TRANSACTIONS OF THE SECTIONS. 63 



could be introduced by a slit, and being then reflected down, met a prism of flint- 

 glass, with its remote side silvered, and placed perpendicularly to the axis of the 

 observing or telescopic part ; the light then reflected back is dispersed as if by a prism 

 of double the refracting angle of the prism of the instrument, and the dispersion 

 is then measured by a micrometer placed at the focus of the eyepiece. 



On an Improvement in the Proportional Compass. 

 By Lieut.- Colonel It. Shortrede. 

 This consists in the introduction of two moveable discs, on which alone the friction 

 takes place, so as to avoid the unequal rubbing of the jaws. This is mischievous, as 

 the jaws invariably become striated circularly at the points of usual setting. Under 

 this unequal action of the jaws they are very apt to shift their position, while at the 

 same time it is very difficult to alter the adjustment by a small quantity when re- 

 quired. These objections have almost thrown the proportional compass out of 

 common use as an instrument for exact work. 



On a Neio Photographic Lens, which gives Images entirely free from 

 Distortion. By Thomas Sutton, B.A. 



The author described a combination by which the effects of distortion are totally 

 obviated, and which gives an image that is mathematically perfect. 



The conditions for obtaining an image free from distortion are these : — 



1st. The axis of every pencil must emerge from the combination in a direction 

 parallel to that of incidence. 



2nd. The axis of every pencil must pass through a certain fixed point. 



3rd. The image of every luminous point of the object must be formed at the 

 point where the axis of the pencil meets the focusing screen. 



The combination is a Symmetrical Triplet, consisting of two equal achromatic 

 plano-convex lenses, one at each end of a tube, placed with its convex side outwards, 

 and a small double concave lens of equal radii placed exactly midway between them. 

 In contact with the double concave lens a small stop is placed. 



It is evident that in this combination a small oblique pencil is incident excentrically 

 upon the front convex lens, — that its axis after suffering deviation passes centrically 

 through the concave lens without suffering further deviation, and that it is then 

 incident excentrically upon the posterior convex lens, from which it emerges in a 

 direction parallel to that of incidence. 



The above is true of every oblique pencil, and their axes all pass through a common 

 point, which is the centre of the Symmetrical Combination, and which point is 

 called C. 



The 1st and 2nd conditions are therefore fulfilled. 



The proof that the 3rd condition is also fulfilled is as follows : — 



The focus of an oblique pencil is in every optical instrument a disc of light, and 

 not an exact point. The size of this disc is reduced by using a small stop. When 

 it is sufficiently reduced, by using a sufficiently small stop the focus upon the screen 

 is said to be good. In that state the ray which passes through C (the axis of the 

 pencil) is one of the rays which compose the small disc or good focus, because C is 

 at the centre of the stop. The focus is therefore at the point where the axis of the 

 pencil meets the focusing screen ; and therefore the 3rd condition is fulfilled. 



By a fortunate circumstance this Triplet gives an image which is equally illu- 

 minated in every part, because the area or base of the oblique excentrical pencil upon 

 the front lens is greater than that of the direct central pencil, and in this way the 

 loss of light from obliquity is counteracted. 



Spherical aberration in the direct central pencil is totally corrected, because the 

 negative aberration of the concave lens counteracts the positive aberration of the 

 convex lenses. There is consequently brilliant definition in the centre. At the same 

 time, the marginal definition is as good and the field as flat as that of any lens now 

 in use. 



In order to get good marginal definition and the proper flatness of field, the distance 

 between the convex lenses should be about one-sixth of their focal length, and the 



