whole instrument is solely supported by the central fixed. stand over which it works. Thus the friction upon the surface of the paper is reduced to a minimum, and there is less vibration than with the use of the comparatively thin arms of a pentagraph. When employed for reduction, as shown in the detail plan (pages 143, 144), the portion of the central bar carrying the bar marked A is heavier than the portion of the central bar carrying the bar marked B. The bar marked A carries the tracer and the bar marked B carries the pencil. The central bar is clamped at C. Hence the balance-weight is placed upon the short end of the central bar to steady the instrument in such a position that the whole is balanced over the fulcrum under C.

The geometrical construction of these intruments is based upon the principle involved in the construction of similar triangles. In both the pentagraph and the eidograph the pencil-holder, the tracer, and the fulcrum should under all circumstances be in a right line when set up ready for use, so that a fine string stretched from the pencil-holder to the tracer-holder should pass over the fulcrum as indicated by the dotted line shown in the diagram (pages 143, 144) which illustrates the eidograph. Otherwise the instrument is not correctly set, and must be re-adjusted.

Comparing the two instruments, the eidograph can cover a greater surface of reduction than the pentagraph. There is no sensible friction upon the single fulcrum centre of support, but to steady the instrument some makers add a movable castor, the roller of which is 2 inches diameter, which can be attached to the main beam with its axis in a direct line to the fulcrum of the central stand when the instrument is to be employed for reduction below onethird. The motions of the pencil and tracing point in a pentagraph are each derived from two circular motions, one about the joints at the ends of the arms, to which they are attached, and the other about the fulcrum. The radii of these travelling movements form the sides of similar triangles, of which the dotted line, passing through the pencil, the tracing point and the fulcrum form the third side. The distances traversed by the pencil and tracing point will maintain a constant ratio to one another when the

instrument is properly set, due to either of the above circular motions, and will therefore have also the same ratio when the two motions are combined. The inscribed space bounded by the arms of the instrument, as stated above, form a true parallelogram, and the proportion of the sides depends upon the setting of the instrument. In an eidograph the pulley-wheels under the ends of the centre bar are of exactly the same diameter, and the wheels are caused to move simultaneously by means of the steel bands attached to them. The tension of the bands can be adjusted by the screw connections when needed. Rules for setting the instrument will be found upon the diagram (pages 143, 144).

The pencil-holder is made to slide easily up and down the cylinder in which it rests, and the draughtsman is enabled to raise it off the paper when not required to mark by gently pulling the silk cord attached to the cranked lever arm, which cord passes over the bars of the instrument to the tracer point to which it can be fastened if desired, so that the draughtsman can prevent false or unnecessary marks being made upon the paper by passing over the cord at the tracer end two fingers of the same hand that moves the tracer. Additional small weights are provided to rest upon the top of the pencil-holder when the pencil is required to make strong marks upon the paper.

When the plan to be reduced contains numerous buildings the use of the proportional compass will be found advisable. The plan to be reduced, and the paper upon which the reduced plan is to be plotted, are covered with squares drawn to their correct scales respectively, and the intersection of the lines is indexed for reference by numbers in the one direction, and by letters in the other direction. Proportional compasses fitted with a rack-gearing for the movement of the slider are the best, as they can be most accurately set by means of the milled-headed adjusting screw shown in the diagram (page 146), and when clamped by the opposite milled-headed screw are not liable to slip. To move the adjusting screw, the clamp screw must be first loosened, and the instrument is then so set that when the arms are opened, the distance between the points marked A and C bears the required proportion to the distance

between the points marked B and D. As shown in the diagram (page 146), the body of the instrument consists of two narrow flat pieces of metal, each having a groove up to the centre, and united by a pair of slide pieces fitted into the grooves, and connected by a pin which traverses the axis of the instrument, and can be clamped in any required position by the milled-headed screw. A steel point is attached at both ends of each arm.

The scale of lines shows the marks at which the index must be set for so fixing the compasses when closed that the distance between the steel points when opened at one end shall bear a definite proportion to the distance between the steel points at the other end. This scale is only available where the ratio can be expressed by some whole number divided or multiplied into one unit, and cannot be applied so readily to ratios of 2 to 3 or 3 to 4, which are very often required.

The scale of circles will divide the periphery of a circle into any number of equal parts up to 20. The slide is set to the number of divisions required, then the points of the long arms of the instrument are opened to the radius of the circle and the distance between the points of the short arms will then indicate the chord to be taken upon the arc of the circle which divides the circumference according to the setting. The scale of plans applies to areas. A circle struck with the long points when the index on the slide is set to any registered number, will describe a circle the area of which will be exactly that registered number of times the area of a circle set out by a radius equal to the distance between the points of the short arms of the instrument. The scale of solids is similarly applied to cubical dimensions, and gives the comparative proportions for relative capacities. (See page 146).