THE CONSTANTS OF THE CUP ANEMOMETER, 
807 
of No. III. (with which I commenced operations) into three groups; the first those in 
which v<5 ; the second those where it is between 5 and 9 ; the third those above 9. 
The final equations are : — 
1. 
a X 1 3 
— 2/3 X 
2 "501 — yX 0*591 = 
71-641 
a= 
12-1 17 
aX 2-501 
— 2/3x 
0-591— yX0-160 = 
11-226 
giving (3= 
24-436 
aX 0-591 
-2 0X 
0-160— yX 0-047 = 
2-217 
y= 
— 59-672 
2. 
a X 13 
— 2/3 X 
3-S31— yX 1-170 — 
49-175 
a = 
9-593 
aX 3*831 
— 2/3 X 
1 " 1 70 — y X 0"368 = 
13-451 
0= 
6-568 
aX 1-170 
— 2/3 X 
0-368-yX0‘021 = 
3-782 
7= 
21-554 
3. 
a X 14 
— 2/3x 
5‘077— yX 1*864 = 
29-319 
a= 
11-975 
aX S'077 
— 2/3 X 
1-864 — yX0’692 = 
10-037 
0= 
14-287 
a X 1 "864 
— 2/8 X 
0*692 — y X 0*259 = 
3-485 
7= 
— 3-617 
All. 
a X 40 
— 2/3 X 
11-409— yX 3-625 = 
150135 
a= 
9-472 
aXH-409 
— 2/3 X 
3-625— yX 1-220 = 
34-714 
0= 
8-469 
aX 3"625 
— 2/3 X 
1-220— yX 0-427 = 
9-484 
7~ 
9-814 
There is here no evidence of dependence on v ; but there is very great discordance. 
The values of a are most consistent, and do not differ much from my measures of it, 
being (except in one number) a little less, as I had expected. [3 is more aberrant ; 
but the range of y is extravagant : its value in 1 is unreal, for it cannot have a 
negative value greater than a. In the case of this set, one cause of error is obvious. 
When v is small, the moment of the anemometer is not sufficient to master these 
casual irregularities of friction, of which I have already spoken ; but at higher speeds 
their effect is much less sensible. Another is the smallness of the coefficients of /3 
and y compared to those of a. In 1 the coefficients of /3 and y compared to those 
of a are 0"38 and 0'045 that of a ; in 2 are 0'59 and 0'09 ; in 3 are 0'72 and 0"13. 
We may therefore expect a to be better determined than 0, and (3 than y. 
To make this clearer by an example. If we determine the a and y of the first 
group, keeping the independent terms of the three equation as symbols, we have — 
a= H X 2 -46 - IT X 26 -0 1 + H" X 5 7 \5 9, 
y=-Hx5579 + H / x659-19-H /, X 1564-41, 
from which it is evident that errors in H will affect y very largely in comparison of a. 
If we suppose the probable errors of the frictions in the observations to equal those 
given by my friction measures at Rathmines, we can compute those of a and y due to 
this cause of error. In three of the thirteen observations the PE of F=ffi5 - 4 ; in 
three, dz35-4 ; in three, ffi9 "7 ; in two, ffil7‘8 ; in one, ffi47'0 ; and in the last, dz3'2. 
MDCCC LX XVIII. 5 L 
