A SILVERED GLASS TELESCOPE. 



16 



true surface beneath. The ghiss will no longer seem to be a plane, but to have a 

 .section as hi Y\<y. 12. Let us examine l)y the aid of M. Foucault's diagrams why it 

 is that the surface seems thus curvcMJ. If the 

 dotted line, Fig. 13, represents the section 

 of the mirror, and the solid line a section of 

 a spherical mirror of the same mean focal 

 length, it will be seen that the curves touch 

 at two points, but are separated by an inter- 

 val elsewhere. If this interval be projected 

 by means of the differences of the ordinates. 



Action (if the Oi):iinie Screen. 



Fig. 13. 



_^ 



Section of Sjiherical aud Splieroidal Mirrors. 



Fig. 12. 



Apparent Section of Oblate Splieioidal Mirror. 



the resulting curve will be found to be the 

 same as that which the mirror apparently 

 has. 



If the opaque screen be drawn a short 

 distance from the mirror, tlu; appearance of 

 the secticui curve will seem to change, thc> 

 bottom of the groove (Fig. 12) between tln^ 

 centre and edge advancing inwards, and the 



mound in the middle growing smaller. If 

 the screen be pushed toward the mirror the 

 reverse takes place, the central mound becoming larger, but the edge decreasing. 

 The reason for these variations becomes apparent l)y considering tlie three diagrams. 

 Fig. 14. The dotted curve in each instance represents the real cur\ e of the mirror 

 described in the last paragraph, while the 

 solid lines are circles drawn with radii pro- 

 gressionally shorter in a, h and c, and re- 

 present sectioas of three spherical mir- 

 rors whose focal lengths also progressi\ely 

 shorten. 



When the oparpie screen is at a gi\'en 

 distance from the mirror under examination, 

 the only parts of the mirror which can offi- 

 ciate well are those which have a curvature 

 corresponding to a radius equal to the same 

 distance. All tlie other parts seem as if they were covered l)y projecting circular 

 masses. In looking at Fig. 14, it is plain, then, if the opaque screen is at a maxi- 

 mum distance from the mirror, that the central parts alone will seem to op(>rate, 

 because the two curves (a) only touch there. If the screen is moved toward the 

 mirror the curves (h) will coincide at some point between the centre and edge, while 

 if carried still farther in only the edges touch and the appearance will be as if a 



Fig. 14. 



Relation of Sjiliercs to OMate Spheroid. 



