l8 JOURNAL OF CONCHOLOGY, VOL. l6, NO. I, JANUARY, I919. 



cantly different from one or more of the others.^ 



How far the nonsignificant might be transformed into significant 

 differences by examining a larger number of specimens is a matter of 

 speculation. It is obvious from the method that the number does 

 make a difference, and the present data supply an illustration. From 

 six of the ten loci shells were collected in more than one lot. Taking 

 the first samples from these six, and the only samples from the other 

 four loci, the number examined in no case exceeds loo, and in all 

 there are 723 instead of 2198. The differences in altitude found to 

 be significant are 25 instead of 30 in the full series. As has been 

 indicated already, the gain in precision is proportional only to the 

 square root of the number examined, and after a time will be a dis- 

 appointing return for the labour involved. 



It is perhaps interesting also to note the result of altering our 

 criterion of difference. If we ask that the absolute difference shall 

 be only twice its standard error, we have 34 significant differences in 

 altitude and 23 in diameter instead of 30 and 19 with the standard 

 three ttmes. If we raise the limit to four times the figures become 

 26 and 17. 



Assuming that further specimens from any locus would have shown 

 the same dimensions as these actually measured, one may of course 

 calculate how many it would be necessary to measure to make any 

 observed difference significant. Such an assumption is, however, 

 unjustifiable, and I raise the point mainly to indicate that it does not 

 necessarily follow that the specimens from every locus would differ 

 from those of every other locus if only a sufficient number were 

 examined. From the present data it seems likely that differences 

 would predominate, but not more than that. The numbers necessary 

 would at any rate remove the question from the sphere of practical 

 conchology.^ 



There are a number of -other interesting problems in the measure- 

 ment of these C. bidentata — the variability, the relation between 

 altitude and diameter, etc. — which cannot be dealt with now. Our 

 original question has, however, been answered to the effect that the 

 shells from each of the ten loci considered do generally differ in size 

 from those from the other nine loci in the same neighbourhood. 

 The differences, too, are such as are easily demonstrable by appro- 



1 One may also examine the question by testing (see Biornetrika, vol. v (igo6), pp. i8i, 316) 

 how far the specimens from one locus differ from the specimens from all ten loci taken together. 

 The result obtained is that A, C, E, G, H, I and J differ in altitude and C, H, and I in diameter. 

 The method does not seem to me so suitable for the present enquiry as the one adopted above. 



2 For average C. bidentata, to establish a difference of 01 m.m. in mean .iltilude as signifi- 

 cant would require about 1,000 specimens in each sample ; a difference of o'oi m.m. about 

 100,090. 



