THE MODERN REFLECTING TELESCOPE. 



33 



^jf inch along the axis, for a mirror of two feet aperture and of ten or fifteen feet 

 focal length. 



Care must be taken wlien testing in this way that the entire mii-ror surface is 

 uniformly illuminated by the cone of light proceeding fioiu tlie illuminated pin- 

 hole; this condition, once secured, is easily maintained, since the illuminated i)inhole 

 remains immovable. 



I have described at considerable length the methods of testing paraboloids at 

 the center of curvature, because of the importance of the subject, and because this 

 will probably continue to be a favorite method, especially among amateurs. But 

 when testing is done at the center of curvature, even with the extremely accurate 

 method just described, the making of a large paraboloidal mirror of great angular 

 aperture and really fine figure is an exceedingly difficult task. This is due in part to 

 the necessity of very frequent tests, in each of which the foci of a large number of 

 zones must be determined ; it is due far more to the uncertainty in determinino' the 

 exact nature of errors of surface (considering the surface as a whole) coi-i-espondino' 

 to focal readings which do not agree witli the computed values. In the case of 

 miri'ors of small or moderate angular aperture, much important information can be 

 gained by viewing the surface as a whole, from the (mean) center of curvature, by 

 means of the knife-edge test; a finished paraboloid, when thus seen, appears to 

 stand out in relief, in strong light and shade, as a surface of revolution whose sec- 



FiG. 8. 



tion is that shown in Fig. 8 ; knife-edge and pinhole are both at the center of curva- 

 ture of the zone a; the apparent curve of the surface should be a smooth one. 

 But in the case of a mirror of large angular apertui'e the change of curvature is so 

 rapid that only a narrow zone can be seen well at one time, i. e., with a given focal 

 setting of the knife-edge. 



Testing a Paraboloid at it,^ Focus. This method was briefly described by the 

 writer in the Astrophysical Journal, November, 1901. It is incomparably more 

 simple, direct, and rigorous than the test at the center of curvature. A well-figured 

 plane mirror, which should not be smaller than the paraboloidal one, is necessary 

 in oi'der that the testing may be done in the optical laboratory. In pi-actice a small 

 diao^onal plane mirror is also used, to avoid the necessity of a central hole through 

 the large plane miri'or. Both of the plane miri'ors are silvered. The arrangement 

 of mirrors is shown in Fig. 9. The diagonal prism is placed at/', with the illumin- 

 ated pinhole very near the axis ; pinhole and knife-edge are in the same plane, at a 

 distance from the vertex equal to c m + tnf, which is equal to the focal length of 

 the mirror. The paraboloid is now tested as a whole, without the use of zones, 

 precisely as a spherical mirror is tested at its center of curvature. 



