THE PLANIMETER.

G

211

measured; then read off the instrument; trace the contour a second time and again read off; subtract the first reading from the second, and multiply the remainder by 10, which gives the reading in square inches, with two places of decimals. Let the first reading of the disc & be 2, that of D equal to 80, but with the vernier reading instead of 80 let it be 805; then the reading of the instrument at starting is to be set down as 2·805; let the second reading be 7-553; this, minus the first, equal to 4.748, which multiplied by 10 equals 47-48 as the contents in square inches.

In tracing the periphery, observe whether the disc G performs an entire revolution, for in that case 10 must be added to the unit in the last reading. If, for example, the second reading above had been 7.553 plus an entire circuit, then we should have had 7.553 plus 10 equal to 17-553, from which subtracting 2.805 and multiplying the remainder by 10, we get 147-48. If the periphery is too long for the instrument to trace at once, the figure may be divided into two or three. The instrument is constructed to give areas in other denominations than square inches; but this is a very convenient one for the English Ordnance Map of one inch to the mile, in which the above computation would give 147 square miles.

Let us now suppose that we are computing from a plan with a scale of 5 chains to the inch; 5 chains square is equal to 250,000 square links; from this we obtain the constant by which to multiply the number of square inches found with the planimeter to reduce the area to square links.

Then for a 1 chain scale we shall have

100

as constants by which to multiply the square inches found with the planimeter, to reduce them to square links, which will be the more easily remembered, from the multipliers being the square of the number of chains to one inch, with two zeros added.

THE PANTAGRAPH.

213

Reducing plans is a simple operation, which, however, requires care and some practice, because the reduced plans are often required at short notice. The work of reducing is often done with proportional compasses, but we prefer having this done by squares; that is to say, the plan to be reduced is divided into a certain number of squares, each perhaps ten chains wide. The paper on which the reduced plan is to be drawn is then divided into the same number of squares, but adopting the proper reduced scale for the width of the smaller squares.

When the plan to be reduced is of any great extent, a large amount of labour is saved by making use of the pantagraph or eidograph, of which illustrations are given.

The pantagraph consists of four flat rulers, made either of wood or brass; the two outside ones are generally from 15 to 24 inches long, and the others about half that length; the longer ones are united together by a pivot, about which they turn, and the two smaller rulers are similarly attached to each other, and to the longer rulers. A sliding box is placed on each of the arms, A B and CD, which may be fixed by a clamp-screw at any part of the ruler; these slides carry a tube, to contain either a blunt tracing point, a pencil or pen, or the fulcrum в, which is a heavy weight of lead, having a point on the under side, to pierce the drawing-board and remain immovable in its proper position, it being the centre upon which the whole instrument turns. Several ivory castors support the surface of the machine parallel to the paper, as well as facilitate its motions.

Two of the arms are graduated and marked with the ratios,,, &c., so that when a copy of a plan is required to be made in any of these proportions, it is only requisite to fix at the required ratio the slides carrying the fulcrum, B, and the tube, with a pencil or pen, and the instrument will be ready for operation. Thus, suppose it were required to make a copy of a plan exactly one-half the size of the original; the slide carrying the pencil, and that working on the fulcrum B, are each fixed by their respective clamp-screws at the divisions marked; the original plan is placed under the tracing point, and exactly parallel

THE EIDOGRAPH.

215

to it is placed a sheet of paper under the pencil, the pentagraph being spread out so as to give room for the tracing points to be passed over every line on the plan, whilst the pencil is making corresponding marks on the copy, which it is evident will be equal to one-half the size of the original. A fine string is attached to the pencil-holder, and passed round by E to G, the tracing point, the pulling at which raises the pencil a small quantity above the paper, to prevent false or improper marks upon the copy. It should also be remarked, that the cup represented on the top of the pencil-holder is intended to receive a weight, to keep the pencil down upon the paper, or when a stronger mark is required.

When the instrument is set for work, the tracing point, the pencil, and the fulcrum must in all cases be in a straight line, which may be proved by stretching a fine string over them.

When it is required to make an enlarged copy of a plan, the setting of the instrument is precisely the same as above stated, only the tracing point and pencil must change places, the original being placed under D, and the copy under c. But when a copy is to be made of the same size as the original, the fulcrum must be placed in the middle at D, and the pencil at B, under which will be the copy, whilst the original must be placed under the tracing point at c.

The eidograph, which is represented in the accompanying engraving, is a far superior instrument to the pantagraph, being more exact in its work, and not so limited as regards ratio of reduction.

The point of support when the instrument is at work is a heavy weight shown at H, from the under side of which three or four projecting needle-points fix the instrument firmly to the drawing paper. Springing from this weight is a short standard or fulcrum, attached to a sliding-box, K, in which slides the centre beam, c, and to any part of which it may be clamped by means of a clamping screw.

At the end of the central beam are two pulley wheels, J J, the centre pins of which revolve in sockets at the ends of the beam. Two steel bands, I I, attached to the pulley