ship; but a more accurate method is that simple one called the Dutchman's log. Having measured a distance on the bank, or by veering one boat a certain distance astern of the other, and noting the time a chip floats from one to the other, the mean velocity may be obtained tolerably near the truth by a rod of wood loaded at one end sufficient to float upright in still water, the greater velocity at the upper surface will make the rod incline towards the stream. Consequently it will float in a oblique position, the top of the rod will move slower than the water at the upper surface of the river, and the bottom move faster than that in the lower. In addition to which a correction is required for the friction at the sides and bottom, for which the following formula has been found by experiment. A the area in square feet. L the length of the sides and bottom. Then V, the velocity in inches per second, 10 Ix 11 It has also been found that water moving with the velocity 3 inches per second will move fine clay. fine sand. coarse. gravel, small. size of bean. inch size. egg size, Soundings for this purpose, or if required for engineering purposes, should be taken in straight lines across the river, which can be done by keeping two objects in one, and taking an angle to a third whenever a change in the depth occurs. The progress of the tidal wave up rivers, and its gradual absorption, are of so great importance that the opportunity of making simultaneous observations throughout its course should not be lost, and the rise and fall at different periods of the lunation should be carefully noted, as they afford the truest indication of the dynamic force. Contour lines from low-water mark on shoals that dry, as well as on the banks of rivers, may be obtained by fixing poles and determining their position, either by the theodolite or sextant angles, and comparing the instant they are left dry, or the moment the flood reaches them, with a tide gauge. Whenever the latter is raised, care should be taken to compare it with some fixed object, so that the observations then made may be referred with accuracy to others at a future period. APPENDIX A. TABLE FOR ROUGH TRIANGULATION WITHOUT THE USUAL INSTRUMENTS AND WITHOUT CALCULATION. (See Fig. 4.) A TRAVELLER may ascertain the breadth of a river, or that of a valley, or the distance of any object on either side of his line of march, by taking about 60 additional paces, and by making a single reference to the annexed table. Suppose that he is travelling in the direction A E, and desires to know the distance of some object, P, from A. Let him proceed as follows: Walk ten paces from A towards E (to b). Back to A. Ten paces towards P (to c). From c to b, counting the paces to the nearest quarterpace (c b is the chord of the angle at A to radius 10). Walk on towards E. The distance A E must be taken as 100. It need not be 100 paces, but may be 100 of any convenient unit of length, as feet, fathoms, minutes' walk, furlongs, &c.; or it may be some simple multiple of 100, as 200, 300, 500, 1000. When 10 paces short of E (at d), mark the spot and walk on to E. Thence towards P (to f). From f to d, counting the paces to the nearest quarter-pace (fd is the chord of B to radius 10). This completes the operation. Nothing has to be recollected but the values of c b, of A E, and of ƒ d. To find A P, enter the table with c b at the side, and ƒ d at the top. The tabular number is the value of these quantities, supposing A E to have been 100. If it be 200, 300, 500, &c., the tabular number must be multiplied by 2, 3, 5, &c., as the case may be. Beyond this, there is no calculation. If A E has been taken in paces, the tabular number will be in paces also; if in minutes' walk, in minutes' walk, and so on. The angles corresponding to the chords, viz. c A b (or P A E), for c b and ƒ Ed (or PE D), for fd, are also given. Examples: cb is 5 paces; A E 100 paces; fd 6 paces; then A P=67; E P-53: c A b=28° 58′; ƒ E d=37° 56' cbis 5 paces; A E 300 paces; fd 6 paces; then A P=201; E P=159: c A b=28° 58′; ƒ E d=37° 56' cb is 5 cb is 10 paces; A E 100 paces; fd 6 paces; then A P=65; E P-56; c A b=31° 56'; ƒ E d=37° 56' paces; A E 100 paces; fd 8 paces; then A P=79; E P=98; c A b=65° 2' ; ƒE d=47° 10' If A E be a north and south line, the bearing of P from A, as represented by the angle c A b, is to be found by simply ascertaining the value of c b. The most methodical way of making these measurements is to select some tuft of grass, or stone, or stick, that may happen to be lying on the ground, as the starting-point, A. Then to mark 6 by placing any object there, or by planting a stick, which can be recovered on returning to b from c. D is to be marked in the same way. E requires no mark at all; neither does c nor f. Particular care must be taken to walk in a straight line from A to E. It will surprise most people, on looking back at their track, to see how curved it has been, and how far Ed is from pointing truly towards A. It is always well to sight some distant object in a line with E, when walking towards it. The triangle PA E must be contrived so that none of its angles are less than 30°, or the chords of the angles at A and E will not be found in the Table. These cases do not give reliable results, and have therefore been omitted. Should a traveller have no tables by him, he can always protract his measurements to a scale on a sheet of paper, or even on the ground, and so solve his problem. If real accuracy be aimed at, it is clear that careful measurements of the base and chords, combined with a sufficiently rigorous calculation, will give it. FRANCIS GALTON. |