Many other instruments have been proposed for esti mating a ship's rate of sailing, but all of them are liable to this insurmountable objection, that, being attached to some part or other of the ship, they give the distance as it is affected by every irregularity of her motion ; whereas the log, with all its imperfections, exhibits the ship's motion in reference to a continuous line, of consi derable length, on the surface of the ocean. And indeed it may safely be affirmed, that no mechanical contrivance, however accurately it is fitted to indicate the velocity of a ship in smooth water, can be employed for the purpose of measuring the distance she has sailed on the surface of the ocean, so long as it exhibits the rectified length of the line actually traced out by the ship, undulated as that line must be, both on account of the inattention of the steersman, and the agitated state of the water. The log, therefore, must be still regarded as not only the best contrivance which has yet been suggested for Pleasuring ^ a ship's rate of sailing, but as affording, in principle, the only sure method by which a knowledge of the dis tance sailed can be obtained.
Of the Instruments necessary for delineating a Represen tation of a Ship's Course and Distance, and solving other nautical problems.
The instruments necessary for this purpose are few in number, as well as simple in their application, includ ing merely a pair of compasses and a ruler, with various lines traced on it, called Gunter's Scale.
This instrument is chiefly employed for describing circles and arcs, Or for laying off or measuring straight lines. The form of the instrument is too well known to render a particular description of it necessary. Suffice it to say, that it consists of two diverging legs, moveable on a well finished joint, the extremities of the legs, which ought to be of steel, being brought to fine points, in order that the instrumeht may be usecl for measuring. with accuracy the most minute distances. In good com passes, the joint is SO contrived as to admit of various degrees of tightness, so as to allow the instrument to play with facility, or be retained in some particular state of opening., WhEll sameness of extension is required.
Though nothing but long practice can enable a person to manage this simple instrument in an easy manlier, some general directions may not be altogether useless for guarding against an awkward and incorrect method of handling it. As it frequently happens that only one hand can be spared for adjusting and applying it, the learner should habitually accustom himself to use the instrument without having recourse to both hands, unless in very particular cases. In applying the compasses to a scale, or in measuring the length of a line, the instru ment should be held nearly upright, no more pressure being applied to it than is sufficient to preserve the points from altering their position. In describing circles or arcs, the head of the compasses should be held between the thumb and middle finger, and then made to roll be tween the thumb and fore-finger, while one of the legs is allowed to rest gently on the paper, and the other is caused to touch it with an uniform pressure.
The various lines on this instrument, as we have stat ed in the history of navigation, were first laid clo.,vn on a
scale by Mr. Edmund Gunter. Thc ruler to which these lines are applied for the use of the mariner is commonly two feet in length, and about an inch and a half, or two inches, broad, both faces of it being graduated. The lines on the one face are employed for the construction and measurement of figutes, both plane and spherical; and those on the other, for resolving, with the liclp of a pair of compasses, the different problems in navigation, and some of the more common operations of arithmetic. To distinguish the lines on the two faces from each other, we shall call the former natural lines, and the lat ter, logarithmic, or artificial.
1. Lines'of equalparts.—The scales to which lines of equal parts applied are of two kinds, and are deno minated simple and diagonal.
The Simple Scale, (see Fig. 1. Pl. CCCI V.) is formed by drawing two parallel lines, and then dividing them at right angles into such a number of equal parts as the destined use of the scale may require. An additional division, AC, on the left hand, is retained, to be after wards subdivided into to equal parts, for the conveni ence of obtaining intermediate lengths between the pri-i mary divisions. This scale can only be used for laying off a line, Ihe dimension of which is expressed by two digits, unless 10 of the primary divisions be employed to represent an unit of the next highest order.
The Diagonal Seale, (Fig 2.) is constructed by draw ing I t equidistant parallel lines, and then dividing the tipper line into as many equal parts us may be thought proper. Through each of the points of division lines are then drawn, cutting the parallel lines at right angles; and the first division, both above and below, is subdi vided as before, into 10 equal parts. In this manner the primary and secondary divisions of the scale are obtain ed. The ternary or third order of divisions, which must be a tenth of the secondary, arc procured by drawing diagonal lines from the 9th of the secondary divisions above, to the 10th of the same division below ; from the 8th above to the 9th below, and so on in the case of each corresponding pair of the secondary divisions. By halving each of the primary divisions, and dividing the last one at the other extremity of the scales by diagonal lines, drawn in the same manner, another scale is ob tained of half the dimensions. With either of these scales, a line, whose dimension is expressed by three digits, may be laid down or measured with the utmost precision. Thus, let it he required to take from one of these scales a line, whose length is expressed by 867; place one foot of the compasses in the intersection of the sixth secondary division, and the seventh ternary one, and then extend the other foot to the eighth primary division. The extent will correspond to 867. The same extent would also answer to 86.7, 8 67, .867, Scc. or to 8670, 86.700, E.cc. according to the local value as signed to the leading digit ; but whatever value is at tached to the primary divisions in the measurement of any part of a figure, the same value must be supposed to belong to them in measuling. all the other parts.