418 MEEISTIC VARIATION. [part i. 



The evidence derived from these numbers lends no support to the 

 expectation that any one particular joint of the 5-jointed form is 

 missing from the 4-jointed, or that any one joint of the 4-jointed form 

 corresponds with any two joints of the 5-jointed ; for if the numbers 

 are treated with a view to either of these hypotheses it will be found 

 impossible to make them agree with either. It appears rather that the 

 four joints of the 4-jointed form collectively represent the five joints of 

 the normal. 



The other question upon which the statistics bear has already been 

 stated in the Introduction. In any appendage the ratio of the length 

 of each joint to the whole length of the appendage varies ; but if it 

 varies about one normal form it will be possible to find a normal or 

 mean value for this ratio, and the frequency with which other values 

 of the same ratio occur will be inversely proportional to the degree in 

 which they depart from the normal value. The curve representing the 

 frequency of occurrence of these values will then be a normal Curve of 

 Error. The form of this curve will indicate the constancy with which 

 the normal proportions of the tarsal joints are approached. If the 

 proportional lengths of the tarsal joints vary little then the curve 

 representing the frequency of their departure from their normal value 

 will be a steep curve, but if these proportions are very variable and have 

 little constancy, then the curve will be flatter. The probable error 

 will thus in the case of each value be a measure of the constancy with 

 which it conforms to its normal proportions. As explained in the 

 Introduction, upon the hypothesis that all constancy of form is due to 

 the control of Natural Selection, it would be anticipated that the 

 4-jointed tarsus, if a variation, would be very much less constant in the 

 proportions of its joints than the 5-jointed tarsus. It was however 

 found that as a matter of fact the proportions of the joints of the 

 4-jointed form were very nearly as constantly conformed to as those of 

 the joints of the normal tarsus. 



The evidence of this is as follows. The total length of the 5-jointed tarsus being 



L, and t 1 , t 2 , &c. being the lengths of its several joints, I, T 1 , T 2 , &c. representing 



t l T 1 



the same measurements in the 4-jointed form, the ratios — &c, — &c, represent 



J-J v 



the proportional length of the several joints in each case. The values of these 



ratios were then arranged in ascending order in their own series and the measures 



occupying the positions of the first, second, and third quarterly divisions noted 1 



(indicated hereafter by Q 1 , M and Q 3 respectively). The probable error or 



t 1 T 1 

 variation of each ratio y , — , &c. will then be represented by the expression 



Q3_ Ql 



— - . Inasmuch as the joints are of different lengths, to compare the results 



each must be converted into percentages of the mean length of the joint concerned. 

 These results are set forth in the accompanying tables. 



the different pairs of legs may seem to point to the existence of some control other 

 than the simple chances of fortuitous injury. As regards the latter point it is 

 not unlikely that the legs of the third pair, being longer and less protected, may 

 be more often mutilated than the others. 



1 As described by Galton, F., Proc. Roy. Soc, 1888-9, xlv. p. 137. 



