164 



Transactions of the Society. 



There is yet another error in this eye-piece, viz. astigmatism ; but 

 as I have already dealt with this in the Journal for 1898, p. 402, it 

 will be merely necessary to say that rays issuing from a point and 

 falling excentrically upon a lens will not be accurately refracted to 

 another point, but will be focussed into two lines separated from and 

 at right angles to one another. The following, therefore, are the 

 errors in this eye-piece : — 



1. Chromatism. 



2. Curvature of image. 



3. Distortion. 



4. Astigmatism. 



Formula. — If we turn to the text-books, we shall find formulas 

 for a telescopic Huyghenian eye-piece which will satisfy the conditions 

 both for achromatism and also for equal deviations at each lens. When 

 we wish to construct a Huyghenian eye-piece suitable for a Micro- 

 scope, these formulae will not t serve us, because the distance from the 

 field-lens of the point where the axis of the excentrical pencil cuts the 

 axis of the eye-piece can no longer be considered infinite ; in other 

 words, the axis of the excentrical pencil incident upon the field-lens 

 is so much inclined to the axis of the eye-piece that to regard it as 

 parallel would introduce too great an error into the calculation. 



Coddington and subsequent authors give a formula that will satisfy 

 the condition of achromatism when the axis of the incident pencil is 

 inclined to the axis of the eye-piece, but none for equal deviations at 

 each lens, under similar circumstances. It is therefore my intention 

 to-night to supply this defect. 



Symbols. — Let us call the focus of the field-lens/, that of the eye- 

 lens /', the distance between the lenses d, the equivalent focus of the 

 eye-piece F, its power m, the distance from the field-lens of the point 



Fig. 43. 



where the axis of the excentrical pencil iucident upon the field-lens 

 cuts the axis of the eye-piece p, its conjugate focus p', the similar dis- 

 tances from the eye-lens a and q, the deviation at the field-lens 8, and 

 that at the eye-lens 8' (see explanation of fig. 43 infra), then the con- 

 dition of achromatism is 



d -P(f+f) 



(i.) 



