1881.] of some Experiments with Whirled Anemometers. 



173 



anemometer and that of the wind. Then . the velocity of the anemo- 

 meter relatively to the wind will be — 



\/V s -2VWcos0 + W* (a) 



The mean effect of the wind in a revolution of the merry will be 

 different according as we suppose the moment of inertia of the 

 anemometer very small or very great. 



If we suppose it very small, the anemometer may be supposed to 

 be moving at any moment at the rate due to the relative velocity at 

 that moment, and therefore the mean velocity of rotation of the cups 

 in one revolution of the merry will be that corresponding to the mean 

 relative velocity of the anemometer and the air. If, as is practically 

 the case, W be small as compared with V, we may expand (a) in a 

 rapidly converging series according to ascending powers of W. All 

 the odd powers will disappear in taking the mean, and if we neglect 

 the fourth and higher powers we shall have for the mean 



so that W 2 -^4V is the small correction to be added to the measured 

 velocity of the anemometer in order to correct for the wind. 



On the other hand, if the moment of inertia of the anemometer be 

 taken as very great, the rate of rotation of the cups during a revolu- 

 tion of the merry will be sensibly constant. If V be the velocity of the 

 anemometer relatively to the air, v the velocity of the centre of one 

 of the cups, and if we suppose the rotation of the anemometer 

 resisied by a force of which the moment is F, then, according to 

 Dr. Robinson's researches, we have approximately 



F=AV /2 -2Bz;V / -C^. 



In the present case friction is not taken into account, and instead of 

 F we must take the moment of the effective moving force. Further- 

 more, it appears from the experiments of Dr. Robinson, in Dublin, 

 that the observations were almost as well satisfied by taking the first 

 two terms only of the above expression for F as by taking all three, 

 and this simplification may be employed with abundantly sufficient 

 accuracy in making the small correction for the wind. We have, 

 therefore — 



F=AY / 2-2BvV / , 



where V is given by (a). In order that the anemometer may be 

 neither accelerated nor retarded from one revolution of the merry 

 to another, the mean effective force must be nil; and taking the 

 means of both sides of the above equation, observing that, in conse- 

 quence of the supposed largeness of the moment of inertia, v is 



