62 



THE AMERICAN MONTHLY 



[April, 



is usual to direct that the objective 

 shall be focussed upon an object at 

 the centre of the disk or traverse 

 lens, so that the sides of the angle, 

 including the telescopic field, may be 

 radii from the optical centre of the 

 apparatus. The chief purpose of this 

 article is to show some reasons, based 

 upon experiment and upon the com- 

 mon principles of geometric optics, 

 for thinking that the telescopic aper- 

 ture, however correctly measured, is 

 not the microscopic aperture. In 

 other words, the telescope and the 

 microscope, though having most of 

 the lenses in common, are not the 

 same instrument, and have not the 

 same angle of aperture. 



In objectives of high power and of 

 very short working-distance, the dif- 

 ference referred to is so small that it 

 may be practically neglected ; but 

 with low powers it is large enough to 

 detract from the usefulness of the 

 common methods of measurement, 

 and if the graduated glass disc or 

 traverse lens is used with a terres- 

 trial eye-piece, in the manner above 

 referred to, even absurd results may 

 be reached. 



In the discussion of the methods of 

 measuring the angle of aperture, atten- 

 tion was naturally fixed upon glasses 

 of high power and wide angle, because 

 the controversy centered about the 

 possibility of increasing the aperture 

 beyond the maximum in air. From 

 time to time, however, complaints 

 were made by one and another that 

 the measurement of low-power glasses 

 was unsatisfactory, and that different 

 apertometers gave very different re- 

 sults. All sorts of reasons were given 

 for accepting the new and rejecting 

 the old methods. The use of slits 

 and stops to shut off extra rays, sup- 

 posed not to be " image-making," the 

 determination of the "available front" 

 of the objective, the necessity for a 

 stop or diaphragm behind an object- 

 ive used in the draw-tube to make a 

 terrestrial eye-piece — these and other 

 problems have been examined and 

 discussed; but the examination of the 



microscopic field itself, and the con- 

 ditions of use of the microscope when 

 used as such, seem to have been neg- 

 lected. 



The natural reason for such neg- 

 lect is found in the fact that the mea- 

 surement of the telescopic field is easy 

 for all lenses, whilst only the lowest 

 powers can be conveniently examin- 

 ed in an analogous way, for the pur- 

 pose of determining the relation of 

 microscopic field to angle. The re- 

 sults I shall here state are the out- 

 come of a determination to see what 

 these low-power lenses can tell us upon 

 this subject. It appears, as is usual 

 in such cases, that actual experiment 

 drew attention to some very simple 

 applications of familiar principles, 

 which seemed to have been over- 

 looked in the discussion. 



Among these, as preliminary, I will 

 state two. The first is the principle 

 applying to conjugate foci, and no 

 better form can be given it than that 

 which Professor Abbe has used in his 

 article on the apertometer. " Let L 

 " be any system of lenses which takes 

 "in and transmits rays from different 

 " objects, and O, O', two limited areas 

 " in planes perpendicular to the axis, 

 " situated at conjugate points of the 

 " axis and conjugate one to another 

 "as to their linear extension, then 

 " all the rays entering the system Z 

 "through the area O will leave the 

 "system through the area O'; and 

 " no single ray can emerge from Z 

 " through the area O' which has 

 " not entered Z through the area O' 

 "from whatever object the rays con- 

 "sidered may start or toward what- 

 "ever points they may proceed."* 

 The second is enunciated in most of 

 the elementary treatises on optics, 

 and is the simple proposition that in 

 order to form an image behind a lens, 

 a luminous object of appreciable size 

 is not placed in the principal focus 

 of the lens, but some distance further 

 from its front. 



* Journal Royal Micros. Soc, l88o, Part 

 I, p. 20. 



