360 ROBERT s. MCEWEN. 



As regards the mathematical procedures used in obtaining the 

 values shown in the table and graphs the following should be 

 said: The record of each fly in any given test was secured by 

 taking the average of its ten trials in that test. The 100 records 

 of all the individual insects of one type (winged or vestigial) 

 were then in turn averaged for each of the four tests indicated. 

 Both in making the graphs and in computing the probable errors 

 the records of the 100 flies obtained as just described were 

 employed, rather than the results of all their individual trials. 

 This was the essential procedure throughout, but the details 

 were slightly modified in certain cases for these reasons. It was 

 realized shortly after the beginning of the experiments that in 

 view of the question at issue it would be highly desirable to have 

 for comparison averages which had been corrected, so far as 

 possible, for the factor of flight in the case of the winged flies, 

 and for slipping upon the unlined glass in the case of the vestigials. 

 The modifications thus made necessary in the case of the winged 

 animals in the unlined horizontal tube were as follows: Since 7 

 insects had been tested before observations on this point were 

 begun, the records of these 7 had to be thrown out entirely. 

 In the cases of the remaining 93 flies, wherever necessary new 

 records were computed for each animal by eliminating any of 

 its ten trials in which use of the wings in any manner had occurred. 

 This process involved, as it turned out, 53 insects, with a total 

 of 157 trials, which is an average of 2.9 trials per insect concerned ; 

 the highest number which any one animal thus lost was 7. 

 The new records of these 53 flies were then averaged in with the 

 40 which required no change to obtain the so-called "corrected 

 for flight" average. In the case of the winged flies in the vertical 

 tube, correction was made in the same manner, except that in 

 this case only the records of the first five animals had to be 

 entirely discarded because observation on this point did not 

 begin until after they were tested. In this instance out of the 

 remaining 95 flies the records of 40 had to be corrected, involving 

 70 trials, an average of 1.75 trials per fly concerned. Again the 

 highest loss suffered by any one animal was 7. The third 

 correction was that for the slipping of vestigial flies in the vertical 

 unlined tube. The same general method was employed as in 



