16 



ON THE CONSTRUCTION OP 



larii-(> mound Avore fixed upon the centre. I have hern careful in (>xi)lainiiig liow 



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



from points of view wliich 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 tliat the; correction will be equally effectual if the mirror be polished witli a 



small rubber on the edge, or on the centre, or partly on eacli. 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, wliile it will remain unclianged in the third. 



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



have either an elli])se, [jarabola, or hyperbola, as its section curve, the appearances 



seen above are reversed. AMiilst 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 tin; 



periijherv outside the focus, and the 

 Fig. 15. ^ . ' . , . ,,. ^ . 



sunnmt of the caustic (rig. 15) is 



turned towards the nnrror. The 

 second test shows a section as in 

 l''ig. 1(1, a depressinn at tlie centre, 

 and (he edges tnrned l)ackwards. 

 'i'he nature of the mo\'ement neces- 

 sary to refluce the surface to a sphere 

 is Ncry ])lainly indicated, action on a 

 /one 11 between the centre and edge. 

 If, liov.'evcjr, a ])arabolic section is 

 required, the /one (/. must not be 

 entirely remov(Kl, and tlu^ surface 

 rendered apparently flat, l)ut as much 

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



If, in still a fourth instance, the mirror is not formed l)y the revohition of any 

 regular curve; u])on its axis, but luis upon its surface /ones of longxn- and shorter 



radius intermixed iiicgularly, a \'ery com- 

 mon case, th(^ two tests still indicate with 

 precision the ])arts in fault, and the correc;- 

 tion demanded. Thus the mirror seen in 

 section in Fig. 17, Avluni the principal mass 

 of light was obstructed by the opaque screen, 

 would still permit tliat 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, whicli 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 h and c with a larger tool. 



Ciui.stii; lit liyin-i-buliu Mirror. 

 I'ig. 16. 



rr 



c 



Apparent Seution of llyiicrbolii- Minor. 



Fig. 17. 



Action of the Op.iqiie Screen. 

 Fig. 18. 



-Apparent Section of Mirror vvitli Rings. 



