6i2 C. B. Davenport and Marian E. Hubbard. 



with few rays ? After some experience with numerically varying 

 qualities one comes to expect such a relation. Moreover, the fact 

 seems not difficult to explain. One of the factors of variability 

 is the very complexity of the developmental process — the improb- 

 ability that, in development, all component events will occur in 

 exactly the same degree, number and order. The fewer the 

 elementary events, the less the chance for a wide deviation from 

 the average condition; the more numerous the events, the greater 

 the number of elements capable of deviating, the greater the 

 probability of a large 'deviation — indeed, the greater the probable 

 deviation. This law is illustrated in the cleavage of eggs. In 

 early cleavage stages cells of the same generation may cleave 

 simultaneously; but in later cleavage stages even cells in symme- 

 trically placed pairs may come to cleave at slightly different times. 

 For the time.of cleavage depends on many elements. When these 

 have become very numerous, as in later cleavage stages, the 

 chances that the accelerating and the retarding influences shall be 

 exactly equal in the history of the two cells become smaller. It 

 appears, then, as a general rule of variability that the fewer the 

 variable parts the less the variability. 



The whole matter of the proper measure of variability is a com- 

 plex one. Some years ago VerschaflTelt ('94), Pearson ('96) and 

 one of us in a note to Brewster's ('97) paper independently pro- 

 posed that the coefficient of variability be employed; that is, the 

 ratio of the index of variability (square root of mean square devia- 

 tion) to the average. Weldon ('97) for a time opposed the use of 

 the coefficient in place of the index and Duncker ('00) discovered 

 a case that he believed to demonstrate the meaninglessness of the 

 coefficient. The two shrimps Palcemonetes vulgaris and P. vari- 

 ans are nearly related. Yet the former has, on the average, 8.3 

 spines on the rostrum and the latter 4.3 spines. Now Duncker 

 assumes that the variability of a race will be much more constant 

 than its mean. As a matter of fact the index of variability of the 

 dorsal spines is .81 and .86 in the two species, respectively. The 

 coefficients are 9.83 per cent and 20.00 per cent, respectively. 

 The coefficients must be, Duncker concludes, meaningless. But 

 since the assumption of the greater conservativeness of the index 



