H. M. Leake 223 



the ratio y was determined for a large series of plants but was found 



to be quite inconstant and useless as a means of identifying types 

 which were readily distinguishable by eye. On the other hand in the 

 leaf factor an expression was found not only for such differences as are 

 of sufficient magnitude to be recognised by the eye but also for such 

 as, though definite and constant, are elusive to the eye and incapable of 

 adequate verbal definition. While there is thus found in the leaf factor 

 a means of defining and expressing to a degree of minuteness hitherto 

 impossible, what appears to be a unit character of the cotton leaf, it is 

 necessary to beware of pressing it too far. It is physically impossible 

 to measure every fully developed leaf and obtain fi:om such measure- 

 ments an average. " Typical " leaves must be selected and in such 

 selection the door is opened for the introduction of a considerable 

 personal element. In the experiments recorded determinations have 

 been made on at least two such " typical " leaves from each plant and 

 the average between the two values so obtained is taken as the leaf 

 factor of the individual. 



Before dealing with this character in detail therefore both the 

 magnitude of the error met with in these determinations and the 

 exact meaning to be ascribed to the term " typical " require brief 

 consideration. 



It is clear that a larger experimental error is to be expected in the 

 leaf factor of types with narrow lobed, than those with broad lobed, 

 leaves. In the latter case the three measurements employed in the 

 calculation are all large and errors of measurement proportionately 

 small. In the former case, on the other hand, the divisor e is small 

 and the errors proportionately large. The experimental error, con- 

 sequently, increases as the value of the leaf factor rises. When this 

 value falls below 2 the error, which is accepted, is normally less than 

 015 from the mean (giving a total range of 0'3) and, when this value 

 lies above 3, this error may reach 0*3 (with a total i-ange of 06). 

 These figures indicate the extreme variation met with. Where the 

 error exceeds this amount duplicate determinations have been made. 



The recognition of this leaf factor was, as has been stated, in the 

 first place purely empirical and resulted from an attempt to find some 

 method of denoting by symbols the differences between the various 

 characteristic shapes of the cotton leaf. In the selection of leaves 

 used in the determinations certain precautions were found to be 

 necessary and were consequently adopted. That such precautions were 



