Studies in the Evolution of Pecten. 613 



over the mean has never been proved and is not justified the argu- 

 ment falls to the ground. 



The advantage of the coefficient is that it is expressed in a uni- 

 versal unit, percentage; whereas the index is a concrete number 

 expressible in the greatest possible diversity of units. For mea- 

 sured, graduated, variates the coefficient gives the only possible 

 means of comparing two qualities measured by different stand- 

 ards. We cannot compare the variability of a race of people in 

 stature and in weight by comparing their indices of variability; 

 for what relation has a centimeter to a kilogfam ? We must there- 

 fore use the coefficients of variability for comparison or nothing. 

 In the case of integral variates, on the other hand, there is a 

 basis of comparison even though the integers are concrete. Four 

 petals and two spines have at least this in common that they are 

 four unit objects and two unit objects, respectively, and the latter 

 is half of the former. In integral variates we can, consequently, 

 compare the indices of variability. 



Now, as to the preference between the index and the coefficient 

 of variability a proper doubt may exist. In comparing variabili- 

 ties should the different planes from which variability must be 

 measured be frankly conceded and, as in altitude determinations, 

 consideration be given only to the end result (the index of vari- 

 ability) without inquiry as to its favoring factors; or should one 

 attempt, as in charting isobars from various barometric readings, 

 to reduce to a common level } 



It seems to us that both measures — both methods — are useful, 

 but for different ends. To illustrate, the altitude of a mountain 

 peak above sea-level is significant when we wish to know the 

 effect of altitude on barometric pressure or upon temperature; 

 the altitude of a peak above the plain at its base is significant when 

 we wish to measure the mountain-forming movements. So in 

 variation studies, the absolute amount of variability (the index) 

 in the numbers of a numerically repeated organ is important as 

 indicating the range of opportunity afforded for evolution in 

 different directions. A Pecten with only 5 rays with an index 

 of variability of ^ ray offers less opportunity for the production of 

 a new race with a new number of rays than does a Pecten with 



