There is a cup at the top of the pencil-holder for receiving an additional weight when required to make a stronger mark on the paper.

The greatest possible nicety is required in fixing a short piece of pencil in the tube, so that when it is brought to a fine point, by revolving it in the tube, it should make a point, and not a circle. This should be adjusted very truly before commencing to use the instrument.

Fasten down upon a smooth board a sheet of paper under the pencil D, to receive the reduced plan, and fix the original plan under the tracer at C.

Then, with a steady hand, carefully move the tracing point C over the outlines of the plan, and the pencil will describe exactly the same figure as the original, but half the size, or rather it is quarter the size, although half the scale.

In the same manner for any other proportion, by setting the two sockets to the number of the required proportion.

If the original should be so large that the instrument will not extend over it at one operation, on the original plan draw a line, or make three or four points, and mark the same also on the reduced plan.

The fulcrum and copy may then be moved into such situations as to admit copying the remaining part of the original, first observing that, when the tracing point is applied to the lines or points marked on the original, the pencil must also fall on the corresponding lines and marks made on the copy.

In very large plans, the better method is to divide the original plan into equal portions by lines, as much as the instrument can easily travel over, and make the copy on tracing paper first, then transfer it to the paper prepared for the reduced plan.

As a general rule, the following instructions should be observed: On the two divided bars which carry the sliding tubes appropriated to the fulcrum and pencil, are usually 21 divisions; those numbered,, up to, are to be used with the fulcrum in the tube B bar, the pencil in the D bar, the tracer being fixed at C.

Its chief value is in reducing figures, although it may be used in copying plans, &c., of the same scale; it will also enlarge, which is never at any time recommended.

The pantagraph is made of brass, from 12 inches to 4 feet in length, and consists of four flat bars, two of them long and two short. The two longer ones are joined at the end A by a double pivot, which is fixed to one of the bars, and works in two holes placed at the end of the other; under the joint is an ivory wheel, to support this end of the instrument. The two shorter bars are fixed by pivots at E and H, near the middle of the longer bars, and are also joined together in a similar manner at the other end, G; ivory wheels being also fixed under each joint, marked a.

By the construction of this instrument the four bars always form a parallelogram.

There is a sliding box on the longer bar, B, and another on the shorter bar, D. These boxes may be fixed at any part of the bars by means of the milled screws; each of the boxes are furnished with a cylindric tube, to carry either the tracing point, the pencil, or fulcrum.

The fulcrum or support, K, is a lead weight, to which is fixed a bright iron pin, e; on this the whole instrument moves when in use.

The pencil-holder, tracer, and fulcrum, must in all cases be in a right line, as shown in the drawing marked b, so that when they are set to any number, if a fine string be stretched over them, and they do not coincide minutely, there is an error either in the setting or in the graduations.

The long tube c, which carries the pencil, moves easily up or down in either tube; there is a fine piece of silk, f, fixed to the pencil tube, passing through the holes in the three small knobs to the tracer point d, where it may, if necessary, be fastened. By pulling this string the pencil is lifted up occasionally, and thus prevented from making false or improper marks upon the copy.

There is a cup at the top of the pencil-holder for receiving an additional weight when required to make a stronger mark on the paper.

The greatest possible nicety is required in fixing a short piece of pencil in the tube, so that when it is brought to a fine point, by revolving it in the tube, it should make a point, and not a circle. This should be adjusted very truly before commencing to use the instrument.

Fasten down upon a smooth board a sheet of paper under the pencil D, to receive the reduced plan, and fix the original plan under the tracer at C.

Then, with a steady hand, carefully move the tracing point C over the outlines of the plan, and the pencil will describe exactly the same figure as the original, but half the size, or rather it is quarter the size, although half the scale.

In the same manner for any other proportion, by setting the two sockets to the number of the required proportion.

If the original should be so large that the instrument will not extend over it at one operation, on the original plan draw a line, or make three or four points, and mark the same also on the reduced plan.

The fulcrum and copy may then be moved into such situations as to admit copying the remaining part of the original, first observing that, when the tracing point is applied to the lines or points marked on the original, the pencil must also fall on the corresponding lines and marks made on the copy.

In very large plans, the better method is to divide the original plan into equal portions by lines, as much as the instrument can easily travel over, and make the copy on tracing paper first, then transfer it to the paper prepared for the reduced plan.

As a general rule, the following instructions should be observed: On the two divided bars which carry the sliding tubes appropriated to the fulcrum and pencil, are usually 21 divisions; those numbered, 1, up to 12, are to be used with the fulcrum in the tube B bar, the pencil in the D bar, the tracer being fixed at C.

The other fractions,,,, downwards to 11, are used with the fulcrum at D, and the pencil at B.

The above directions are to be followed when a plan is to be reduced; but when it is required to be enlarged, the pencil and tracer must be changed.

Example 1. It is required to reduce a plan in the ratio of 10 to 11. The fulcrum at D being set to the divisions marked 10 to 11, and the pencil at B at the corresponding division 10, 11.

Example 2. It is required to reduce a plan to of its size; place the slide on each of the divided bars at, the pencil placed in D slide, the fulcrum in B slide.

Example 3. To copy the same size, but reversed, place the two sockets at 1, the fulcrum at D, and the pencil at B.

Example 4. To reduce 6 chains to 8, place the two sockets at, the fulcrum at D, and the pencil at C.

Frequently plans have to be reduced when none of the divisions on the bars will answer the purpose; then shift the sockets by repeated trials until the proper division is found, taking care always to prove that the three sockets are all directly in a right line.

Where a mass of buildings has to be reduced, the proportional compass will be found to be a most valuable auxiliary.

THE EIDOGRAPH.

Fig. 2, Plate 36. The construction of this instrument is dif ferent to the pantagraph, but its use is similar.

A B C, the three subdivided arms; the pencil, D, has three small weights at top; E, a fine silk cord from the tracer at G to the crank at F, which lifts the pencil when required; H, the lead weight or fulcrum, on which the whole instrument moves; I is an elastic cord attached to the two pulley wheels K and L; M is a screw to regulate the elastic cord; N is a movable slide, with a vernier or index plate; a and b are two holes in the pulleys to set the divisions on the bars A and B.

To set the instrument, to reduce, or enlarge to any required proportion.

Take the sum and difference of the fractional terms; then, as the sum is to the difference, so is 100 to the number required, and to this number the arms and centre bar are to be set.

For example. Let it be required to reduce one-third.

The arm carrying the tracer is to be lengthened to division 50. The centre bar is to be set to the division 50, on the pencil side of O, and the arm carrying the pencil is to be shortened to division 50.

The instrument thus set will give a tracing with the pencil one-third of the size of that traced by the tracer. This arrangement is to be reversed when the instrument is required to give an enlarged tracing of any subject.

The only adjustment which may be put out is the parallelism of the bars passing under the wheels. This is to be corrected as follows: Place all the verniers to O, and, with the arms at right angles to the centre bar, make a mark with the tracer and pencil points; then wheel the instrument half round, and placing the tracer into the mark made by the pencil, the pencil should fall into the mark made by the tracer; if it does not, half the error is to be corrected by letting out and taking up the spring passing over the wheels, by means of the screws in the middle of the wires.

See Table, No. 17, for Reducing and Enlarging.

H. S. MERRETT'S PATENT IMPROVED QUADRANT.*

Fig. 1, Plate 37. The simplicity and portability of this instrument will make it particularly useful to the surveyor or engineer where angles of inclination or declination are required for practical purposes, in the same manner as the theodolite.

It is made of boxwood, having two arcs of 90 degrees, divided into degrees and half degrees, being sufficiently near for the purposes to which it would be required.

There are two tables, Nos. 12 and 18, engraved on it. One

* This instrument can only be obtained of the author.