Example II.—Sailing towards the land, I mounted the shrouds of my yacht till my eye was about 16 feet above the level of the ocean, where I sighted the top of a known lighthouse that I was looking for, which the chart informed me was 145 feet above the level of the sea. Required the distance of the lighthouse.
In the table,
| Opposite 16 feet stands | 5.29 miles | |
| Opposite 145 feet stands | 15.93 | |
| —— | ||
| Distance | 21.22 miles |
Upon seeing the flash of a gun I counted 30 seconds by a watch before I heard the report. How far was the gun from me, supposing that sound moves at the rate of 1,142 feet per second?
The velocity of light is so great, that the seeing of any act done, even at the distance of a number of miles, is instantaneous. But by observation it is found that sound moves at the rate of 1,142 feet per second, or about one statute mile in 4.6 seconds: consequently the number of seconds elapsed between seeing the flash and hearing the report being divided by 4.6 will give the distance in statute miles. In the present example the distance was about 6-1/2 miles, because 30 divided by 4.6 gives 6-1/2 nearly.
To find the difference between the true and apparent direction of the wind.
Suppose that a yacht moves in the direction C B from C to B, while the wind moves in its true direction from A to B, the effect on the boat will be the same as if she be at rest, and the wind blow in the direction A C with a velocity represented by A C, the velocity of the yacht being represented by B C. In this case, the angle B A C will represent the difference between the true and apparent direction of the wind, the apparent being more ahead than the true; and, the faster the vessel goes, the more ahead the wind will appear to be. We must, however, except the case where the wind is directly aft, in which case the direction is not altered.
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.