THE CONSTANTS OF THE CUP ANEMOMETER. 
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compute the entire of No. I. on this hypothesis, but ten on which I tried it showed similar 
advantage. 
(41.) I think these results warrant 11 s to believe — first, that if the constants were 
properly determined, the equation (III.) with or without y would give V' with 
sufficient accuracy for all practical purposes ; and secondly, that for 9 -inch cups the 
same constants avail for arms of 24 and 12 inches. It also deserves notice that the 
substitution of ^-inch tube for knife-edged arms in No. III., makes very little 
difference in the value of V', as is seen by comparing 164 with 163. 
(42.) By using the differential formulae (V.) and (VI.) to correct the constants, the 
mean value of AY' might be considerably reduced ; but I think this unnecessary, and 
I hope to get more accurate values of them by another process. 
The plotting of No. II. is shown in Plate 67. It is far more confused than the 
previous two, and shows that the disturbing agents were still more powerful. It is 
not possible to detect the curvatures, and we can only infer that a right line can be 
drawn giving the average direction of the system, while the breadth of that system 
shows that we may expect the range of AV 7 to be considerable. This was to be 
expected, as the impelling force a (V' 3 +ff) is only one-fifth of its value in I., while the 
frictions are nearly the same, therefore any irregularity on the latter will be felt more 
powerfully ; the same result will also be produced by the lesser momentum of No. II., 
which has less power to equalise fluctuation of motion. That such fluctuation exists 
is evident from examination of the chronograph sheets on which the time of each 
revolution of the anemometer is recorded. For instance, in 125 the maximum time 
of one revolution during the four minutes of the experiment was 4*5 8 s , giving r=l'87; 
the minimum time 2 -39 s , v— 3 '5 8 ; and there were many intermediate values. For 
higher speeds the difference was not so great: in 132 the maximum time was 1 '06 s , 
r=8"16 ; minimum 0‘72 s , v=ll'97. With 9-inch cups these variations are scarcely 
perceptible in the high speeds, but notable when v is very small. Thus in 182 maxi- 
mum time is 6"80 s , v=0'62; minimum 4'50 s , , r=0'95. In such cases it is evident 
that the mean v cannot give the mean V', as m is not constant. If the arms of the 
anemometer had been of sharp plate, it is not improbable that the x and z of Nos. I. 
and III. might have availed here also ; but as their section is 0 - 87 of the area of the 
4-inch cups, y, and in still greater degree /3, bear a much greater proportion to a. 
The character of the plotting prepared me for bad results from minimum squares : 
34 gave a=3T00; /3=9’6607; y= — 31T40, a cannot be larger than that given by 
my measures : and the y would give V 7 imaginary for v above 8. The result was not 
improved by omitting three of the smallest v’s. Assuming y— 0, I had «/= 1 '681 ; 
/3'=2’602 ; both evidently too small. I then tried, as in previous cases, nine-tenths 
of my measured a, and had by six various combinations, a=2"084 ; /3=4"4065; 
y= — 7'626. Still, as formerly remarked, y is too large, and avoiding it entirely I 
got a'=2 - 084 ; /T = 3'489. Then taking twelve distributed over the entire set, I 
computed the values of AV 7 for them, and from these found by (VI.) y— — 0 8146 ; 
£=1-7390 ; 2=2-209. The results are given in 
