808 
DR. T. R. ROBINSON ON THE DETERMINATION OP 
The errors must have the same sign in each H. Hence I find PE of a=fi = l - 30 ; 
PE of y= = p39'06 ; thirty times that of a. The errors of W must also be injurious ; 
the more so as they affect every term of the three equations, but it is impossible to 
measure them, and if known the calculation of their influence would be very com- 
plicated. 
(34.) We cannot test surely the accuracy of these constants by trying which of 
them gives the best value of V', for it is to he noted that they, and especially y, may 
be changed to a considerable extent without ceasing to satisfy, at least approxi- 
mately, the original equations.* Supposing F unchanged, we have for one of them 
m 3 Aa — 2A/3xm — Ay=0. Combining this with a second one we obtain Aa( — - — ) 
= A /3 ; A y= — AaXmm (V.); and the constants so increased will satisfy these two 
07b “I - OYb^ 
equations. But it will be found that, except v is very small, — — - and mm do not 
A 
differ much for any other pair ; and therefore if we take their means for an 
entire set we shall be able to find the /3 and y belonging to a small change of a. 
Twenty pair from No. I., and as many from No. III., give Af3=Aa X 3'293 ; 
Ay — — Aa X ll‘463.t 
(35.) As y seems the chief difficulty, if it could be found a priori the others would 
be much better determined ; but no means of doing this has occurred to me. By 
causing No. I. to revolve in quiescent air, convexes foremost, it was found that the 
resistance = vr X 2 8 ; but this coefficient is far greater than what it would be in a 
current of air. When moving down that current, whose velocity is always more than 
2v, the convexes experience hardly any pressure, when against it, the pressure is 
largely included in the expression of a' . (V^+ifi). Therefore y must be much less 
than 28 — a. We may, however, consider a as tolerably determined by the process 
described in paragraph 27. 
(36.) In this state of uncertainty I consulted Professor Stokes, and his reply was 
so instructive that (with his permission) I annex it in an Appendix. 
In it he suggested that as the equation (IV.) has only two variables £ and 77 , it 
could be plotted on a plane surface ; that such plotting might give valuable informa- 
tion, not only as to the existence of the errors which I suppose to affect the V, &c., 
but as to the equation (I.) really representing the conditions of the anemometer 
* This is well shown in the Appendix. 
t The same may be done without changing a by making A y= — 2A/3X mean to. I tried this in rather 
an extreme case on the constants given in paragraph 38, changing them so that y x = — sq 3 - I got a value 
for Xy identical with that obtained on this hypothesis from thirty- three of the equations in Table XII. It 
mav be remarked that this supposition gives a formula analogous to M. Dohrandt’s Y' =vx 1 + 
This, of course, gives good results for many of the observations, but is astray both for high and low 
values of v. Its maximum AV'= + 5 - 56; its minimum = -i-2'37; while those of Table XVI. are +2'68 
and — IT 7. Its probable error is twice that of (III.). 
