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 quantities 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 relationt between the variables.