806 
DR. T. R. ROBINSON ON THE DETERMINATION OF 
B=24 oz. ; /+ B'=2145-4. 
No. 
D. 
S. 
N. 
A. 
b. 
V. 
V. 
W. 
/"'■ 
Log. p. 
m. 
255 
56 
240 
131 
69 
61 
2123 
2-46 
2-46 
60-9 
0-00442 
7-618 
256 
66 
144 
105 
55-4 
2333 
3-75 
2-73 
77-6 
5-763 
257 
76 
156-8 
130-5 
53 
25-405 
4-66 
2-85 
97-7 
if 
4*837 
- 
On examining these tables it is seen that to, the ratio of the wind’s velocity to 
that of the anemometer, is different in each of the four instruments, and varies in 
each. In No. I. the extreme values are 21'58 and 2'32 ; in No. II. 8'81 and 3‘63 ; 
in No. III. 18‘00 and 2’41 ; in No. IV. 1 6 ‘ 1 4 and 3'44. " It decreases with the 
increased size of the cups and length of the arms, and with increased v it increases 
with F. On examining its rate of decrease with an increasing v it is seen to be of an 
asymptotic character, such that it may be expected to remain finite even when v is 
quasi infinite. All these conditions are satisfied by equation (I.), the positive root 
of which gives ^=f+ \/^+l+~?=*+ \A+Ai ( m 4 
If, as is probable, /3 and y are proportional to a, the variation of to depends upon 
F .... - 
— alone; and its limiting valu e=x-\- ^/z. It follows from this that the variation of 
to will be less in proportion as F is less, the cups larger, and the arms longer. 
(31.) We can now proceed to determine the constants a, /3, and y, as already 
indicated, by combining the equations given by the observations by minimum squares. 
The present case, however, is not favourable for the employment of this method, 
which supposes that the error of each equation, besides being small, depends solely 
on errors of the constants, and that their coefficients are exact. This is by no means 
true here. V' and v are both liable to errors which are variable, and F to variable 
ones which may be of considerable amount, and also to casual ones even larger. Still, 
the result so obtained is probably better than what would be obtained by dividing the 
equations into three groups and proceeding by elimination. 
(32.) I put the equations into the form (II.), 
a— 2^X~-y X “ = ; or, a—2/3g-yg~=r) (IV.), 
both to avoid the large numbers that would occur in dealing with the original form 
(I.) and to diminish the influence of errors of V'. The measures of a, given in Tables 
VI., VII., and VIII., show that (I.) contains no term of V' ; and in the first instance 
I tried one lv, but found that it led to values of V' so much astray that the presence 
of it is inadmissible. 
(33.) As it was possible that a, &c., might be functions of v, I divided the equations 
* These numbers explain my assuming in my original paper that the limiting value of to is 3. The 
anemometer with which I experimented had 3-inch cups, 6-incli arms, and considerable friction. 
