Images from Plane Mirrors in rapid rotation. 61 



nodes, that circumstance contributed to add greatly to the va- 

 riety and beauty of the phenomena. 



When the instrument, which may be called a katoptrizotrope, 

 is held in such a position as to receive, at the same time, the 

 direct rays of the sun, and the refracted light proceeding from 

 a prism, the curves unite the utmost elegance of form, with the 

 pleasing diversity of colour exhibited by the solar spectrum ; 

 and by gradually varying the direction of the incident light to 

 the axis of rotation, and causing the reflected rays to fall on 

 different planes, an endless diversity of curves is obtained, 

 which, in every case, are sketched with the most perfect sym- 

 metry. When the experiment is made in a large and pro- 

 perly darkened apartment, it is scarcely possible to describe, 

 in suitable terms, the splendour and variety of the optical ap- 

 pearances which it exhibits. 



Those acquainted with the origin of the curves derived from 

 the various sections of the cone, will readily perceive that these 

 curves must be obtained when the axis of rotation coincides 

 with the direction of the luminous ray, — the position of the 

 plane on which the flitting images are received determining, 

 in that case, the peculiar description of the curve, whether 

 a circle, an ellipse, a parabola, or hyperbola. The same de- 

 scription of curves is also obtained after two reflections, in par- 

 ticular dispositions of the mirror, to be afterwards mentioned. 



In cases, however, in which the axis of rotation is inclined 

 to the direction of the light, the angle of incidence, and con- 

 sequently, also, the angle of reflection, are subject to a con- 

 tinual and gradual change, which is confined between certain 

 limits ; and hence, the determination of that angle for every 

 position of the revolving mirrors, constitutes an essential ele- 

 ment in the construction of the resulting curves. To obtain, 

 in the first place, an analytical expression for the variable 

 angle of incidence, it will greatly facilitate the investigation 

 to conceive the plane of rotation, as well as the planes of the 

 two mirrors, to be great circles of the sphere ; the axis of ro- 

 tation, and the axis of the mirrors (regarded as passing through 

 the centre of the sphere), will evidently make with each other 

 the same angles as the planes of the circles to which they re- 

 spectively belong. 



