the top of high cliffs could only be conveniently observed upon at considerable distances at sea.

Under such circumstances, first, as regards the town, we must have recourse to the best traverse we can lay out, that is, with the least possible number of angles and sides, and this quite irrespective of the buildings which may be attended to at some future time, with the exception, however, of those with distinct prominent features, on which careful observations should be made.

Considerable attention should be given to set out such a traverse before the angles are taken, so as to obtain the longest sides possible; to make the lines whole numbers in length, and so that minor triangles may be formed by observations, as may be seen illustrated at Fig. 109, where the side O O' may be calculated by taking either of the sides O a, or a b, as the bases of the triangles Oa O', or a b O'; similarly from the length of b O' found by calculation, may be obtained be and e O'. In another instance the line of coast may be so bounded that the traverse will consist entirely of a number of short lines, when we may proceed in a different manner, as in Fig. 110; set out a buoy at B, on the line OO', with the theodolite, so that from B observations may be taken to all the stations a, b, c, &c.; the length of B O' may be calculated from the triangle O' Bg, with O'g as base, all the angles being measured with the sextant, for sine B : sine g:: O'g: BO'; this length being then set out on OO', the position of the stations a, b, c, &c., may be tested from B by measuring the angles O Ba, a Bb, b B c, c Bd, &c., from a boat at B, and laying them off from B on the plan with a station pointer, an instrument we shall explain the use of presently; exactly the same operation may be repeated at A, which will in most cases be a sufficient check; we may, however, have another buoy at C, which we may determine the position of by taking the three angles CA B, ABC, A CB, and then take bearings from C on all the stations above-mentioned. It will be observed that if we take D B O' for another triangle, with B O' last found as base, we may compute the length of the side dB; and from d B, in the triangle d A B, we may compute the length of A B; and OA+ A B+ BO' should by computation be equal to the length which O O' plots on the plan.

The examples illustrated at Figures 108, 109, and 110, are sufficient to explain and suggest the variety of methods we may adopt under various circumstances; for instance, for Figures 109 and 110 we may calculate O O' in the manner illustrated at Fig. 76, and explained under the head of traverse.

Buoys. If any description of buoy is used merely with line and grapnel, it will be drawn under water as the tide rises, and when the depth exceeds the length of line; if sufficient line is allowed to prevent this, the buoy at low water will shift about with wind or current, and so continue to vary from its intended position during the fall and rise of every tide; this is prevented by adopting a particular system; the following is the description of buoy given by Sir Edward Belcher in his "Nautical Surveying" as used by himself; a sketch of it is given at Fig. 111

"A cask of 32 gallons is furnished with double staves and of greater width at bung and opposite, as well as double heads. Holes are bored through the bung and opposite staves to admit of the passage of a spar 34 inches diameter.

"This spar, previously well parcelled and tarred, is driven firmly home; cleated to prevent its working out, and caulked round the cleating. Three feet project on the larger end, and nine on the smaller. The larger end is furnished with irons for a topmast, which is 22 feet in length. Close to the cask at a a thimble is secured, through which the mooring cable passes, as well as one similar at b, where the cable is clove hitched, parcelled, and its parts seized to the spar to prevent chafe. Ballast equal to 2 cwt. is attached at three fathoms below the cask. They were moored taut in the line of the stream, had latterly full-sized buntin flags, and were found to stand bad weather well, and maintain an erect position in very strong currents and tides."

Such buoys answer our purpose perfectly well, but if they are of a much less size it is quite sufficient, and six or seven feet of topmast is all we require.

Another description of buoy is shown at Fig. 112, with details at Fig. 113, in which the conical buoy B is made of zinc, about 2 feet in diameter at top, and about 18 inches deep; at top and bottom, as well as in the centre, are fixed thin pieces of wood to stiffen the zinc against any accidental blows it may receive; inside and out it is well paid over with boiled tar; through the centre of this is a tube of zinc to receive the mast M, projecting about four feet above the cone and two feet below; it is rigged in the same manner as the last. A buoy may also be constructed of pieces of 3 or 4-inch plank, as shown in elevation and plan at Figs. 114 and 115; c and d are two square pieces, above and under the star-like arms, the whole being strongly spiked together and paid over with boiled tar; through the centre the mast is passed in a hole to receive it, and fastened in the same

manner as the first; it is rigged as the other two; it measures across about 2 feet, or a little more. Station Pointer.-This instrument is so similar to the protractor, that a glance at the

appended figure will explain its construction, A and B being two arms provided with verniers to work along the graduated limb, so that either any one or two angles may be set out at once. It is used in the following manner: if out at sea, the boat being on a line fixed in position by objects on shore, an angle is taken with the sextant, between such line and an object on shore or on the water, and shown on the plan; then this angle being set out on the station pointer between the centre bar and the arm A or B, it is only necessary to lay the first along the above line, and make the second A or B coincide with the other object, when the centre of the instrument will be on the plan in the position from which the observation was made in the boat; and it may be either pricked off through the centre of the instrument; or a line may be drawn along the arm A or B, the intersection of which with the other line will also determine the position of the station required. But we may have no line fixed, and require to determine on the plan the position of a point of observation on the water; in this case it will be required to take from the boat the two angles between any three objects on shore, the positions of which have already been carefully determined on the plan; the two angles being taken, the arms of the station pointer are opened so as to contain them,

and the instrument being laid on the plan so that the three arms shall coincide with the three objects, the centre will again be over the station required. In the absence of a station pointer, we may lay down the two angles on a piece of tracing paper, and produce the three lines to a sufficient length; it will be seen that these three lines may be used as a station pointer by making them coincide with the three objects between which the angles have been measured. Even a sheet of paper with the above lines partly cut out may be made to answer the purpose for once or twice.

It will be readily perceived that the station pointer, or that imitation of one which we have just described, may be used for observations on land as well as on the water, and may be made to render very good service in testing the accuracy of any plan; for if from any well-defined position we take any number of angles to well-defined objects, we have only to fix the arms of the station pointer to those angles, when if the plan is correct they will intersect the objects on it, when the centre of the instrument is placed over the point on the plan representing the station of observation on the ground.

The position of the station required may be determined geometrically in the following manner, though the process is much too tedious to be often repeated in practice. Let A, B, and C, Fig. 116, be any three stations on shore or otherwise, of which the positions have been determined; say that from a boat in any position, which we will call D, the angle A D B measures 30°, and BDC 50°; from 180° subtract twice A D B = 60, leaving 120°; from A and B lay off half the remainder = 60, as BAE and A BE; the lines A E and BE will meet at E, where the angle E will be twice the angle A D B, and E will be the centre of the circle A B D; repeat a similar operation at B and C, with regard to the angle B D C = 50, and F will be the centre of the circle BCD; the intersection of the two circles at D will be the position of the boat which was required.

It will be observed that this would be a very lengthy process, if every one of the numerous soundings required had to be thus laid down on the plan; and so indeed would be the use of the station pointer, if two angles had to be measured and laid down for every sounding also. It is for this reason that it has already been pointed out that certain lines along the shore require to be laid down in a systematic manner, for the purpose of facilitating some rapid mode for taking angles, and also for afterwards laying down on the plan the stations from which the observations have been made,

The object, in fact, to be attained is the readiest mode of measuring numerous inaccessible distances and setting these off on the plan; and there is no way more simple than that illustrated at Figures 98 and 99, in which one line is set off perpendicular to another, and therefore containing a right angle; if any number of third sides are set off visually, connecting the first two, and either of the other two angles in the triangles thus formed is measured, the third angle is obtained by the most simple calculation, merely subtracting the measured angle from 90°. In Fig. 117 the line G, F...E has been selected as facing the offing, from which the whole or the greater part of it is visible; the length of it has been calculated from the bases A B and A D in the manner above explained, and portions of it have been measured to verify the calculations; let it be required to set off a portion of it, as B C, equal to the round number 2500 feet, this length having been selected as suitable from a former chart, from which it has been judged whereabouts C will fall; set off B a at right angles to B Č, and make Ba very accurately equal to any assumed round number as 200 feet; assuming Ba as radius, and BC as tangent, divide 2500 by 200 = 12.5000. Amongst the tabular tangents look for the nearest number to this, which is 12-5199, the tangent to 85° 26'; the next nearest is 12.4742, being the tangent of 85° 25′; the difference is 0.0457, about one-third of which subtracted from 12.5199, will be the tangent near enough for our purposes, and the angle we require will be 85° 26', one-third of a minute, which will give 85° 25' 40", or as near as we shall be able to read off. If this angle be set off from a, as Ba C, the intersection of a C with the line BC will be the station required; it being, of course, understood that whilst C is fixed with the theodolite from a, the assistant at C is careful to keep on the line GB C. To fix a buoy at b, 500 feet 2000 nearer to B; = 100000; the nearest tabular number is 200 10-0187, the tangent of 84° 18'; proceeding as before we shall find the angle B a b to be (near enough) 84° 17′ 30′′. To deter1500

mine point c, 500 feet nearer again to B; = 7.500; and

200

proceeding as above we shall find the angle B a c = 82° 24′ 20′′. În the same manner we may determine the positions of the two remaining stations between c and B. Having determined the station C, it may so occur that the line of shore prevents b and c from being visible from B; then move the theodolite to C, and set out the radius C d; and from d proceed as we have just done