420 Mr, Howard Gruhh [Aj^ril 2, 



This gives a very beautiful support, but it is not so convenient, as it is 

 difficult to keep the disc sufficiently steady while the polishing opera- 

 tion is in progress, without introducing other chances of strain. 



So far I have spoken of strain or flexure during the process of 

 working the surface ; but even if the surface be finished absolutely 

 perfectly, it is evident from the experiment I showed you that very 

 large lenses when placed in their cells must suffer considerable 

 flexure from their own weight alone, as they cannot then be sup- 

 ported anywhere except round the edge. 



To meet this, I proposed many years ago to have the means of 

 hermetically sealing the tube, and introducing air at slight pressure 

 to form an elastic support for the objective, the pressure to be regu- 

 lated by an automatic arrangement according to the altitude. My 

 attention was directed to this matter very pointedly a few years ago 

 from being obliged to use for the Vienna 27-inch objective a crown 

 lens which was according to ordinary rules much too thin. 



I had waited some years for this disc, and none thicker could be 

 obtained at the time. This disc was very pure and homogeneous, but so 

 thin that if offered to me in the first instance I would certainly have 

 rejected it. Great care was taken to avoid flexure in the working, 

 but to my great surprise I found no difficulty whatever with it in 

 this respect. This led me to investigate the matter, with the 

 following curious results. 



If we call / the flexure for any given thickness t, and /' the flexure 



f f^ 

 for any other thickness t\ then -p = j^tor any given load or weight 



approximately. But as the weight increases directly as the 

 thickness, the flexure of the discs due to their own weight, which 



/ ^. 



is what we want to know, may be expressed as ^ = -, 



Let us now consider the effect of this flexure on the image. In 

 any lens bent by its own weight, whatever part of its surface is 

 made more or less convex or concave by the bending, has a corres- 

 ponding part bent in the opposite direction on the other surface, which 

 tends to correct the error produced by the first surface. This is 

 one reason why reflectors which have not this second correcting sur- 

 face are so much more liable to show strain than refractors. If 

 the lens were infinitely thin, moderate flexure would have no effect 

 on the image. The effect increases directly as the thickness. 

 If then the flexure, as I have shown, decreases directly as the thick- 

 ness, and the effect of that flexure increases directly as the thickness, 

 it is clear that the effect of flexure of any lens due to its own weight 

 will be the same for all thicknesses ; in other words, no advantage is 

 gained by additional thickness. 



This has reference, of course, only to flexure of the lens in its 

 cell after it has been duly perfected, and has nothing to do with the 

 extra difficulty of supporting a thin lens during the grinding and 

 polishing processes. 



