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 of one number, a, to another number, b. Suppose to represent the reading to which the instrument should be set, then the centre beam and arms are each divided at their fulcrums into portions whose lengths are 100 and 100 + a respectively, from which we find that the ; thus if the proportions are as 1 to 2, we have x = 100 (b - 1) strument 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. PARY "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 also to be set to the same reading on the side of its centre or zero nearest the pencilend, 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. 325 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 Ан 50 50 t Fig. 325. Fig. 326. tracer, and F the place of the fulcrum. Fig. 326 represents in the same way the setting to make the linear dimensions of the copy one-third of those of the original." Enlarging and Reducing by Squares.-Failing the replotting of the work for the purpose, the only satisfactory and accurate method of enlarging and reducing plans is by means of squares and proportional compasses. This may perhaps be best shown by the following example: Let Fig. 327 represent the plan of an estate which it is required to copy on a reduced scale of one-half. The copy will therefore be half the length and half the breadth, and consequently will occupy but one-fourth of the space of the original. Take a sheet of tracing paper and draw two lines at perfect right angles to each other, as OJ, 09, at the top and left of the sheet; now very accurately and carefully divide these lines into spaces of some convenient length, say, 1 to 2 ins., as a, b, c, d, e, f, g, &c., and 1, 2, 3, 4, 5, 6, &c., and draw the squares formed by the intersections in fine blue lines. Now place this piece of tracing-paper over the plan to be enlarged or reduced and fasten it well down with drawingpins. Then take another piece of tracing-paper and divide it into squares larger or smaller according to the proportions required: in Fig. 328 they are half the size, consequently whatever the divisions o a, o b, o 1, o 2, &c., are (Fig. 327), those in Fig. 328 will be half. Beside the plan to be reduced, on the right-hand side lay down a piece of drawing-paper, upon which shall be laid a piece of transferpaper, and upon this is laid the sheet of smaller squares, all of which having been firmly secured by weight or drawing-pins. In the proportional compasses fix the line across the slides to be coincident with the line opposite the 2 on the left side of the groove (Fig. 305), by which means a в is twice c D, to test which upon a line pick off any length A B, then if the points CD accurately bisect this length you have the right proportion. And as a further test, try your squares in the same way, A B being fixed at one of the subdivisions in Fig. 327, then if the sheets of squares have been accurately drawn, C D will exactly measure the length on the reduced sheet of squares. To reduce the plan, mark those points on the large squares above the fences, &c., intersect and measure vertically and horizontally the distance from the nearest intersection of the horizontal and vertical lines with the A B end of the compass, and at similar points on the small squares mark the same distances with the C D end of the compasses and make marks, then if with a fine pencil you draw the lines connecting these points, you will not only have a record of the work you have accomplished, but it will be transferred to the paper beneath. Copying a Plan. To copy a plan it has been recommended to place it over a sheet of clean paper, and to prick through all the fences, buildings, &c., and then to connect the punctures by drawing the lines first in pencil and then in ink. Such a system is to be condemned: first, because it spoils both the plan and the copy by the prick marks; secondly, there is a liability of the plan becoming shifted, in which case there is no possibility of readjusting it; and thirdly, it takes just twice the necessary time to accomplish; added to which, there is always a liability of error. The method I recommend is to make a neat tracing of the plan, and to place this upon transfer-paper over a sheet of drawing-paper. Then place a clean sheet of tracing-paper over the whole, and retrace the plan, by which means you have an accurate record of how much of the work you have accomplished, and no injury is done to the paper upon which the plan is to be copied. General Hints.-In plotting a survey the following hints may be useful: 1. Dust your table, and well cover that part of the paper upon which you are not working. 2. Do not wear your watch in your waistcoat pocket. 3. Do not have an inkstand or your colour pans on the same table. 4. Always clean your scales, protractor, set-squares, straightedge, &c., before use. 5. Rule in your survey lines in lake or carmine before you commence to plot your details. 6. Always use fresh ink every day, and do not colour over work recently inked in. 7. Before commencing to plot, draw a scale on the paper, and also a north point. 8. Do not make calculations upon slips of paper, but always have a foolscap scribbling-book at hand, in which enter all your calculations and the dates upon which they are made. 9. Keep a separate field-book for each survey, and be careful to enter the dates of each day's work. CHAPTER XIII. LAND QUANTITIES. THE surveyor has not performed all his duties when he has plotted and finished his plan, for a matter of the greatest importance, next to an accurate survey, is to have a true record of the areas of the various properties shown upon the plan. There are so many works which deal more or less exhaustively with the subject of computation of areas and quantities, that I do not propose to do more than briefly consider the various methods which may be adopted for the purpose, and to endeavour to apply them practically for the information of those who may not have had an opportunity of perusing such books, or to whom possibly the meaning of all that was contained therein has not been made sufficiently clear. To commence, then, it may be useful if I give the following table of superficial measure : To convert Acres into Square Miles multiply by 0015625. Keep forcibly in mind that a strip of land 10 chains long and 1 chain wide is 1 acre; that 10 chains = 1 furlong; that there are |