EXAMPLE I.—A ship's rate of sailing by a log-line, the interval between knot and knot of which is 45 feet, is 9 miles per hour, estimated by a glass which runs 35 seconds.—What is the true rate of sailing ? True tate= 5 X 9 X 45 — = 7-1 miles per hour. 8 x 35 — 280 Besides the sources of error connected with the length of the log-line, and the inaccuracy of the half-minute glass, there arc others almost inseparable from this mode of estimating the distance, which cannot be so easily ob viated. Of these, the most difficult to appreciate, and make allowance for, is the change of place to which the log is liable, after it is thrown overboatd; for, in order that the quantity of line run off the reel may afford an accurate measure of the rate of sailing, it is evident that the log ought to retain, during the running of the sand glass, the exact position in which it was at the instant the whole of the stray-line had made its escape. But the agitation of the surface of the sea, the influence of the winds, and the effect of currents, as well as the tension of the log-line itself, all conspire to give a motion to the log, and thus to produce a considerable degree of unceTtainty with regard to the indications of the log-line. Different methods have been proposed to render the log stationary, or at least to counteract, as much as possible, the opera tion of the causes by which the stability of its position is affected, though none of them can be said to have fully answered the purpose.
One of the best contrivances to guard against the fluc tuations to which the log is exposed at the surface of the water is that of BououEn, an account of which was Vnr XIV Pt T first published in the Memoirs of the French Academy for 174.i. The log received thc ferm of a tone, the dia ameter of whose base was 3 inches, and the slant height 6 inches. The log-line being passed through the axis of this cone, was fastened to it after 50 or 60 feet of the line had been drawn through, with the apex or point to wards the reel. At the end of the line was attached a contrivance made of metal, called the Diver, which was made sufficiently heavy to allow the cone just to float with its apex at the surface. The diver was constructed of
two square plates of tin, placed at right angles, and sol dered together at the intersection of their diagonals. 'flie size of the plates, to suit a cone of the above dimensions, is recommended by Bouguer to be 91 inches in the length of one of the sides. The diver is fixed to the line by a bridle, as in the case of the common log, one end of the bridle being fastened at one extremity of the diagonal formed by the intersection of the two plates, and the other by a pin at the opposite extremity of it, so as to admit of being detached when the log is to be pulled home. When this compound log is used, the diver will sink sufficiently deep to be beyond the influence of the superficial agitation, and thus the log itself will remain nearly in a fixed position, the cone being only affected by that part of the motion at the surface, which is the re sistance of the cone to that of the diver. The relative resistance, in the case of a cone and diver of the dimen sions adopted by Bouguer, is as 1 to 5, so that a log thus formed will drive only a fifth part of what a common log would do in like circumstances, and consequently the distance inferred by means of it will be, in many cases, nearer the truth.
When this log is employed, it is recommended to be thrown alternately with the common log. The differ ence between the rates given by the two, being aug mented by its fourth part, is the correction to be applied to the rate obtained by the common log, at the middle time between the hours when they were respectively hove; and is additive or subtfactive, according as the result given by the compound log is greater or less than that given by the common log..
The angle formed by the directions of the two logs being increased by its foutth part, will be an approxi mated correction to be applied to the apparent course, being allowed towards the right or left hand, according as the compound log, when a person looks from the ship towards it at the time it was hove, was to the right or left of the common log.