30 THE MODERN REFLECTING TELESCOPE. 



optician's body for a period of t^-o or three minutes, at a distance of three feet 

 fi'om a mirror which was set up for testing, would thi'ow a previously plane mirror 

 convex by an amount many times greater than the smallest amount which can be 

 detected by the knife-edge test. When the thickness of mirrors is made equal to 

 about one-seventh of their diameter, their sensitiveness to all such temperature 

 effects is very greatly decreased. Furthermoi-e, in the case of silvered glass minors 

 which are used for solar work, the writer has found that thick mirrors suffer very 

 much less change of figure fi-oia exposure to the sun's heat than thin mirrors do. 

 Silvering affords a gi'eat pi'otection from changes of temperature, since the silver 

 film furnishes an almost totally reftecting surface for heat radiations. 



CHAPTER XIII. 

 TESTING .AND FIGURING P.\RABOLOIU.\L MIRRORS. 



The work of changing a spherical mii-ror to a paraboloidal one is accomplished 

 entirely by the use of polishing tools, by shortening the radii of curvature of the 

 inner zones, instead of by increasing or lengthening those of the outer zones. The 

 methods of effecting this change of curvatuie will be described after the methods 

 of testing a paraboloid have been discussed. 



Such testing can be done at the center of curvature, by determining there the 

 foci or the I'adii of curvature of successive zones of the mirror; it may be done at 

 the focus of the paraboloid, by the aid of a finished plane mirror which should be 

 at least as large as the paiaboloidal one ; and it may be done directly on a star. 

 The first two methods named have the very great advantage that they may be 

 conducted without interruption, under the practically perfect atmospheric and 

 temperature conditions of the optical laboratory. 



Testing a Paraboloid at the Center of Gurvatwre. A knowledge of the pi'o})- 

 erties of the parabola enables the optician to compute the positions of the centers 

 of curvature of successive, definite, narrow zones of the mirror, and the surface 

 must be so figured that the radius of curvatui'e of each zone agrees with the com- 

 puted value. In testing, each zone in succession is exposed by means of a suitable 

 diaphragm, all of the rest of the surface being covei'ed. In practice, two entirely 

 different fornuilje may be used, depending upon the position of the illuminated 

 pinhole. 



Let F be the focal length of a finished paraboloidal mirror, and R the semi- 

 diameter of any extremely narrow zone or ring of its surface, concentric with the 

 vertex or center of the mirror; the normals to this zone cross the axis at a point 



T>2 



whose distance from the vertex is 2 F+— p; hence, if the illuminated pinhole be 



T> 2 



placed very close to the axis, and at a distance of 2 F + — p; from the vertex, the 



4 r 



rays of light reflected from the narrow zone will form a focus or image in the same 



