Grubb — Flexure on Performance of Telescopic Oljectives. 151 



one surface got convex tlie other would get concave by an equal 

 amount ; and the only reason why flexure in a lens does distort the 

 image is, that after the rays are disturbed from their true path, by 

 the alteration of curvature of first surface, they have to travel some 

 distance {i. e. the thickness of the lens) before they are corrected 

 by the other ; and the effect, therefore, of any given flexure on the 

 image varies directly as the thickness (almost exactly for moderate 

 thickness) . 



As, therefore, the flexure varies inversely as the thickness, and 

 the effect of that flexure varies directly as the thickness, it follows 

 that the effect on the image, from flexure of the discs due to their 

 own weight, is about equal, no matter what the thickness is. 



This curious result explains to me how it is that we just as often 

 find evidence of flexure in thick as in thin lenses, and other for- 

 merly puzzling matters. 



The above result is only strictly true when the bending or 

 refraction is equal on both surfaces, which is approximately the case 

 with the crown lens of the ordinary form of telescopic objectives, 

 but not with the flint ; from which it follows that it is more neces- 

 sary to have thickness in the flint than in the crown. 



It is well known among opticians that this is practically the 

 case, but the reason generally assigned is, either that the form of 

 the flint is not so well calculated to resist flexure, or that the spe- 

 ciflc gravity being higher, the load is really greater. 



It would, however, appear now that there are other reasons. 



It also follows from the above that objectives constructed on the 

 " Gauss " system, in which the refraction is very different on the 

 different surfaces, will suffer more from any flexure due to their 

 own weight than those constructed on the more ordinary system. 



