bands II are adjusted so as to bring the arms of the instrument into exact parallelism, they will remain parallel throughout all the movements of the pulleys in their sockets, and thus will always make equal angles with the centre beam. If, then, the two arms and the centre beam be all set so that the readings of their divisions are the same, a line drawn from the end of one arm across the fulcrum to the end of the other arm will form with the beam and arms two triangles, having their sides about equal angles proportionals, and being, therefore, similar; hence any motion communicated to the end of one arm will produce a similar motion at the end of the other, so that the tracing-point being moved over any figure whatever, an exactly similar figure will be described by the pencil. To adjust the Eidograph, and examine its accuracy.-Set the indices of all three verniers to coincide with the zero divisions on the centre beam and arms, and make marks at the same time with the tracer and with the pencil; then move the pencil point round until it comes to the mark made by the tracer, and if the tracer at the same moment comes into coincidence with the mark made by the pencil, the arms are already parallel, and the instrument consequently in adjustment; but if not, make a second mark with the tracer in its present position, and bisecting the distance between this mark and the mark made by the pencil, bring the tracer exactly to this bisection by turning the adjusting screws on the bands. The instrument being now in adjustment, if the zero division be correctly placed on the arms and beam, the pencil point, tracer, and fulcrum will be in the same straight line, and they will still remain so when the instrument is set to give the same readings on the three scales, whatever those readings may be, if the dividing of the instrument be perfect. The instrument being adjusted, we have next to set it so as to make the dimensions of a copy, traced by its means, bear the desired proportion to the original. It must be borne in mind that the divisions on the instrument are numbered each way from the centres of the beam and arms up to 100, and that the verniers enable us to read decimals or tenths of a division; so that if the indices of the verniers were a little beyond any divisions, as 26, and the third stroke of the verniers coincided with the divisions marked 29, the reading would be 26.3. Now suppose it were required to set the instrument so that the proportion of the copy to the original should be that E of one number, a, to another number b. Suppose to repre sent the reading to which the instrument should be set, the the centre beam and arms are each divided at their fulcrum into portions whose lengths are 100- and 100+ respect 100. -30 α ively, and consequently the required reading x= 100+x b are as 1 to 2, we have x= b+a from which we find that ; thus, if the proportions instrument must be set with the third divisions of the verniers beyond the indices on the third divisions of the instrument beyond the 33rd. We have, therefore, the following simple rule: Subtract the lesser term of the proportion from the greater, and multiply it by 100 for a dividend, add together the two terms of the proportion for a divisor, and the quotient will give the reading to which the instrument is to be set. The following readings are thus obtained :— When the copy is to be reduced, the centre beam is to be set to the reading found, as above, on the side of the zero next to the arm carrying the pencil point, and this arm is 50 Ан 50 Fig. 1. Fig. 2. also to be set to the same reading on the side of its centre or zero nearest the pencil end, while the tracer arm is to be set with the reading furthest from the tracer. When the copy is to be enlarged, these arrangements must of course be reversed: thus, 50 being the reading for the proportion 1: 3, Fig. 1 will represent the setting to make a copy having its linear dimensions three times those of the original; where P represents the position of the pencil point, t that of the tracer, and F the place of the fulcrum. Fig. 2 represents in the same way the setting to make the linear dimensions of the copy one-third of those of the original. After all, the most perfect copying-machine is the photographic camera. In fact, photography has now fully taken its place as an auxiliary to engineering operations. By its use the mechanical engineer is enabled to send forth correct representations of his machinery; and works of civil engineering have their monthly progress recorded, and the results sent home, to give ocular proof of their truth to chiefs and directors. A practical knowledge of photographic processes has hence become almost a necessary, certainly a most desirable portion of every young engineer's education. Several special manuals on the art of photography, in English and French, are to be found. Of the apparatus used for the reduction of maps and plans a full description will be found in Part III. of this volume. CHAPTER VI. INSTRUMENTS FOR MEASURING LINES AND AREAS ON PLANS. THE OPISOMETER. THIS simple instrument measures the length of roads, rivers, fences, walls, &c., on any map or plan which is drawn to a scale, without requiring any arithmetical calculations. The principle of the opisometer is that after having been applied to any line it retraces or measures backwards precisely the same length on the scale with which the line is to be compared. It consists of a milled wheel, with a steel screw for its axis, mounted on a convenient handle. To measure the length of a line, as the distance between two towns by the road traced upon a map, turn the milled wheel up to one end of the screw until it stops, and place the instrument on the map in an upright position, as represented in the draw ing, the wheel resting upon one extremity of the line to be measured; then run the wheel along the road, following every bend as closely as possible. Care must be taken to keep the wheel in contact with the paper, but the pressure need not be such as to injure the map. When the wheel has arrived at the other extremity of the line, lift the instrument carefully from the paper, and carrying it to the zero end of the scale, run the wheel backwards along the scale until it stops at the same end of the screw from which the measurement began; the division of the scale at which the wheel stops shows the length of the line measured on the map. Should the scale be shorter than the line measured, when the wheel arrives at the end, carry it to the zero mark again as often as may be necessary, counting the number of repetitions. The difficulty of measuring lines of double curvature, such as a rhumb line, i.e., the line of a ship's course on a globe, is entirely removed by the use of the opisometer. The accuracy of the result given by the opisometer is unaffected by the dimensions of the instrument itself, and depends entirely on the care with which it is used. The chief point is to see that the handle of the instrument is perpendicular to the surface at the beginning and end of each step of the measurement. The computation of the area represented by a plan, espe cially if the outline be very irregular, is both a tedious task and liable to many sources of error, which, after all, forbid us from looking at the result as any more than a careful approximation. In the first place, the irregularity of the outline is dealt with by drawing straight lines, which, in the estimation of the computer, shall go as far outside the figure on one part as they fall inside on another, so as to form a rectilinear figure estimated to be equal to the plan. This is called the give-and-take principle, and is, of course, a mere guess, depending for its degree of accuracy upon the skill and practice of the operator. Then the polygon thus formed has either to be divided into triangles, the area of which must be separately computed, or a triangle must be constructed, by the principles of geometry, equal to the whole polygon, and then the area of this triangle will be the estimated area of the surface represented by the plan. Any means of instrumentally getting at the computation with greater expedition, without producing greater inaccuracy than this mode of computation, must be hailed as a boon, and we have a very simple and inexpensive instrument, which is now much used for this purpose, in the COMPUTING SCALE, OR COMPUTER. The computer is designed to measure only the areas of figures constructed to one particular scale, and as many com 627 Fig. 1. puters, therefore, would be required by the surveyor as he adopted scales for his plans. The simplicity, and consequently inexpensive nature, of the instrument prevent this from being felt as a serious disadvantage. The computer (Fig. 1) consists of a rule, B B, of box-wood, graduated and figured to show the number of acres and roods in a slip of land of a given width. In that from which the annexed figure is drawn, the graduations on the rule itself show the number of acres and roods in a slip of land one chain wide, and it is adapted to a plan of 3 chains to an inch. The scale occupies 20 inches of the length of the rule, and therefore represents 60 chains in length, and an area of 60 |
