782 
DR. T. R. ROBINSON ON THE DETERMINATION OF 
being the pressure of an unit of wind on the cup estimated in a direction normal to 
the arm. But as the arm carries on the other side of the anemometer’s axis another 
equal cup equidistant and in a reversed position, the action of the wind on its convex 
surface will oppose the motion with the pressure ~R!' 2 a\. The actual force therefore 
= a l( V 3 -f- v3 — 2 V-y sin 6) — a\ (V 2 + -y 3 + 2 V v sin 9) = (cq — a\) (V s — 2Vv sin 0(oq + a^) . 
This force is opposed first by the moment of friction at the centres of the cups, 
secondly by the resistances depending on v~, of which the chief are the resistance to the 
arms and the reaction of the cups on the air which forms an air vortex in the plane of 
the anemometer. When these opposing forces balance each other through a revolution, 
the angular velocity of the instrument must be constant (except for small periodical 
fluctuations, the effect of which is much lessened by the moment of inertia of the arms 
and cups ; still more so if four cups are employed). If we could find the mean values 
in a revolution of cq ; a\ ; a i sin 6 ; a\ sin 6, we could express this state of permanent 
motion by the equation aV 2 — 2/3 Ve — y?; 3 — F = o (I.), in which F can be obtained by 
measurement. <q and a\ must be functions of the angles F and F' which the resultants 
R and R 1 make with the arm that carries the two cups, and which are given by the 
, . . V sin 6 + v 
equation sin F= — — - • 
It or R 
(12.) But even in the case where the cups are at rest and v—o, we do not see our 
way to a determination of these functions. In the case of the concave surface, one 
would naturally suppose that when 0= 1. 80°, the wind being parallel to the mouth of 
the cup can exert no pressure on it ; but so far is this from being the case that a single 
cup will only be in equilibrio 30° beyond this position, notwithstanding the pressure on 
the convex surface. I cannot say how it behaves at 6=o, for then the equilibrium is 
unstable and the cup gets into rotation. Yet more ; the centre of the wind’s pressure 
on the concave varies with 6 ; before 90° it is within the centre, after it outside ; and 
its place depends on the deflection of the air stream-lines, the law of which is unknown. 
Equally uncertain is a\ ; but it is evidently a different function. It acts through the 
entire circumference ; the surface which the convex exposes to the wind varies accord- 
ing to a different law, and the deflection of the stream-lines on it is of an entirely 
different character. I thought it possible that eddies might introduce terms depending 
on the first powers of Y and v, but it will hereafter be shown that this is not sensibly 
the case ; though the expression for F implies that v should lessen a by diminishing 
the arc of 6 through which R is effective. But as cq must be small at the beginning 
and end of the semicircle, it is possible that this influence is not important. These 
considerations, I think, justify me in believing the equation (I.) to be a close approxi- 
mation to the general conditions of anemometer motion. 
If we had a series of observations in which V', v, and F were accurately known, 
we could determine by minimum squares the three coefficients a, /3, and y. If on 
applying these to the successive values of v and F, we reproduce the values of V', 
the correctness of (I.) is established; if not, the march of the errors may enable us to 
