1062 
DR. T. R. ROBINSON ON THE DETERMINATION OF 
negative direction. It would give for y -—-; but I think this action must be small 
in a current of wind moving with nearly three times the velocity of the cups. It is 
found to increase as the diameter of the cups and the length of the arms diminish ; 
for E it gives + but for E + (to be soon described) —3’3406. This sup¬ 
position would give smaller values of V; for No. II. of Table XXI., where Y with 
y— 1 is 35’255, the difference is 1’871, and the true value is certainly between these. 
I will use y= 1 as certainly known. 
(70.) For x, as Iv and E x are similar and equal, it must be the same in both, and 
the means of obtaining it are explained in paragraph (67). Here I need only show 
j /_ j 
how 7 its first approximation is got: Supposing iv= 0, w 7 e have 2Yvx=^ — ~^ J r( vJ r v ') > 
but as in Iv r/j is small, and may here be neglected, we have Y =v(x± ^/a; 2 — lj), and the 
sum of the equation becomes 
+*)XS*=8*^+S{*+i0 (VII.) 
V V 
from which x is easily found. When E is not similar to Iv the process is simpler: the 
reading of K gives Y, and we have 2xYv' — Y~-j- yv'~ — <£', whence 
2ccxSv=SY+yS^-s| (YIII.) 
Both these formulae are defective from omitting w, but are near enough to begin 
with. 
(71.) The following table gives the results of the comparison of K and E,, which is 
equal and similar to K. The second column gives the wind’s direction ; the third log. 
air’s density; the fourth the time in seconds ; the tw 7 o next A and A', the number of 
turns made by K and E. ; the seventh log. of —— or A : the two next the velocities 
j i ° uxD r 
of the centres of K and E ; the two next the computed velocities of the wind; and the 
twelfth A"'—Y. Y and Y r 
Y'=v(x-\- ,sj z +~^j w ^en 
were computed by the formulae Y = r (,r-(- x /z\) -j- 
_ 0 -| 
z—x A — 1 , 
$ 
2v \/*\ 
