1898.] 



APPENDAGES IN THE ARTHROPODA. 



94: 



individual joints expressed correspondingly as fractions. The values 

 so obtained were then arranged in ascending order in their own 

 series, and those occupying the positions of the first, second, and 

 third quarterly divisions noted. Following the terminology of 

 Galton (31) these are indicated by Qj, M, and Q3 respectively. 

 The probable error of variation of the series from its mean A^alue 



will then be expressed by G-alton's formula — ^-^ — ^• 



Table F. — Periplaneta americana. 

 Five-jointed tarsus. 



Four-jointed tarsus. 



It will be seen that the percentage variation of the several joints 

 is very little greater in the case of the reproduced than in that of 

 the normal tarsi. Too much reliance should not be placed on the 

 results obtained for the smaller joints, as in their case the errors 

 of observation are necessarily greater proportionately. At the 

 same time it is probable that we are justified in accepting the 

 indication that these joints ai'e in a somewhat less stable condition 

 than the proximal and terminal joints, for the above result goes 

 hand in hand with the facts elicited from a consideration of the 

 cases of " malformed " tarsi already described. 



Subsequently to the construction of the above table, which has 

 already been published (2), with the kind assistance of Mr. Alfred 

 Hax'ker 1 tested the closeness of the correlation between certain of 

 the joints by the method devised by Galton (32). This method 

 deals with the relations between any two parts of a structure 

 whose dimensions are capable of expression by numbers, and its 



