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The limits of the bulk and cost of the work have forbidden any extensive excursion into the sciences in which the instruments are used; but it is hoped that a large mass of information has here been placed in a small compass without sacrificing perspicuity to undue compression.

An Appendix has been added, in which notices will be found of the chief improvements that have been recently effected in instruments of these classes.

J. F. H.

A TREATISE

MATHEMATICAL INSTRUMENTS.

ON

PART I-ON MATHEMATICAL DRAWING INSTRUMENTS.

In this branch of the subject the limits of our little work will not permit us to enter upon all the beautiful contrivances which have been invented for facilitating the operations of the draughtsman; but we shall endeavour to describe the constructions and applications of such as are in most general use, and, as far as our space will allow, to exhibit the principles upon which they are founded, so that the student may readily extend his views, after having completely mastered the matter here presented to him, to the principles of any other instru ments, which may be useful to him in whatever particular professional branch of practical mathematics he may wish to employ himself. With this view we shall describe the instruments in the ordinary case of drawing instruments, as sold by any mathematical instrument maker; viz.,

Compasses with moveable point,
ink point, and pencil point.

Whole and hálves.
Proportional compasses.
Triangular compasses.
Marquois's scales.

Drawing pen and pricking

point.

Hair compasses.

Bow compasses.

And we shall also give some account of the following; viz.,

Plain scale.

Sector.

Beam compasses.
Plotting scales.
The pantagraph.
Sliding Rule.

ON DRAWING COMPASSES.

This instrument consists of two legs moveable about a joint, so that the points at the extremities of the legs may be set at any required distance from one another; it is used to transfer and measure distances, and to describe arcs and circles.

The points of the compasses should be formed of well-tempered steel, that cannot be easily bent or blunted, the upper part being formed of brass or silver. The joint is framed of two substances; one side being of the same material as

B

p

the upper part of the compasses, either brass or silver, and the other of steel. This arrangement diminishes the wear of the parts, and promotes uniformity in their motion. If this uniformity be wanting, it is extremely difficult to set the compasses at any desired distance, for, being opened or closed by the pressure of the finger, if the joint be not good, they will move by fits and starts, and either stop short of, or go beyond the distance required; but, when they move evenly, the pressure may be regulated so as to open the legs to the desired extent, and the joint should be stiff enough to hold them in this posi tion, and not to permit them to deviate from it in consequence of the small amount of pressure which is inseparable from their use. When greater accuracy in the set of the compasses is required than can be effected by the joint alone, we have recourse to the

Fig. 1

Fig. 2

Hair Compasses, in which the upper part of one of the steel points is formed into a bent spring, which, being fastened at one extremity to the leg of the compasses almost close up to the joint, is held at the other end by a screw. A groove is formed in the shank, which receives the spring when screwed up tight; and, by turning the screw backwards, the steel point may be gradually allowed to be pulled backwards by the spring, and may again be gradually pulled forwards by the screw being turned forwards.

Fig. 1 represents these compasses when shut; fig. 2 represents them open, with the screw turned backwards,

Fig. 3
Mr

and the steel point p, in consequence moved backwards by its spring s, from the position represented by the dotted lines, which it would have when screwed tight up.

Fig. 3 represents a key, of which the two points fit into the two holes seen in the nut, n, of the joint; and by turning this nut the joint is made stiffer or easier at pleasure.

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