrews). 
Ir 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." 
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 ef seq. 
410 
