158 



and d y, draw an arc cutting the perpendicular d b in z ; then through 

 the point z draw the line c m, in such a way that it shall equal c y, 

 and with c as a centre and distance c y, draw the arc y m, which will 

 form the side of the condenser. 



All the requisite data are now ascertained, d being the focus and 

 centre of the concavity, d b the longitudinal distance of the centres 

 of convexity and concavity, and b c the amount of excentricity from 

 the axis. 



In order to avoid taking off any of the reflective power of the con- 

 vex sides by the brass setting, it is as well to remove the base line, 

 x y, some little distance lower, to s s, and leave the intervening por- 

 tions of the sides, x s, y s, unpolished. The side y m, being the arc 

 of a circle, allows the axis of motion to be changed while the glass is 

 undergoing the process of polishing. The space I I (fig. 2) is filled 

 with some opaque substance, to intercept any central rays. 



Fig. 1. 



Fig. 2. 



The action of the instrument is as follows: — The light is reflected 

 from the plane side of the mirror in parallel rays, k k, and falling 

 perpendicularly on the base, s s (fig. 2), suffers no refraction, but 

 passes on to the convex surface, y m, &c, where, as the angle of in- 

 cidence is in no part less than 45°, it is totally reflected and comes 

 to a focus at d, uninterrupted on emerging from the glass, as each 

 ray falls perpendicularly on the concave surface, m z. 



It will at once be evident that the radius of the concave surface is 

 immaterial, provided the centre be truly situated at the point d, (a 



