60 Dr Anderson on Curves generated by 



eight leaves, and, consequently, causes the axis of the pinion to 

 revolve fifteen times for each revolution of the wheel. 



In fig. 1, (Plate I.) A B represents the wheel; BD,the pinion; 

 Z E F, the axis of revolution; M M and N N, two mirrors, which, 

 by means of the adjusting screws S S, may be inclined at any 

 angle with the plane of rotation, to which E F is perpendicu- 

 lar. The rectangular appendage, I K V W, is graduated by a 

 scale of tangents, adapted to the radius K I ; so that the angle 

 RIK, which is equal to the angle that the direction of the 

 solar ray makes with the axis E F, is determined by the point 

 R, where the extremity of the shadow of K I falls upon K V W. 

 The instrument being held steadily by the handle X X, a rapid 

 rotation is given to the wheel by means of its handle c d. As 

 the wheel may be easily made to perform two turns in a se- 

 cond, the pinion, with the attached mirrors, revolves thirty 

 times in the same time — a velocity of rotation which far ex- 

 ceeds what is necessary to maintain the sensation of a continu- 

 ous curve, re-entering into itself, when such a curve is gene- 

 rated by the images of the reflected light, proceeding from the 

 revolving mirrors. 



After I had duly prepared the apparatus, and made the ne- 

 cessary arrangements for exhibiting the experiments which I 

 had in view, I was much pleased with the magnificence and 

 variety of the curves I obtained, which I soon found included, 

 among others, all the conic sections. In the expectation that 

 a still more interesting description of curves would result from 

 the images produced by the reflection of the light from one 

 mirror to another, I applied a second mirror, with its reflect- 

 ing plane facing that of the first, their line of common section 

 being at right angles to the axis of rotation ; and found, as I 

 anticipated, that the reflections were greatly more diversified 

 in appearance : the form and magnitude of the curves to which 

 they gave birth being modified in every conceivable variety, 

 by the inclination of the mirrors to the plane of rotation, and 

 the direction of the incident light. Some of the curves pro- 

 duced by the double reflections intersected those occasioned 

 by the primary reflections ; and as they exhibited, in certain 

 cases, lines of contrary flexure, with symmetrically disposed 



