THE CONSTANTS OF THE CUP ANEMOMETER. 
1069 
(79.) It is more difficult to account for the similar dependence of x on the size of 
the cups ; d priori, there seems no reason why small cups should be more resisted than 
large ones, but such is evidently the case. Unluckily I did not place the 12" and 4" 
cups at the same distances as the 9", so that the effect of the cups on x is mixed with 
that of It. I tried to eliminate the latter by interpolating for the values that the 9"x 
would have at the B/s of Nos. 1, 5, and 6, but this could not be done very exactly from 
the three values. However, this gives x for the 12" 0'005 less than for the 9" ; for 
the 4", in No. 5, 0'2894 greater, and in No. 6, 0'7517. The only way in which I can 
conceive the possibility of such an occurrence is the existence of powers of r and Pt in 
the factors, which express the mean effects of wind on the concave and convex surfaces 
of the cups. In equation III. I suppose the mean v to be that of the centre of the 
cups, and that the mean impulse and resistance act at these points. But this is not 
necessarily the case. The effect of the resultant on an element of the cup is (1) as 
the square of that resultant; (2) as the perpendicular pressure on the element; (3) as 
the resultant of that pressure perpendicular to the plane of the cup’s mouth ; (4) as the 
distance from the axis at which the projection of that resultant meets the arm ; and 
(5) as the magnitude of the element. Of these five factors the first contains v and v 2 . 
(4) 
Now v as the element =vX - , which contains It and r; r 3 also enters the fifth, so 
_LL 
that the differential may contain It 3 and r 5 . As to the second we are ignorant of its 
formula, and it is pretty certain that it will depend on powers of the sine and cosine 
of incidence and (at least for the concave) on the curvature. If we knew its exact 
form we could integrate the differential which they form and get the impulse and 
resistance for a given 6, and multiplying this by dO, and again integrating from 0 to 
77 we should find their mean values. Of the terms in this last integration those which 
have sin 3 6 as a factor disappear ; ttv 2 (the surface) will be a factor of the others, 
T 
among which may be the three first powers of — ; and these may produce the change 
of x. 
(80.) In paragraph (41) I inferred from the work with the whirling machine that 
with 9" cups the x is the same for 24" and 12" arms ; but what precedes shows that 
this is not the fact, and that each type of anemometer has a special x. I would 
therefore suggest to meteorologists and opticians the propriety of confining them¬ 
selves to two types : one for fixed instruments, the other for portable ones. For the 
first the Kew type should, I think, be adopted; if the determination of its constants, 
given in paragraph (70), be not thought sufficiently exact, there would be little 
difficulty in making more observations like those described there, and under more 
«e=2‘0709 less than in No. 4, but so large as to make it evident that there must be some other cause of 
the increased value of x, 
