W. LeConte Stevens — Microscope Magnification. 61 



icist whose work in microscopical optics has been so thorough, 

 that scarcely anything in this domain can be undertaken by 

 his cotemporaries which he has not already mastered. It is to 

 be regretted that the makers of microscopes generally should 

 be so slow in following a good example. 



The determination of the lower limit of the tube length is 

 slightly complicated by the fact that a microscope objective 

 consisting of two or more systems of lenses, has no fixed point 

 through which all axial rays will cross when the position of 

 the point of radiance is varied. Its equivalent focal length 

 varies within narrow limits according to the distance of the 

 focal plane in which the image is formed. According to the 

 writer's experiments it increases slightly as this distance is 

 increased. The objective labeled R. \\ in Table II was exam- 

 ined on an optical bench, the distance, I, between the points of 

 radiance and convergence being varied from 160 mm. to 700 

 mm., an dfi calculated for 20 successive values of I. The mean 

 of the first 10 values was 32*14 mm.; that of the second 10 was 

 32-38 mm., the extremes being 32*0 mm. and 32*5 mm. This 

 objective consisted of two systems of lenses. A three-system 

 objective of nominal \ inch focal length, and an objective of 

 one system, were likewise examined, with the result shown in 

 Table IY : 



Table IV. 



Label of Objective W.3 R.1J G'± 



Number of systems 12 3 



Limits of I, in mm 202-800 160-700 130-520 



Number of measurements 12 20 14 



/ from first half, in mm 5005 32-14 5'60 



/ from second half, in mm 50-00 32-38 5'70 



From this table it is seen that the variation does not exceed 

 a tenth of a millimeter in the highest of these powers, a quan- 

 tity that is negligible in comparison with the whole tube- 

 length. Assume then that the distance from the top of the 

 microscope body to the extremity where the objective is 

 screwed in is a little shorter than the desired tube-length ; for 

 example, 160 mm., if 180 mm. is selected for tube-length. 



Then in the formula, — i — - — — ,, we have #'=180, and f is 

 p p> j- 



known, hence p is calculated. The "working distance" be- 

 tween a slide and the exposed lens can be measured ; and on 

 subtracting it from^? we have the distance, within the objec- 

 tive, of the point which for the given tube-length behaves like 

 an optical center. This point, by the given formula, is known 

 to be 20 mm. from the extremity of the microscope body, and 

 hence the desired allowance can always be made in the mount- 

 ing to put this point in its proper place. The optical tube- 



