!>K. !,'. A. SAM I Si )X M\ A 



said that "an ol.ject -glass cannot be made on paper," but the possibilities of new ami 

 .,n,|ili.-ated .-onst ructions must in all cases first be demonstrated on paper, 

 .,; never conveniently vary more than a single factor at a time. 



Study is directed N the Cassegrain because of the great advantage which this design 

 possesses in shortening the tube of the instrument for given focal length, and in 

 placing the observer at the lower, in place of at the upper, end of it. 



The best introduction to the subsequent work will be in the form of a few remarks 

 upon SCHWARZSOHII-D'S results. These are not meant as a complete criticism or 

 estimation of it but are merely such as arise naturally in relation to the points with 

 which I deal afterwards. The traditional form of Cassegrain telescope consists of a 

 great concave mirror faced by a small convex one, which is placed between the great 

 mirror and its princijxd focus, and throws the image out through a hole cut centrally 

 in the great mirror. The small mirror increases the effective focal length in the 

 ratio of its distances respectively from the final principal focus and from the 

 principal focus of the great mirror. This ratio for example is 5 '4 in the great 

 Melbourne telescope, 3 J to 4$ in the Mount Wilson 60-inch when used as a Cassegrain, 

 and it can hardly fall much below 2 unless the small mirror is to cut off a dispro- 

 portionate amount of the area of the great mirror. The Cassegrain is, therefore, 

 generally speaking, a long focus instrument. From all these features SCHWARZSCHILD'S 

 forms ditt'er widely, except that they place the small mirror between the great mirror 

 and its principal focus. His small mirror is concave in place of convex, and shortens 

 the effective focal length, bringing the beam to a focus between itself and the great 

 mirror. The effect of this change in design is to render possible a flat field. Spherical 

 aberration and coma are removed from the image by modifying the spherical figures 

 of the two mirrors into definite hyperboloidal and ellipsoidal forms. To confine 

 reference to the case which he considers generally the best (loc cit., II., 11), the 

 necessary deformations are given respectively by b t = -13'5, & 2 =+r97, where 

 - 1 would deform a sphere into a paraboloid. The image-surface for this case 

 would In- very nearly flat, and the images of points would be very nearly circles, 

 .vhich r.-ached a diameter of 8 seconds at an angular distance of about 1 degree 

 IVum the centre of the field. This may seem somewhat large but it is a quantity 

 proportional to the aperture-ratio, which in this case is large also, namely 1 : 3'5. 

 is in brief a very rapid instrument of short focus and of field about 

 1-le to that of a good long-focus refractor. The chief objection to it is found in 

 that it requires. Until some one turns such curves out, it must remain 

 >l>"tl>er it is feasible at all to make the construction a practical success. 

 VMWAK/.S, HILD'S analysis is the use of a concave small mirror. This 

 > destroy coma, which may equally be removed in the Cassegrain 

 <".s of Ike mirrors, and those indeed of less pronounced degree than 

 n..ds necessary. But as will be shown below there then remains a 

 That severe and irremovable curvature of the field 



