174 Prof. G. G. Stokes. Discussio?i of the Results [May 12, 



sensibly constant during one revolution of the merry, we have on 

 employing the approximate value of the mean of V or (a) already 

 used — 



0=A(V» + W8)-2B^V+ 



But if U be the constant velocity of air relatively to the anemometer 

 which would make the cups turn round at the same rate, we have 

 similarly — 



0=AIJ2-2Bz;IL 

 Eliminating B?;/A, between these two equations we get — 



u(v+-^T)=V2+W2 ...... (,), 



and as the fourth and higher powers of W have been neglected all 

 along, we get from the last — 



u=v+ w • • • • • • • • W > 



so that, on this supposition, the mean correction for the wind is 

 3W 2 /4V, or three times the correction of the former supposition. 



The mean value of the radical (a) is given by an elliptic function ; 

 but even in an extreme case among the experiments, when the ratio of 

 the velocity of the wind to that of the anemometer is as great as 3 to 5, 

 the error of the approximate expression Y + W 3 /4Y amounts only 

 to about 0"01 mile an hour, which may be quite disregarded. The 

 error in employing (d) for the determination of U instead of (c) is 

 of about similar amount. 



Three anemometers were tried, namely, one of the old Kew standard 

 pattern, one by Adie, and Kraft's portable anemometer. Their dimen- 

 sions will be found at the heads of the respective tables below. With 

 each anemometer the experiments were made in three groups, with 

 high, moderate, and low velocities respectively, averaging about 28 miles 

 an hour for the high, 14 for the moderate, and 7 for the low. Each 

 group again was divided into two subordinate groups, according as the 

 cups were direct, in which case the directions of rotation of the merry 

 and of the anemometer were opposite, or reversed, in which case the 

 directions of the two rotations were the same. 



The data furnished by each experiment were : the time occupied bv 

 the experiment, the number of revolutions of the merry, the number 

 of apparent revolutions of the anemometer, given by the difference of 

 readings of the dial at the beginning and end of the experiment, 

 and the space S passed over by the wind, deduced from the difference 

 of readings of the fixed anemometer at the beginning and end of the 

 experiment. 



