TTTE MODERN REFLECTING TELESCOPE. 23 



polishing, all irregularities of figui'e which occur are perfect zones or rings concen- 

 ti'ic with the edge of the glass; that is, the surface is always a peifect surface 

 of revolution. If, liowevei", these precautions have not been taken, or if the glass 

 has been improperly su])[)oited during grinding and polishing, or if it has been cut 

 out of thick rolled plate-glass, so that it is weak in the direction of one diameter, an 

 astigmatic niii'i'or may be produced, in which the radius of curvature is slightly 

 different aloni^ two diameters at richt ancles to each othei'. 



Astigmatism is easily recognized with either the knife-edge or the eyepiece 

 test. Let the plane of the apparent focus be determined with the knife-edge 

 advancing from the left, then from above, then from the right, then from a number 

 of directions between these three ; if astigmatism exists the planes of the various 

 foci thus found will not coincide; and the directions of greatest and least curvature 

 of the surface are readily determined. When the eyepiece test is used, an astig- 

 matic mirror does not give a shai'p image even at the best focus; if the eyepiece be 

 moved outside and inside of this focus the expanded disk becomes elongated, and 

 is not uniformly illuminated ; the direction of elongation outside is at right angles 

 to tliat inside, and the distribution of light in the expanded disk is entii-ely different 

 outside and inside of the focus. 



LENS 



— rn~- 



, PIN HOLE 



1^'--- 



DIAGONAL PRISM 



---UJ 



■ — _ __^L/\riP 



__ — —-"' rlJ^ME 



? s 



Fig. I. 

 Arrangement hv which Artificial Star is used very close to Optical Axis. 



The general character of the tests having now been described, let us con- 

 sider some important matters of detail which are necessary for the gi'eatest refine- 

 ment in testing all forms of mirroi's. 



By the use of a small lens and a diagonal prism, in the manner shown in Fig. 

 1, the lamp can be kept well out of the way, and the illuminated pinhole and its 

 reflected image brought very near to the axis of figui'e of the niiri'or. This is of 

 much importance in testing nairrors of short focus or of great angular aperture, as 

 the danger of errors in testing due to woi'king considerably out of the axis of figure is 

 avoided. As may be seen in the figure the pinhole is now placed at the surface of 

 the diagon.al prism nearest to the mirror being tested. The arrangement should 

 be such that the cone of rays proceeding fiom the lens is considerably larger than 

 is needed to fill the concave mirror. 



When being figuied, mirrors are usually tested while unsilvered, since very 

 frequent tests are desirable. While the amount of light reflected from the polished 



