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



confident that under the circumstances the tangential motion of the air 

 at the level of the cups was so small as not to need consideration in 

 the discussion of the results. As in one or two points of its revolution 

 the anemometer passed close by some small trees in full leaf, we 

 should have observed any eddies or artificial wind had it existed, but 

 I am sure we did not." 



3. Influence of the Variation of the Wind ; first, as regards Va.riations- 

 which are not Rapid. — During the 20 or 30 minutes that an experiment 

 lasted, there would of course be numerous fluctuations in the velocity 

 of the wind, the mean result of which is alone recorded. The period 

 of the changes (by which expression it is not intended to assert that 

 they were in any sense regularly periodic), might be a good deal 

 greater than that of the merry, or might be comparatively short. In 

 the high velocities, at any rate, in which one revolution took only 

 three or four seconds, the supposition that the period of the changes 

 was large compared with one revolution is probably a good deal 

 nearer the truth than the supposition that it is small. 



On the former supposition, the correction for the wind during two 

 or three revolutions of the merry would be given by the formulae 

 already employed, taking for W its value at the time. Consequently, 

 the total correction will be given by the formula? already used, if we 

 substitute the mean of W 2 for the square of mean W. The former is 

 necessarily greater than the latter; but how much, we cannot tell 

 without knowing the actual variations. We should probably make an 

 outside estimate of the effect of the variations, if we supposed the' 

 velocity of the wind twice the mean velocity during half the duration 

 of the experiment, and nothing at all during the remainder. On this 

 supposition, the mean of W 2 would be twice the square of mean W, 

 and the correction for the wind would be doubled. At the high 

 velocities of revolution, the whole correction for the wind is so very 

 small, that the uncertainty arising from variation as above explained 

 is of little importance, and even for the moderate velocities it is not 

 serious. 



4. Influence of Rapid Variations of the Wind.— Variations of which 

 the period is a good deal less than that of the revolutions of the 

 whirling instrument act in a very different manner. The smallness of 

 the corrections for the wind hitherto employed depends on the cir- 

 cumstance that with uniform wind, or even with variable wind, when 

 the period of variation is a good deal greater than that of revolution of 

 the merry, the terms depending on the first power of W, which letter 

 is here used to denote the momentary velocity of the wind, disappear 

 in the mean of a revolution. This is not the case when a particular 

 velocity of wind belongs only to a particular part of the circle de- 

 scribed by the anemometer in one revolution. In this case there will 

 in general be an outstanding effect depending on the first power of W, 



