30 CORRESPONDENCE, 



may be justified by its couvenieuce, as enabling a single trade-name to 

 be given to the combination. Scientific accuracy would seem to demand 

 that the maker should at least state the limits for each combination, 

 but I know of no maker anywhere who has as yet adopted this plan. 



Different modes of computing the focal lengths of objectives from 

 theii" magnifying power under given conditions have been proposed. 

 I have been in the habit of using a very simple rule, viz. : — The 

 equivalent focal length of the objective in fractions of an English 

 inch is of course equal to the distance from the optical centre of the 

 objective to the screen, divided by the magnifying power. Since the 

 optical centre cannot be determined with precision in compound 

 objectives, we may substitute, without material inaccuracy, the dis- 

 tance from the micrometer to the screen, provided this be made so 

 great that the unmeasured quantity represents a very small fraction 

 of it. For all objectives from the -^-th upwards, therefore, if the 

 distance from micrometer to screen be considerable (say such a dis- 

 tance as I have taken above), the magnifying power at that distance 

 divided into the distance will give the focal length with reasonable 

 precision. 



For longer focal lengths, or in any case those who demand 

 the nearest approach to accui-acy may use Mr. Cross's formula,* 



/ = — **~^„ where n is the reciprocal of the magnifying power, 



(^ + 1) . ^ . 



and I the sum of the conjugate foci or the distance from micrometer 



to screen. Taking then the magnifying power at dry uncovered as 



the basis of the calculation, the above lenses of Powell and Lealand 



may be characterized as follows in decimals of an English inch. 



Name of Objective. 



Powell and Lealand's ^Lth . . 



J^th .. .. 

 J^th (No. 1) 

 Ti,th (No. 2) 

 ith (No. 1) 

 ith (No. 2) 



It will be perceived that all the above objectives therefore 

 closely approximate, when worked dry uncovered, to what their 

 nomenclatiu-e would demand, the ^ths deviating most from the stan- 

 dard, and being in fact, more nearly |,ths than |ths. It must also be 

 borne in mind that with the most sincere endeavours on the part of 

 the maker, it is not easy to give precisely the same magnifying 

 power to any two objectives, and if any commercial titles are adopted 

 a certain amount of deviation from the standard indicated must be 

 expected. 



With regard to the QUALITY of the performance of the above 



* ' On the Focal Length of Microscopic Objectives.' By C. R. Cross. Boston, 

 1870. 



