194 THE F.NTOMOUKilST's RECORD. 



whilst there in 1903, one perhaps put up from 6 to 12 $ s of Xeweo- 

 phila plantcKi'mia during a morning, but never a S , whilst, in the after- 

 noon, millions of J s flew rapidly up and down the grassy slopes, but 

 only by the most careful searching could a $ be detected. The morn- 

 ing observer would conclude that the ? s largely outnumbered the <? s, 

 the afternoon observer that the <? s outnumbered the $ s by tens of 

 thousands ; no doubt both conclusions are equally erroneous. I was 

 much interested, and not a little amused, a shore time ago, at some 

 elaborate, and, up to a point, interesting, mathematical results worked 

 out by Mr. G. Smith [Hntoni., xxxiv., pp. 276 et seq.) on some data 

 that I had no doubt were almost wholly erroneous'''. Mr. Smith 

 assumed that : — (1) The various species of Erehia are extremely 

 variable in their wing-facies. (2) There is a great preponderance of <? s 

 over the ? s in the majority of species. The first assertion is certainly 

 open to question as a general statement, and, taking into account the 

 specimens of a given locality, the second has not in my own opinion 

 the slightest foundation in fact. Mr. Smith does not appear to tell 

 us (1) how many times he had made these special investigations that 

 he relies upon for his facts in the English Lake district and Savoy, 

 nor on what species they were based (surely not on epiphmu and li(ica 

 alone) ; (2) how many specimens on each occasion he captured for 

 comparison ; (3) how much difference there was in the various localities 

 in different years ; (4) how long he had stayed in each locality on each 

 occasion to make sure that he had a clear idea chat the material he 

 obtained and generalised on was taken at the commencement, middle, 

 and end of the period that the particular species was on the wing in 

 the given locality, and therefore a good average ; (5) that he had taken 

 fully into account the difference of habit of the sexes at these different 

 times so as to be able to average up his material with some hope of 

 success. We are getting a good many calculations published relative 

 to this and allied problems, based on haphazard material collected 

 without aim, and, without any detailed remarks to show that it has 

 been obtained with due regard to the purposes to which it has been 

 put. It is cheerfully said that one can prove anything by mathe- 

 matics, but by some obscure process of reasoning this same "mathe- 

 matics" strangely asserts as an Euclidian axiom, that if the premises 

 are all wrong the conclusions are sure not to be accurate. 



To a real student, who will allow for the fact, that the insects were 

 bred in confinement, and that the conditions of confinement are 

 generally in favour of the ^ as compared with the $ , some of Stand- 

 fuss' figures may be very suggestive. Thus we find that he reared : — 



1. Papiliopmhtlirhis in 1887 and 1892, obtained 453 c? sand 441 ? s, i.e.,102-7 : iOO. 



2. Piipilii) tiuirlition in lsit2 and 18H:-5, obtained 628 cT s and 607 ? s, i.e., 105 : 100. 

 a. I'liaU cerUiii in 1890 and 1891, obtained 170 <? s and 154 ? s, i.e., 1)0-4 : 100. 



[Of this species the 1890 specimens gave 123 f s and 92 ,} s, but the 1891 

 lot 47 cT s and 62 ? s.J 



4. Thai^ poh/xoia in 1884, 1890, and 1891, obtained 758 js and 752 ? s, i.e., 



100-8 : 100. rOf this species the 1H90 specimens jjave 192 ^ s and 141 ? s. 

 but the 1891 lot 542 <? s and 595 ? s.] 



5. Doritis (ipollinti.^ in 1S87. 1888, 1889, 1890, and 1891, obtained 54 o' s and 53 ? s, 



i.e., 101-8 : 100. [The specimens giving this near approach to equaHty 



* The remark on p. 90 re Erehia ligea and E. eiiri/ale is very remarkable so 

 far as the capture of E. var. ocellarix in the St. Gervais' valley goes. I know this 

 country moderately well, but have not seen this variety, which I have always 

 considered an eastern form. 



