THE CONSTANTS OF THE CUP ANEMOMETER,. 
10G1 
S(Y'_y) 
If the number of observations be sufficient, S(ffitr) = 0, and we have Ax= — 
Aa; 2 d 2 Y 
This will give an x nearer the truth (not exact unless X 
S(e-e') ' 
3 be insensible), and a 
CtJu 
second computation will in general be sufficient. When the constants give the mean 
Y—V / =0, the Y so obtained must be very nearly =U, as shall be shown presently. 
(68.) First as to a: in the case of v=0, we have the measure of it given in para¬ 
graph (27). These must be reduced by some hypothesis as to the action of friction. 
In the first part of my paper I assumed that the momentum of the cups carried them 
past the point of equilibrium, induced to this by the small value of a given by min. 
T—/ 
squares (paragraph 39), =99. This gives a-. 
My preliminary work with 
(V—W) 3 ‘ 
the two instruments showed that this was too small, and I recurred to the more 
natural supposition that the cups stop when the wind’s force = T -\-f This gives 
a= 15‘315 at Bar. 30° and Therm. 32°.* For 4" cups it is 3‘357, very nearly in the 
proportion of the areas. I know no means of determining whether this constant varies 
with v ; the individual measures seem to show that it does not change with Y. The 
lateral pressure on the upper bearing of the shaft causes a resistance as V 3 , and will 
diminish a; but the probable value of its coefficient is axO‘00051, which may safely 
be neglected. The change of a, if it exist, cannot have much influence on Y; for 
dY _ 0 
da. 
2 a 
/ y'- 
+ 
</> 
Taking I. and X. of Table XXL, where <f> is a minimum and 
maximum, we have dY=daX 0'0573 and claX 0T603. 
(69.) As to y, if there be no resistance as Y, except what appears in the resultant, 
the equation of motion is Y 3 + / y 3 — 2Yvx —- = 0, from which we see that y, the co¬ 
efficient of v z , =1. This is its major limit; if we diminish y by Ay, the equality of Y 
and Y' may still be preserved by diminishing x. But the value of Y is a little 
_ # /\ j/ ^ 'U 
decreased: so the AV= v /V 2 —A yxvv '\— V, or, in the case of K, - -*~ y . Such 
diminution can only be affected by an expenditure of power in driving air before the 
cups, or throwing it outwards : and I tried to find a limit by making them revolve in 
quiescent air. For this purpose I mounted four forms of E on a vertical spindle driven 
by Huyghen’s maintaining apparatus, and noted the time and moment at the cups. 
The resistance was always more than twice the action of direct wind on the convex 
sides, and I think its excess may be taken as the extreme possible value of y in the 
* I tried to measure it by the spring balance, but the oscillations were too extensive to permit any 
continuous observations. By noting tbe time, and counting the turns of K while the oscillations of E., 
were clear of the sides of the box, I got two values of «, 15’165 and 19‘562 ; but the possible difference 
of wind must be remembered. 
