connected with Astronomical Physics. 



271 



the point of convergence of the rays, or nearer the image formed 

 by the chief mirror. But then the cone of rays, reflected 

 through 90° by the front mirror, would evidently be too 

 short to reach the lens in the ocular tube. 



As a mathematical question, it might then present some 

 theoretical (if not practical) interest, to discover the nature 

 of a surface which is competent to deviate the cone of rays 

 through an angle of 90°, and at the same time to reduce its 

 convergency to any desired degree. The Cassegrain system 

 (as w r e know) fulfils the second of these conditions, but it (of 

 course) does not deviate the axis of the cone of rays through 

 90°. The question then becomes — What surface will accom- 

 plish both these results at once ? 



It might be objected that such a reflecting surface, even if 

 it theoretically existed, would be difficult to figure in practice. 

 But Foucault's ingenious optical methods for verifying the 

 figure of the reflecting surface of the mirror [independently 

 of observations with the telescope] are of course available. 

 And since the optical result to be expected from a correct 

 figure is known beforehand, it becomes always possible to 

 improve any surface so as to approach towards perfection of 

 optical form : comparing the observed results with the ideal 

 theoretical. And this is known to be accomplished with 

 satisfaction in the case of paraboloid surfaces. The annexed 

 diagram having been sent to Mr. S. H. Burbury: — he has 



b ,-* 



found that an ellipsoid of revolution (part of the exterior 

 surface of the same) would be the theoretically correct shape 

 for the reflecting surface of the front-mirror, in order to 

 fulfil the above conditions. 



In the " Newtonian "-telescope, the total reflexion of a 

 rectangular prism is sometimes preferred to a " flat/'' Why 

 not grind the two prism-surfaces adjacent to the right-angle,, 



