A SILVERED GLASS TELESCOPE. 



15 



Fig. 11. 



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

 section as in Fig. 12. Let us examiae by the aid of M. Foucault's diagrams why it 

 is that the surface seems thus curved. 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 wiU 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, 



Fig. 12. 



Apparent Section of Oblate Spheroidal Mirror. 



Action of the Opaque Screen. 



\ 



Fig. 



13. 



i 



h^ i __-^^l-..-,-_ i ^ 



Section of Spherical and Spheroidal Mirrors. 



Fig. 14. 



the resulting curve wiU 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, the appearance of 

 the section curve will seem to change, the 

 bottom of the groove (Fig. 12) between the 

 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 by considering the three diagrams. 

 Fig. 14. The dotted curve in each instance represents the real curve 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 sections of three spherical mir- 

 rors whose focal lengths also progressively 

 shorten. 



When the opaque screen is at a given 

 distance from the mirror under examination, 

 the only parts of the mirror which can offi- 

 ciate weU are those which have a curvature 

 corresponding to a radius equal to the same 

 distance. AU the other parts seem as if they were covered by 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 operate, 

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

 mirror the curves (&) 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 



Relation of Spheres to Oblate Splieroid. 



