THE 



LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE 



l\&*Ar 



*-,. ^ 



[FIFTH SERIES.] 



/&V.T OFf \C^ 



AUGUST 1897. 



XX. A new Definition of Focal Length, and an Instrument 

 for determining it. By T. H. Blakesley, M.A.* 



I HAVE been frequently struck with the very imperfect 

 way in which the facts of focussing with lenses and lens- 

 combinations are treated in works which purport to deal with 

 such matters in a practical way. In many cases such works 

 are by authors who in other respects give information and 

 rules which are unimpeachable and the result of painstaking 

 study, so that the defect in the particular to which I have 

 alluded must be due either to the inherent inconvenience in 

 the usual formulpe, so invariably and unnecessarily involving 

 the inverse of distances of Object and Image from theoretically 

 fixed but practically undetermined points, andthe Focal Length; 

 or to the imperfect way of quoting the rules in the theoretical 

 text-books. If the latter be even partially the cause, and can 

 be remedied, it will be quite unnecessary to inquire if the 

 former is also operative. In addition to the troublesome 

 formula of inverse distances, a difficulty is unnecessarily 

 introduced by defining the focal length as the distance between 

 two points, generally the principal focus and a focal point, or 

 the lens itself if thin, instead of being an abstract length of 

 straight line characteristic of the lens or lens -combination. 



To illustrate my meaning, I may point out that the Coeffi- 

 cient of Self-induction of a coiled conductor is expressed as a 

 length which is fixed so long as the coil remains unaltered in 

 geometrical conditions ; but no one would ask between which 



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

 Phil. Mag. S. 5. Vol. 44. No. 267. August 1897. L 



