64 LINEAR REPETITION. [ixtrod. 



addition to this the statement that the varying limb is perfect 

 conveys a number of ideas that cannot be readily formulated ; for 

 example, that the joints are to all appearance properly proportioned 

 and serviceable, shewing no sign of unfitness: they have in fact 

 much the same appearance as they have in those of the Orthoptera 

 in which the tarsus is normally four-jointed. But besides these 

 attributes, which though useful enough for ordinary description 

 are still in their nature formless and of no precise application, 

 there is another which in the case of these varying legs we are 

 entitled to make. We have said that these four-jointed tarsi are 

 to all appearance normal, save for the number of the joints. Now 

 the measurements which, at my suggestion, Mr Brindley has been 

 kind enough to make, entitle us to go beyond this, and to assert 

 that the four-jointed, tarsus has another character bv reason of 

 which it is actuallv in a sense a "normal" form. A brief considera- 

 tion of this will clearly illustrate the meaning of the term "per- 

 fection" applied to Variation. 



We saw above that in a monomorphic form, the frequency with 

 which, in respect of any given character, it departs from its mean 

 condition follows a curve of Frequency of Error. This is, indeed, 

 what is meant by the statement that the mean condition is a 

 normal. 



Taking the five-jointed tarsus, measurements shewed that the 

 ratio of the length of any given joint to the length of the whole 

 tarsus varied in this way about a moan value. Measurement of 

 the joints of the four-jointed form shewed that the ratios which 

 they bear to the total length of their respective tarsi vary in a 

 similar way about their mean values, and that there is thus a 

 "normal" four-jointed condition just as there is a "normal" five- 

 jointed condition. In the same way, then, that the ratio of the 

 length of each of the five joints to that of the whole tarsus is not 

 always identical but exhibits small variations, so the ratios of the 

 several joints of the four-jointed tarsus to the length of the whole 

 tarsus also vary, but in each case the ratio has a mean value 

 which is approached with a frequency conforming to a curve of 

 Error. 



The measurements established also another fact which is of 

 consequence to an appreciation of the nature of totality in 

 Variation. It not only appeared that the departures from the 

 mean value of these ratios in the four-jointed variety were dis- 

 tributed about the mean in the same way as those of the five- 

 jointed form, but it was also shewn that the absolute varia- 

 tions from the mean values of these ratios were not on the 

 whole greater in the four-jointed tarsi than in the five-jointed 

 tarsi. In other words, the four-jointed tarsus occurring thus 

 sporadically, as a variety, is not less definitely constituted than 

 the five jointed type, and the proportions of its several joints 

 are not less constant. It is scarcely necessary to point out that 



