138 Mr. T. H. Blakesley on a 



points is this length to be measured. So the focal length of 

 a lens-combination is simply an abstract length, and not 

 necessarily the distance between two particular points. 



But the Royal Society method of finding the focal length 

 of a lens-system, as carried out at the Kew establishment, is 

 based on the definition that the focal length is the distance 

 between a focal centre and the principal focus ; and these points 

 having been separately found by processes not free from 

 objection, the distance between them is indirectly measured 

 [vide Major Darwin's paper, ' Proceedings of the Royal 

 Society/ 1892). 



Various methods have been described in an admirably 

 arranged bibliographical review of the subject by Prof. S. P. 

 Thompson. In this paper the author also describes a method 

 of his own with an apparatus for carrying it out, but that 

 method depends on the same idea that the focal length is a 

 distance between two points. The apparatus fixes those points 

 and measures the distance between them. And the same may 

 be said of all but one of the methods proposed by others, 

 described in that paper. 



I have to propose and explain a far more general definition 

 of the focal length of any system of Coaxial Lenses, which 

 leads naturally to more general methods of determining that 

 length than any of those alluded to. 



Now any function of the two distances of object and image 

 from their appropriate focal centres and the focal length may 

 be employed in conjunction with the usual formula to eliminate 

 either of those distances ; and if that function is at the same 

 time an easy one to determine experimentally, and if the 

 elimination leads to a simple formula for working purposes, a 

 considerable gain in convenience and exactitude may be the 

 result. Such a function is found in the magnification, which 

 I define as the linear relation of Image to Object and which I 

 symbolize under the letter m, and take as positive if the image 

 is erect and is not inverted with regard to the object. Thus 

 in the case of the object and image being at equal distances 

 from, and on opposite sides of a thin double-convex lens of 

 equal radii of curvature, I should describe the magnification 

 as —1. In this notation the negative sign will indicate 

 reversal, the numeral the arithmetic magnification. 



Let A be the position of one of a pair of conjugate foci on 

 the axis of some coaxial lens-system, and let v be its distance 

 from any fixed point on the axis measured positively in the 



