818 
DR. T. R. ROBINSON ON THE DETERMINATION OF 
(54.) It is not easy to tell beforehand what difficulties may beset this mode of 
investigation. The most obvious one is the irregularity of wind which may be ex- 
pected to vary from one anemometer to the other, and also at each during an 
experiment. If it blow in the direction W.E., or vice versd, there is danger that 
the eddy caused by the windward one may reach the others; if it be S.N., different 
streams of the current may fall on each. The extent of these disturbances may be 
studied by making the friction of E equal to that of S ; and it will also show what 
length of time is required to make the average V the same in both. The changes 
of V during the experiment may, I think, be eliminated by sorting the two v into 
sets, of which the individuals are all in the same proportion, and comparing them 
separately. This can easily be done by measuring the intervals on the chronograph 
sheets. 
How far these precautions will avail can only be ascertained by trial, but I hope 
that it may he given to me to make this trial to its full and decisive extent. 
Appendix. 
The object of the experiments being to determine the relation between the velocity 
of actual wind supposed uniform (the air also being at, or reduced to, a normal density), 
the velocity of the cups and the friction, I assume in the first instance as correct, the 
values of those two quantites given by the experiments with the whirling machine, 
and proceed to consider the relation. 
Let V' be the velocity with which the air passes the anemometer, that is, in the case 
of the actual experiments, the velocity of the centre of the anemometer itself corrected 
for the velocity of the wind produced by it ; let v be the velocity of the centre of 
the cups, F the moment of the total friction. Then supposing the density of the air 
normal for a given anemometer, v will depend only on V' and F, that is, there will be 
a functional relation between the three variables V', v, F, leaving two of them 
independent. 
In investigating experimentally the relation between two variables, it is often very 
useful to plot the results of experiment, as the general character of the relation 
sought, and the allowance to be made for errors of observation can thus be estimated. 
The relation between three variables would be expressed graphically by a surface 
instead of a curve, and it is troublesome to model a surface. If, however, we can find 
a relation between the variables which is satisfied, provided some other relation is 
satisfied, we can thereby reduce the number of independent variables from two to one, 
and employ ordinary plotting in investigating the relation between the variables. In 
fact, the relation sought is reduced from one of the form Y' = (p(v, F) to one of the 
form /(V', v, F) = i//{/ l (V', v, F)}, where </>, xp denote unknown, and f / L known 
functions. 
