418 M ERISTIC VARIATION. [PAUT i. 



The e\ id.-nce derived from these numbers lends no support to the 

 expectation th.-it any one particular joint of the 5-jointed form is 

 mi ing from tli.- 1-jointed, <>r that any one joint of the 4-jointed form 

 corn-pond^ with any two joints of the 5-jointed; for if the numbers 

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

 iinp.iible ;,, make them agree with either. It appears rather that the 

 four joints of tin- I 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 eachjoinl 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 

 in. -an 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 must aney, then the curve will be natter. 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 

 1 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 

 I 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 l , t-, A:c, being the lengths of its several joints, I, T 1 , T 3 , &c. representing 



t l T 1 



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



Lt I 



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

 ratios \\ere thru arranged in ascending order in their own series and the measures 

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



(indicated hen after hy v 1 . - 1 / and V 3 respectively). The probable error or 



fi j'i 

 variation of each ratio , , Are. will then bo represented by the expression 



1 j t 



n.i _ o\ 



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



a 



each must he oonvi rte.l into percentages of the moan length of the joint concerned. 



These results are set forth in the accompanying tables. 



the dift'ei.-nt pairs of legs may -.em to point to the existence of some control other 



than the Dimple . -l,ane,s of fortuitous injury. As regards the latter point it is 

 not unlikely thai ill. legs of the third pair, being longer and less protected, may 

 lie more often mutilate. 1 than the otln 



1 As described by (i.u.iox, !'., I'roc. Hoy. Soc., 1888-9, XLV. p. 137. 



