an instrument for drawing ellipses. The trammel is an instrument which has long been known and used for describing ellipses. On the principle of the trammel Mr Farey constructed his elliptograph in a form much more commodious for drawing; Mr Farey's elliptograph is represented at Plate CCXVIII. fig. 5. The circle A slides between the two parallel rulers D, E. The circle B slides between two parallel rulers F, G, at right angles to the former. In this way, if a line joining the centres of the circles is made to revolve, M, the extremity of that line, will describe an ellipse in the same manner as the extremity E of the line CDE, fig. 1, does in the trammel. The elliptograph may be considered as a trammel, in which the pins C and D, fig. 1, are enlarged into the circles A and B, fig. 5. The pinion at K, fixed to one of the arms of the lower circle, acting on a rack screwed to the upper circle, serves to alter the distance of the centres of the circles A and B; and, by so doing, this pinion serves to vary the eccentricity of the ellipses which the instrument describes. When the centres of the circles A, B coincide, the describing pen M draws a circle. When the centres are removed from each other, and on the circles being turned round, an ellipse is described by the pen; and when the distance of the centres in increased, the eccentricity of the ellipse is increased. When the pen is at the centre it describes a straight line, continually moving to and fro on that line when the circles are turned round. The two circles are fixed together by screws, and can only be made to slide the upper circle over the lower by the action of the pinion K. The pinion at L moves a rack, by which the describing pen M, which draws the ellipse, is brought nearer to the centre for the purpose of drawing a small ellipse, and removed farther from the centre of the ellipse when a large one is to be drawn. The size of the ellipse may be increased as far as the size of the instrument will admit. The pair of rulers D, E are placed below the pair F, G, as is seen in fig. 6. The instrument, when used, is held upon the paper with the thumb and a finger of the left hand at the nuts N, O; and the circles are moved by applying the right hand to the pins f; the pen M, pressing by its weight on the paper, then describes the ellipse.

Fig. 7 shows H, the socket for the compasses, with the centre pin on which the socket moves; and the pinion L and rack h, for moving along the frame g between the bars; and the other pinion K, for separating the circles.

The ruler P has two points, to fix the instrument to the paper. The ruler is united to the frame by screws, which serve to adjust the position of the instrument after the ruler has been fixed to the paper.

By means of the elliptograph any ellipse can be described, of which the long and short axes are given, provided it does not exceed the size of the instrument. When an ellipse is to be described, draw on the paper the longer and shorter axes, bisecting each other; place the instrument on the paper, so that the centre of the four rulers appears to coincide with the centre or the intersection of the two axes of the ellipse; and fix the instrument in this situation by the points that go into the paper. By the pinion L move the pen to one extremity of the short axis of the ellipse; turn the circles half round, to see if the pen comes to the other end of the short axis; if it does not, adjust the error one half, by moving the pen by the pinion L, the other half by moving the frame on the paper; continue this adjustment till the pen, setting out from the one end of the short axis, arrives in a half revolution at the other end. Next, by means of the pinion K, bring the pen to one end of the long axis of the ellipse; turn the circles half round, and if the pen reaches the other extremity of the long axis of the ellipse, the instrument is rectified; if not, one half of the error is to be corrected by moving the circles by means of the pinion K, and the other half by moving the instrument to a side on the paper, by means of the nuts N, O. The instrument is now adjusted, and the pen resting on the paper traces the ellipse required when the circles are turned round by the handles.

An instrument similar to the elliptograph has been employed for engraving ellipses on copper plates, and for providing these ellipses accurately, so as to give the perspective representation of a circle divided into equal parts, both in the case where the distance of the eye is limited, and in the orthographic projection. The Society for Encouraging Arts rewarded Mr Farey with their gold medal for his invention, and a description of the elliptograph is contained in the thirty-first volume of the Transactions of that society.