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XXI. Note on Mr. Blakesley's paper, " A new Definition of 

 Focal Length, fyc." By Prof. A. G-kay *. 



I HAVE read Mr. Blakesley's paper on "A new Definition 

 of Focal Length, &c.," with much interest. It is true, 

 as Mr. Blakesley states, that the treatment of lenses and 

 combinations of lenses in ordinary text-books is frequently 

 faulty, and that much advantage would be gained by a con- 

 sideration of the question from other points of view than that 

 generally adopted in treatises on geometrical optics. Some- 

 thing of this kind has been achieved by the admirable series 

 of papers on points in physical optics which have appeared 

 from time to time, during the last fifteen years, from the pen 

 of Lord Ray lei gh, and the lucid and elementary discussion of 

 the propagation of waves through lenses, and their reflexion 

 from mirrors, published by Dr. S. P. Thompson, in Oct. 1889. 



I think further clearness in the presentment of the action 

 of lens systems in important cases would be obtained if more 

 use were made of the notion of the apparent distance of an 

 object seen through a system of lenses. This idea, which 

 is at least as old as Smith's ' Oompleat System of Opticks ' 

 (Camb. 1738), seems to have been strangely neglected until 

 attention was called to it again by Lord Rayleigh in the 

 Phil. Mag. for June 1886. Yet the formula for the apparent 

 distance of an object situated on or near the common axis of 

 a system of lenses, and viewed along that line, yields at once 

 from its mere form many most valuable theorems : for example, 

 that the interchange of position of the image and object, 

 without change of position of the lens-system, does not affect 

 the magnification ; that the magnification of an object, seen 

 through such a lens-system, is equal to the ratio of the real 

 distance of the object from the object-glass to the apparent 

 distance of the object from the eye, or the ratio of the breadth 

 of the pencil at the object-glass to the breadth of the pencil 

 at the eye. 



In this mode of discussion attention is, as in Mr. Blakesley's 

 paper, focussed on the magnification produced by the lens- 

 system. Hence the method of determining the focal length of 

 a combination by comparisons of the magnifications for (1) 

 two positions of the object at a measured distance apart, or for 

 (2) two positions of the image at a measured distance apart. 

 If I denote the distance in either case, m, n the magnifica- 

 tions, the focal length is / in (1), and in the 



° m — n m — n 



* Communicated by the Physical Society : read June 11th, 1897. 



