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XLII. On some Improved Formula! and Methods connected 

 with Lenses. By Thomas H. Blakesley*. 



IN a paper read before the Physical Society on June 11th, 

 1897, I pointed out the connexion between the distance 

 of an object from the first principal focus of a lens and the 

 relation of its linear magnitude with that of the image pro- 

 duced : viz. that every change in that distance by the amount 

 of the focal length of the lens produced a unit of change in 

 the relation of these magnitudes ; and I described methods by 

 means of which the focal length might be very accurately 

 determined upon these grounds. 



I also explained how the position of the two principal foci 

 might be accurately determined by placing the lens upon a 

 plane mirror and finding the spot at which if an object be 

 placed its image inverted will coincide with it, 



The rules given apply equally well to combinations of coaxial 

 lenses as to single lenses. 



Hence all focussing properties of lens-systems are really 

 determined when the three following matters are known : — 



(1) The focal length with proper sign. 



(2) The position of the first principal focus. 



(3) The position of the second principal focus. 



The first principal focus is defined as the point such that if 

 a beam of light before impact on the lens- system is diverging 

 from it or converging to it, then after passage through the 

 system the beam will consist o£ parallel rays. 



The second principal focus is the point such that if before 

 impact the beam is one of parallel rays, after passage it will 

 consist of rays either diverging from or converging to that 

 point. 



In the present communication I wish to point out the rules 

 by means of which, when these elements are known for any 

 two systems, the elements for the combination of the two 

 systems are readily obtained. 



Each lens of course carries its own system of points with it, 

 but an independent variable is necessarily introduced in com- 

 bining systems at different distances. 



The simplest magnitude will be found to be the distance 

 between the second principal focus of the first system and the 

 first principal focus of the second system, which I call k, and 

 which has a positive value in the direction of the propagation 

 of light. 



* Communicated by the Physical Society : read December 8, 1899, 



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