PROGRESS IN THE STUDY OF VARIATION. 563 



captivity, when the attracted males could be taken in the 

 way often followed with such species. This would of course 

 only give information as to the male population, but that 

 would 00 far towards answering the question. 



The numbers which it would be desirable to collect in 

 each sample should of course be as large as possible, but 

 there is a tendency among those not practically acquainted 

 with such problems to greatly exaggerate the need for exces- 

 sive numbers. To rightly assess the importance of minute 

 and insensible variations, doubtless vast numbers of indi- 

 viduals are needed, but in cases like that of betularia probably 

 a very moderate number would in the first instance suffice to 

 give a broad but reliable indication of the facts. If in 100 

 specimens^ there were thirty dark and ten intermediate, the 

 subsequent collection of 1000 would probably change the 

 absolute percentages a little, but it is unlikely tiiat it would 

 materially modify any conclusion based on the first sample. 



No doubt in districts where the variety was very scarce 

 'large numbers would be needed, and it is doubtful whether 

 such cases are suitable for statistical investigation. In the 

 Cambridge district, for instance, donbledayaria is still almost 

 unknown. In addition to a typical specimen of the variety 

 I lately took, I can learn of only two others, which were 

 taken severally some years ago. The ordinary form, how- 

 ever, is common, and it is likely that a few hundred speci- 

 mens would contain no doiibledaycwia at all. 



In order to follow up the statistical study of wild speci- 

 mens and to obtain experimental proof of the modes of 

 transmission of the varying characters by artificial breeding, 

 a wider range of observation is necessary, and, from a few 

 experiments only, contradictory results are almost sure to 

 follow. 



The difficulty arises especially from the fact that the 

 power of transmission of the individual is undoubtedly 

 aftected by its own back-breeding, a quantity for the most 

 part unknown. In illustration of this I may refer to the 

 discrepancy between the results obtained by Burckhardt, 



^ It is assumed, of course, that the specimens are collected in such a 

 way as to preclude the possibility that they are all one family. 



