an instrument contrived for reducing, enlarging, or copying plans. It has been constructed in a variety of forms, all of them depending on the same geometrical proposition. If from the corners A, B, C, D (fig. 1) of any polygon, lines be drawn to a fixed point P, and be continued to distances Pa, Pb, Pc, Pd, proportional to PA, PB, PC, PD, the figure abcd is similar to ABCD.

In order to utilize this property, a bar EPe (fig. 2) is made to turn freely upon the point P; on E and e are jointed two other bars EF, ef, having their lengths in the ratio PE

to Pe, and being kept constantly parallel to each other by some mechanical contrivance. In this way the points F, P, and f are maintained in a straight line, and the ratio of FP to fP is preserved constant; so that if the point F be led along the contour of any figure, f must mark out a similar figure.

In the old form of the pantograph the parallelism of the bars EF, ef was secured by a thin rhomboidal frame like the common parallel ruler, the several joints being supported on small ivory castors. Hence the whole apparatus moved by jerks, and it was impossible to follow with precision any delicate outline. In the eidograph of Professor Wallace, the parallelism is maintained by means of two light wheels, round which a chain is passed, and the machine is supported by long axes; while in Dunn's pantograph, the rhomboidal frame is used with long axles. With these improved forms a free and smooth motion is obtained, so that very minute work can be gone over.

At one of the points F, f there is placed a tracing-style of steel, delicately pointed, but not sharp, to be led along the outline of the plan, and at the other a tracing-pencil, kept pressing on the copy-paper by a small weight which can be pulled up when required. There are also arrangements for altering the lengths of the arms to suit the ratio in which the plan is to be diminished or enlarged.

The pantograph is extensively used in the arts; thus, the machine-embroiderer leads the longer arm over a magnified copy of the figure to be produced, and guides with ease and precision the successive strokes of the needles. To this simple contrivance we owe much of the beauty and cheapness of flowered muslins and embroidered silks. (E.S.)