188 Experiments with Whirled Anemometers. [May 12, 



blem of determining d as a function of V and F, where v is positive, 

 but F may be of any magnitude and sign, and therefore, V also.* 

 Negative values of F mean, of course, that the cups instead of being 

 retarded by friction, are acted on by an impelling force making them 

 go faster than in a frictionless anemometer, and values greater than 

 F x imply a force sufficient to send them round with the concave sides 

 foremost. 



Suppose now F to be so large, positive or negative, as to make v so 

 great that V may be neglected in comparison with it, then we may 

 think of the cups as whirled round in quiescent air in the positive or 

 usual direction when F is negative, in the negative direction when F 

 is greater than F 1 . When F is sufficiently large the resistance may be 

 taken to vary as v 2 . For equal velocities v it is much greater when 

 the concave side goes foremost, than when the rotation is the other 

 way. For air impinging perpendicularly on a hemispherical cup, 

 Dr. Robinson found that the resistance was as nearly as possibly four 

 times as great when the concave side was directed to the wind as 

 when the convex side was turned in that direction. f When the air 

 is at rest and the cups are whirled round, some little difference may 

 be made by the wake of each cup affecting the one that follows. 

 Still we cannot be very far wrong by supposing the same proportion, 

 4 to 1, to hold good in this case. When F is large enough and 

 negative, F may be taken to vary as v 2 , say to be equal to — Jjv~. 

 Similarly, when F is large enough and positive, F may be taken equal 

 to LV, where in accordance with the experiment referred to, L' must 

 be about equal to 4L. Hence we must have nearly — 



rj= — L£ 2 , when £ is positive and very large ; 

 ?7=4L£ 2 „ negative „ „ 



Hence if we draw the semi-parabola OAB corresponding to the equa- 

 tion «/=4L£ 2 in the quadrant ^0 — £, and the semi-parabola OCD with 

 a latus lectum four times as great in the quadrant £0— ?/, our curve 

 at a great distance from the origin must nearly follow the parabola 

 OAB in the quadrant tjO — £, and the parabola OCD in the quadrant 

 gO — rj, and between the two it will have some flowing form such as 

 PN"MK. There must be a point of inflexion somewhere between P 

 and K, not improbably within the positive quadrant gOrj. In the 

 neighbourhood of this point the curve NM would hardly differ from 

 a straight line. Perhaps this may be the reason why Dr. Robinson's 

 experiments in the paper published in the "Phil. Trans." for 1878 

 were so nearly represented by a straight line. 



# Of course v must be supposed not to be so large as to be comparable with the 

 velocity of sound, since then the resistance to a body impelled through air, or haying 

 air impinging on it, no longer varies as the square of the velocity. 



f " Transactions of the Royal Irish Academy," vol. xxii, p. 163. 



