AND DIRECTION OF THE WIND AT SEA. 461 
what will be the direction and the velocity of the wind which a person in the 
ship will feel ? 
Now, the motion of the ship from A to B being equivalent to a wind moving 
with equal velocity in a contrary direction, or from B to A, then any particle 
of air at rest at A will be driven, if acted on by the impact of this adventitious 
wind only, to a distance, equal to AB, beyond A, and in the same direction, or 
to E; but if acted on only by the natural wind, the particle will receive a velo- 
city and a direction equal to that, and be driven from A to F; but as the particle 
is acted on instantaneously by both forces, it will neither go to E nor to F, but in 
an intermediate direction, and closer to one or other according to the relative 
strength to the two forces, or in the diagonal of the parallelogram of which A F 
and A E form two sides. AG, therefore, in the parallelogram AE FG, repre- 
sents, by its length and position, the distance to which, and the direction in 
which, a particle at A will be driven under the united influence of the natural 
wind blowing over the sea, and the artificial wind caused by the motion of the 
ship; i.e, AG represents the apparent wind, or that which a sailor would 
observe. 
For convenience of illustration we may complete the parallelogram A BDC, 
which is similar to the parallelogram A EK FG, and where A D is consequently 
equal to AG; and we may now, for the purposes of calculation, omit all but the 
triangle A B D, in which the sides A B, A D, being given by observation, and the 
included angle B A D being obtained from the difference of the observed directions 
of the ship and of the apparent wind, we have merely to compute by the usual 
rules for plane triangles, the length of the side B D, or the velocity of the true 
wind; and the angle ABD, which, being added on to the course of the ship, 
gives the direction of the true wind. 
Considering, however, the necessary length of time which such a computation 
must occupy in the hands even of the most expert (the mere preparation of the 
angles for computation would of itself be no small matter, on account of the 
rough character of the subtraction of the course of the ship from the direction of 
the wind—both observed by compass points—the reduction of this to degrees, 
then the re-reduction of the resulting angle into points, and the addition of them 
to the course of the ship): considering, also, the almost infinite number of times 
the calculations would have to be gone through in any voyage, and the extreme 
improbability of any amateur undertaking so large a quantity of an unimproving 
sort of labour, I have had a set of scales made for solving the problem by 
inspection, and the entry being made with the velocities and directions observed, 
the velocity and direction of the true wind are immediately given. 
These scales, which are represented in Plate XI, are formed of two ordinary 
jointed rulers, having moveable circles marked with the points of the compass on 
the joints, and three sets of divisions on the legs, to include all possible velocities 
