150 Scientific Proceedings, Royal Dublin Society. 



evident that in the ease of a refractor no supports are admissible 

 once it is placed in its tube, except on a narrow band round the 

 extreme circumference. It is therefore evident that the most 

 perfect support we can give can only go so far as to support it 

 equally round the whole circumference. 



The whole lens, therefore, alters its shape in accordance with 

 the altitude of the object under examination : the higher the alti- 

 tude, in the case of the crown lens,'; the less convex the first surface 

 becomes and the more convex the second. This, in a moderately 

 thin lens, becomes a measurable quantity ; but provided the support 

 be perfectly equable round the whole circumference, the effect on 

 the image is imperceptible : it is practically the same, in fact, as if 

 the first surface were increased in radius by an almost infinitesimal 

 amount, and the second diminished by the same, the gross result 

 being almost exactly the same. In general, too, it may be assumed 

 that any flexure which does not cause one or other of the surfaces 

 to cease to be a surface of revolution is of no consequence, unless, 

 indeed, it amounts to such a quantity as to cause polarization. 



When, however, a large thin lens is supported on three fixed 

 points only round its circumference, or that, from any cause, the 

 support is not equable round the edges, there must be, and is, a 

 considerable variation from a surface of revolution, and as this 

 flexure will naturally increase largely as the thickness of the lens 

 diminishes, I have been much surprised to find the effect on the 

 image due to this flexure no more troublesome in thin lenses than 

 in thick, and this it is that has led me to investigate the matter. 



The general result of my investigations is rather remarkable, 

 and goes to show that in the more usual construction of telescopic 

 objectives, and suppposing all the surfaces to be truly surfaces of 

 revolution as they came from the polishing machine, the thickness 

 of the lenses (within moderate limits) is of very little consequence, 

 and for the following reasons : — 



The flexure of the glass we may probably assume to follow the 

 ordinary law, as being inversely proportional to the square of the 

 thickness for any given weight or load ; but as the weight of the 

 glass itself diminishes directly as the thickness, the flexure due to 

 its own weight will be just inversely as the thickness (not as square 

 of the thickness) . But now as to the effect on the image. If the 

 lens were infinitely thin, the effect would be nil, for wherever 



