It is owing to the difference between the true and apparent directions of the wind that it appears to shift its direction by tacking ship; and if the difference of the directions be observed when on different boards (the wind on both tacks being supposed to remain constant, and the yacht to have the same velocity, and to sail at the same distance from the wind), the half-difference will be equal to the angle B A C. By knowing this, together with the velocity of the yacht B C, and the angle B C A, we may obtain the true velocity of the wind; or by knowing the velocity of the wind and of the yacht, and the apparent direction of the wind, we may calculate the difference between the true and apparent directions of the wind.
Thus, if the velocity of a yacht, represented by B C, be 7 miles per hour, that of the wind, represented by A B, 27 miles per hour, and the angle with the yacht's course, with the apparent direction of the wind B C A, equal to 7-1/2 points, the difference between the true and apparent directions of the wind will be obtained by drawing the line B C, equal to 7-1/2 points; then with an extent equal to 27 miles, taken from the scale, and with one foot in B, describe an arc, to cut the line A C in A; join A B; then the angle B A C, being measured, will be the required difference between the true and apparent directions of the wind.
_Sailing in my yacht, I saw a lighthouse bearing E. by N., and, after sailing 14 miles N. by W., it bore S. E. Required the distance of the yacht from the lighthouse at both stations._
SOLUTION.--Describe the compass E. S. W., and let its centre X represent the place of the yacht at the first station; draw the N. by W. line, X Y, equal to 14 miles, and Y will represent the second station.
Draw the line E. by N., X Z, of an indefinite length, and the line Y Z parallel to the S. E. and N. W. line of the compass: the point of intersection Z will represent the place of the lighthouse, and the distance Y Z, being measured by the same scale of equal parts with which the 14 miles of course is laid off, will be found to be 16-3/4 miles, and X Z 9-1/4 miles.
Charts can be purchased, at a very reasonable rate, of all the important harbors and the whole coast-line of the United States. They come nicely backed with cloth, so as to stand considerable hard sea-usage. They should be kept, when not in use, rolled up in a large tin box made for the purpose, or a long, narrow wooden trunk, called a chart-box.