CERTAIN LAWS OF VARIATION. 215 



specimens of the shell were obtained from each of ten 

 different localities in America, and from three in Great 

 Britain. The variation was estimated by determining 

 the ratio of breadth to length in each shell, or the ven- 

 tricosity, and expressing the result as a percentage of 

 the one on the other. The extreme variations recorded 

 were respectively 80 per cent, and 104 per cent., or a 

 difference of 24. As a measure of the variability 

 Bumpus took the difference in the extreme values ex- 

 hibited by each sample of shells, and he found that the 

 amplitude of variation of the American shells was in 

 every case in excess of that of the British shells. Thus 

 it was respectively 18, 19, 20, 19, 17, 20, 20, 18, 18, 

 and 20 in the American samples, and 15, 14, and 12 in 

 the British. Obviously, however, this is not a very 

 good method of estimating variability, as it is more or 

 less a matter of chance if specimens of shells exhibiting 

 the most extreme variations happen to occur in any 

 given sample of 1000. Thus in two-thirds of all of 

 Bumpus 7 series, the extreme variations were repre- 

 sented by only a single specimen. Fortunately the true 

 value of these extensive series of observations has not 

 been lost, as Duncker * has taken the trouble to work 

 through them and calculate the variability by an exact 

 method. The following are the values obtained by 

 him for the mean ventricosity, and its variability (as 

 expressed by the error of mean square) in each 

 sample. 



From the table we gather that the average ventri- 

 cosity of the American shells is slightly greater than 

 that of the British (91.01 as against 89.78, or 1.4 per 



*Biol. Centralblatt., vol. xviii. p. 569, 1898. 



