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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).

CHAPTER XIV.

COMPUTING SCALES AND

PLANIMETERS.

COMPUTING Scales made in boxwood are generally kept in stock for application to plans drawn to the Ordnance scale of either, go, or of 6 inches to 1 mile, but they can be made to any scale. Makers, however, generally require a week's notice for a computing scale different from their stock sizes, as they find the planimeter is so rapidly superseding the use of a computing scale that it does not pay to keep various sizes of this scale in stock. The annexed illustration shows a computing scale made to the Tithe Commission pattern of 3 chains to 1 inch (page 150). The large figures in the portions of the accompanying samples of computing scales denote acres, and the sub-divisions numbered 1, 2, 3 indicate roods. A projecting frame having a fine wire drawn across its centre is attached to a scale admitting of sliding motion in the direction of its length. The perches are engraved upon the ivory scale attached to this movable metal frame, the use of which will be understood upon reference to the annexed drawing (pages 151, 152), showing a complete instrument. The application of a plan is explained in note 1. Four scales are shown upon this instrument. (See note 2.) The example given supposes the plan to be drawn to a scale of 4 chains to I inch, in which case the calculated distance between the parallel lines upon the tracing paper is seen to be inch, which is ruled off in the direction of the greatest length, in order to have as few strips as possible and form a gridiron tracing of parallel lines inch apart. The number of square chains in 1 inch upon the plan, divided by the number of lineal chains to an inch upon the scale, will give the number of parallel lines or spaces to be ruled within a

depth of 1 inch upon the computing paper. Thus, with the use of such tracing strips, when the upper scale marked i is to be employed, a length of 2 inches is seen to measure an acre. The object of the calculation given in note I upon the diagram for the determination of the value of X, is to arrive at the actual width required to suit the scale of the plan for recording an area of 1 acre for an actual length of rectangle registered as an acre upon the computing scale. Thus, referring to note 2, the length upon the scale of 12 inches records 5 acres in the case of scale 1, because one-fifth of 12 inches multiplied by inch square ğ inches, and since by the scale of the plan 16 square chains equal square inch, an area of paper square inches equals IO square chains or 1 acre. In the case of scale 2, we have the same total length of 12 inches, reading two acres, and

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hence the divisions upon the lines for the tracing paper would need to be inch apart, which. would not be so suitable as scale 1 for this special plan. The wire line C in the frame A B is first so set that the frame rests against the stop-piece F. It is then placed upon the tracing paper over the area to be calculated so as to start from zero at the line V, with the edge of the scale parallel to the lines upon the tracing paper. The scale is maintained in position by the pressure of the hand, and after carefully moving the frame so that the line C traverses from M to N the instrument is then lifted up and replaced with its edge parallel to the lower lines upon the tracing paper, so that the wire C starts from O at the same position on the scale as it indicated when at N. The frame is traversed over each rectangle successively from M to N, O to P, Q to R, S to T, &c., by

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