16 



ON THE CONSTRUCTION OF 



Fig. 15. 



large mound were fixed iipon the centre. I have been careful in explaining how 

 a surface may thus seem to present entirely different characteristics if examined 

 from points of view which vary slightly in distance, because a knowledge of these 

 facts is of the utmost importance in correcting such an erroneous figure. It is now 

 obvious that the correction will be equally effectual if the mirror be polished with a 

 small rubber on the edge, or on the centre, or partly on each. The only difference 

 in the result will be, that the mean focal length will be increased in the first instance, 

 and decreased in the second, while it will remain unchanged in the third. 



If the mirror, instead of having a section like that of an oblate spheroid, should 

 have either an ellipse, parabola, or hyperbola, as its section curve, the appearances 

 seen above are reversed. Whilst by the first test there is still an aberration round 

 the image at the best focus, the eye-piece must now be drawn from the mirror to 

 include it. The cone of rays is most dense round the axis inside, and at the 



periphery outside the focus, and the 

 summit of the caustic (Fig. 15) is 

 turned towards the mirror. The 

 second test shows a section as in 

 Fig. 16, a depression at the centre, 

 and the edges turned backwards. 

 The nature of the movement neces- 

 sary to reduce the surface to a sphere 

 is very plainly indicated, action on a 

 zone a between the centre and edge. 

 If, hov/ever, a parabolic section is 

 required, the zone a must not be 

 entirely removed, and the surface 

 rendered apparently flat, but as much 

 of it must be left as experience shows to be desirable. 



If, in still a fourth instance, the mirror is not formed by the revolution of any 

 regular curve upon its axis, but has upon its surface zones of longer and shorter 



radius intermixed irregularly, a very com- 

 mon case, the two tests still indicate with 

 precision the parts in fault, and the correc- 

 tion demanded. Thus the mirror seen in 

 section in Fig. 17, when the principal mass 

 of light was obstructed by the opaque screen, 

 would still permit that coming from certain 

 parts to find its way into the eye. 



Figure 18 represents an irregular mirror, 

 that was produced in the process of correc- 

 tion of a hyperbolic surface, which had an 

 apparent section like Fig. 16 previously. 

 The zone a had been acted upon with a 

 small local polisher, and the mirror was 

 finished by subsequently softening down b and c with a larger tool. 



Caustic of Hyperbolic Mirror. 

 Fig. 16. 



Apparent Section of Hyperbolic Mirror. 



Fig. 17. 



Action of the Opaque Screen. 

 Fig. 18. 



Apparent Section of Mirror with Ringa. 



