180 Prof. G. G. Stokes. Discussion of the Results [May 12, 



the air relatively to the anemometer according as the rotations are in 

 opposite directions or in the same direction, we see that in five out of 

 the six cases they are slightly greater when the rotations are opposite. 

 The sole exception is in the group " Adie, high velocities," which is 

 made up of the groups "AdieH — " and "AdieH + ." On referring 

 to the principal table for the Adie, we see that Experiments 3 and 4 

 in group H + give percentages usually high, depending on the high 

 values of N. These raise the mean for the group, and make the 

 mean error far greater than those of the other five groups for high 

 velocities. There appears little doubt, therefore, that the excess of 

 percentages obtained for rotations opposite is real, and not merely 

 casual. It is, however, so small as to give us much confidence in the 

 correctness of the mean result, unless there were causes to vitiate it 

 which apply to both directions of rotation alike. 



It may be noticed that the difference is greatest for the Kew, in 

 which the ratio of r to R is greatest, r denoting the radius of the arm 

 of the anemometer, and R the distance of its axis from the axis of 

 revolution of the machine, and appears to be least (when allowance is 

 made for the two anomalous experiments in the group " Adie H+ ") 

 for the Kraft, for which r/R is least. In the Kraft, indeed, the 

 differences are roughly equal to the probable errors of the means. In 

 these whirling experiments r/R is always taken small, and we might 

 expect the correction to be made on account of the finiteness of R to 

 be expressible in a rapidly converging series according to powers of 

 r/R, say— 



We may, in imagination, pass from the case of rotations opposite to 

 that of rotations alike, by supposing R taken larger and larger in 

 successive experiments, altering the angular velocity of revolution so as 

 to preserve the same linear velocity for the anemometer, and suppos- 

 ing the increase continued until R changes sign in passing through 

 infinity, and is ultimately reduced in magnitude to what it was at 

 first. The ideal case of R=oo is what we aim at, in order to repre- 

 sent the motion of a fixed anemometer acted on by perfectly uniform 

 wind by that of an anemometer uniformly impelled in a rectilinear 

 direction in perfectly still air. We may judge of the magnitude of 

 the leading term in the above correction, provided it be of an odd 

 order, by that of the difference of the results for the two directions of 

 rotation. Unless, therefore, we had reason to believe that A' were 0, 

 or at least very small compared with B', we should infer that the 

 whole correction for the finiteness of R is very small, and that it is 

 practically eliminated by taking the mean of the results for rotations 

 opposite and rotations alike. 



