2. Example.-A plan originally drawn in the scale 1: 1440 has shrunk 1 per cent.; 100 mm. of the plan are therefore equal to 145.44 m. in the full size. The scale of the plan, in consequence of the shrinkage, is 1: 1454. If it is required to reproduce this plan in the scale 1: 960, i.e. enlarge it, the setting x in accordance with formula (1) with pole at the end is: x = 840.960 554.6 and in accordance with formula (2) with pole in the centre (Fig. 76) the setting is x = 1454. 840 = 505.95 mm. The following table gives the greatest dimensions of a rectangle which can be traced with the tracer F of a pantograph of 960, 840, 720, or 600 mm. length, without shifting the pole, when the pole lies between the tracer F and the pencil point Z. II. GENERAL RULES FOR USING THE PANTOGRAPH The table on which the instrument is to be used should be as even as possible, approximately horizontal, and preferably rectangular in shape the size varies with the size of the pantograph used. The width may be from 0.9 m. to 1.20 m. The length should be about twice the length of bar of the pantograph. Slate or marble table-tops covered with thick smooth linoleum have been found very suitable. The pantographs of the types I and II are, when put in their cases, set to the ratio (or) so that they must always be set to the same ratio before being returned to their cases. The sleeves F and Z, as also P are placed in the middle of the case, the joint C to the right. When taking the instrument out of the case and carrying it to and from same, hold it with the right hand near the joint C at the two bars 1 and 4, the left hand being placed against the joint B at the bars 2 and 3, to avoid bending the bars or straining the joints; for the same reason the instrument should be supported by a book or the like at the points of suspension h and h' when laid on the table, before being suspended. The setting of the pantograph to a determined ratio is effected only after it is suspended and adjusted horizontally, as the sleeves of the bars 1 and 3 can only be properly adjusted with the whole instrument in a horizontal position. The bars must be carefully protected from bending and always clean, so that the sleeves can be moved easily on same. The points Z and F and their sleeves must always be kept clean and free from oil or dust, so that the points fall freely into the sleeves. When it is necessary to clean the latter a strip of soft cotton-cloth about 4-5 cm. long, twisted at the corner, should be drawn through the sleeve; the points should be rubbed occasionally with a soft, dry rag. III. DESCRIPTION OF THE PANTOGRAPH 1. Pantograph type I For reducing, enlarging, and copying full size. (a) Setting with pole in the centre (Figs. 76 and 77) The bars 1, 2, 3 and 4 are hard-drawn brass tubes of rectangular cross-section. Their joints move between pointed screws, so that very easy working is obtained and any play can be at once removed by their adjustment. On the bars 1 and 3 sleeves are fitted which can be moved easily along their whole length; to these sleeves the pointed screws for the joints A and B are attached by adjusting these screws the distance CA and PB can be varied. On the bar 2 is a similar sleeve carrying the guide for the pole pin and enabling its distance from the joint B to be varied; a shorter sleeve in each case carries the necessary micrometer screw for the fine adjustment. All the sleeves can be fixed to the bars from underneath by the means of set screws; the screw of the short sleeve is first tightened and, after the instrument is set the screw of the longer sleeve. The bars 1, 2, and 3 are divided on one side of their upper surface in millimetres, with divisions on the other side for the most usual ratios. The latter are marked to and to to . The figures for the arrangement with pole at the end (Fig. 75) are on the left, those for the arrangement with pole in the centre (Fig. 76) on the right of the respective division. Each sleeve carries a vernier for mm. and an index for setting to the ratio division. The zero of the divisions and of the verniers is so arranged that the latter indicate accurately the distances of the adjustable axis A from C, and B from P or the turning point (pole) of the instrument from the joint B; with the verniers the distances calculated by the formulæ x = R. L and x = R.L can be immediately set. The instrument is principally supported by the frame K, in the foot of which at P (Fig. 80) the pivot bearing of the instrument, a hollow half sphere recessed in a steel cylinder, is fixed. Vertically over the pivot P is the axis piece k', k", on a crane-like arm, around which the suspending wires turn. This axis piece is taken out when forwarding the instrument and is provided with a hole, through which an ordinary pin or point is passed for screwing same on firmly. The straight line Pk' should be vertical, which is effected by means of the two set screws S, S and the box level; whether the latter is correctly placed, i.e. whether the axis Pk is shown to be truly vertical by the box level, can be easily verified by the supporting tube 1. The fork end of this tube is supported at P, where the ball bearing screws into the steel cylinder, the other end is attached to the suspending bolt at h" by means of the longest wire and at k" to the frame, so that the supporting tube can be turned in a horizontal plane almost 360°. The small level accompanying the instrument is now placed in the two positions parallel to the straight line adjoining the set screws S, S and rectangular thereto on the supporting tube, as near as possible the frame, on the same side of the tube. By means of these set screws S, S and the eyelet screw h" the level can be brought into all three positions for determining if the axis of rotation Pk is quite vertical; the box level should now indicate this; if not, it must be adjusted without shifting the frame, by means of the correcting screws (two draw-screws and two pressure-screws). If the pantograph is to be used as shown in Fig. 76, i.e. with pole in the centre, the frame K is placed on the table so that its foot P is in the centre of the table and the straight line joining the set screws S, S forms with the longitudinal edge of the table an angle of about 45° and the box levels balance. The instrument is now placed on the table, the pole-ball in the sleeve Z on bar 2 is placed in the bearing of the frame and the bolt drawn over it. The supporting tube is pushed through under the caster of bar 4, its fork end placed against the pole cylinder, the other end suspended by means of the longest wire at h" and at the top eyelet of the frame at k" and the tube adjusted horizontally, as stated above by means of the eyelet screw h”. The sleeve on bar 2 carrying the pole pin must now first be set to the ratio at which it is required to work. The wire, provided with one suspension hook only, is attached to the eyelet h'"' on bar 2, the clamping piece, with ball recess adjustable on this wire, is placed over the small ball at the top end of the pole axis k and the length of wire adjusted so that bar 2 is approximately horizontal. By means of the screw eyelet h"" on bar 2, the bar is then placed exactly horizontal, then by means of the screw on the caster r, bar 4 is placed horizontal, and likewise bar 1 by means of the screw on the caster r'. By reason of the unavoidable deflection of the bars it is advisable always to place the level in the middle of same. It will then be seen if the axis Pk of the frame is vertical. If the pantograph is correctly suspended and horizontal it will, when guided by the handle G, move easily in all directions. B P R F According to the ratio set, a smaller or greater part of the weight of the instrument rests on the caster r' of bar 1. So as to obtain for all settings a uniformly easy motion for the exact guiding of the tracer, a regulating device is attached to the caster. A part of the weight rests on the support p (Fig. 79), the other part on the caster r'. If the caster r' alone carried the weight, the motion of the instrument would be too light; if the weight rested on p alone. the motion would be too heavy. If the spiral spring is strengthened by screwing up the nut m, the caster r' supports a greater weight and the motion is easier; if the nut m is unscrewed the spiral spring is slackened and the motion becomes heavier, as then carries a greater load; in this way the desired heavier or lighter motion can be easily obtained. FIG. 78. In Fig. 78 the necessary points for the pantograph are illustrated-viz., tracer point F, pencil point B, pricking point P, and the ink point R. (The latter is only supplied to order.) All the shafts of the points are exactly cylindrical, of uniform diameter and fit properly in the three sleeves F, Z, and P. Faber leads of 1.9 mm. diameter fit the pencil holders. The point of the lead should be as central as possible, so that, if the pencil resting on the paper is turned in its sleeve Z, a dot only is made on the paper and not a circle. The pin t can be put in at the top with one or more loading discs, to obtain finer or thicker lines. The pin t, with loading weights, can also be placed on the pricker P. The latter carries a screwed protecting sleeve, which can be adjusted so that the point does not project more than it will enter the paper; when the pricker is not in use this sleeve is screwed out to cover the point, and protect it from injury. The tracer F is screwed at the top to take the nut with spring sleeve shown in Fig. 79. This serves to keep the tracer off the paper when the reduction is only to be pricked, in which case the tracer can be quickly moved from one angle of the original drawing to the other. By pressing with the index finger on the tracer the point of the latter can be pressed down at the precise place to obtain a very accurate setting. When tracing the lines of the original, if the drawing is to be reproduced in pencil or ink, it is, however, better to screw up the spring sleeve so that the tracer rests on the prop c, placed so that the tracer point travels just clear of the paper. When using the ink point, the lines can be made in ink at once: 3 r P FIG. 79. 3 t G the pen is so ground that it enables uniform fine lines to be made in all directions (also transversely to the split opening of the pen): the indian ink must, however, be very thin and the stem of the pen kept very clean, so that it falls freely in the sleeve without requiring to be loaded. The handle G (see Fig. 79) embracing the tracer sleeve, serves both for guiding the instrument and raising and lowering the pencil (pricker or pen). It can be moved vertically; if the handle is drawn down the pencil also sinks on' the paper; when using the pricker the handle is pulled down quickly which imparts a free falling movement to the pricker. A spiral spring keeps the handle raised, so that, when at rest, the pencil is also raised. The arrangement and action of the releasing cord is to be seen from Fig. 79; the releasing lever turning around a horizontal axis engages its front horizontal arm in the groove of the handle G, the back arm is drawn down by a spiral spring, which on the one side is attached to the tracer bar and on the other side to a part adjustable on the arm. If the latter is pushed towards the pivot of the lever, the action of the spring becomes weaker. This position is used when working with the pencil or ink point. In order to strengthen the action of this spring, to enable it to draw the pricking point out of the paper, the point of suspension is removed from the turning axis (pivot) of the releasing lever. As when using the pencil the hand gets overtired, through constantly pulling down the handle during the tracing, the vertical pin t is fitted to the handle G. By turning the handle, when |