THE CONSTANTS OF THE CUP ANEMOMETER. 
783 
trace whether they be casual or depend on extra powers of v ; and I entertained such a 
hope when I entered on the experiments, but it has been but very imperfectly realised. 
(13.) In the first place, we have instead of real wind the transport of the anemo- 
meter with the velocity Y through air which is not quiescent, but moving in the same 
direction with a velocity W. Therefore we must use instead of Y, Y'=V — W. 
Here are two elements of uncertainty. It is not certain that a body moving through 
a fluid even if this be quiescent, is equally resisted with one at rest sustaining the 
impulse of a current fairly uniform, much less so if the fluid be in a state of dis- 
turbance ; and secondly, though Y and v are given with sufficient accuracy by the 
chronograph* it is otherwise with W. We cannot measure it in the actual track of 
the anemometer, and must reduce our measures to that track's centre on some 
hypothesis ; while we may be sure that it varies in every part of the circumference 
described by the cups. But even in the line of its measurement it will be found very 
irregular and disturbed by powerful eddies ; and besides these vorticose motions in the 
direction of V, there is another Z of very irregular character in a direction normal to 
this, so that the air moves in spirals not in circles, and instead of V — W, we should 
use \Z(V — W) 3 +Z 3 , but I see no possible mode of estimating the effect of Z cor- 
rectly, on account of its intermittent character. W oltman’s fly, which was used by M. 
Dohrandt to measure W, seemed unknown to our opticians ; but at a latter period 
I was informed by a scientific friend that it was called here an air meter, and he lent 
me one, which I found useful. But I could scarcely have used such a one for habitual 
measurement without chronographic registry, and I wished for something that would 
show the changes of the vortex more evidently. Fig. 3 (Plate 70) shows the method 
I adopted. A slip of deal, \ inch square and 23 feet long, was suspended by a fine 
thread from the summit of the dome ; to prevent bending, it was braced by other threads 
fastened 4 feet above it ; to it were suspended two of those thin caoutchouc balloons 
which are sold for playthings for children. They were about 8 inches diameter and a 
little higher, and hung 4 feet below the rod, their centres on a level with that of the 
anemometer, and 14 inches outside it. Threads connecting them with the ends of 
the rod prevented their being drawn in among the cups. From this it will be seen 
* A second of time measures on the chronograph 0 - 208. Now the highest value which I obtained for N 
was one revolution in a second, for v 1'67 ; so that even in this last case -—gth of a unit of A = 0'012 inch, a 
quantity quite visible. It must, however, be remarked that my Y belongs only to the cup whose arm is per- 
O 
T" 
pendicular to the horizon, whose 0 = 90°. For any other# it =V(l+i xcos 3 0). For Nos. I. and II. 
this is 1 + R243 X cos 2 6. At its maximum the addition is g T of the whole ; in its mean value through the 
semicircle half this. But this increase of Y is counteracted by its obliquity to the plane of the anemo- 
T 
meter motion, which lessens its power to turn the cups The tangent of this = ^costf; it = 12° 26' at 
maximum. If we knew the forms of a and a! we could compute the effect of this obliquity ; but as it is, 
we can only say that both these disturbances are greatest when a and a are least, so that probably their 
influence may be neglected. 
MDCCCLXXVIII. 5 H 
