Universal Apertometir. 195 



only the front lens, which was ven- far from a hemisphere. 

 I need not say that he immediatel)' saw that something was 

 wrong, and candidly confessed that such a method of deter- 

 mining angular aperture was unreliable. This experiment, 

 the credit of which is due to Mr. Wenham, strikes a fatal 

 blow at the nomenclature derived from the old method of 

 measuring angular aperture. I then took an excellent " pro- 

 fessional " i-8th of Spencer, and closing the systems, put a 

 small dot of ink on the flat surface of the front lens, just large 

 enough to cut off the little circle of light that appears when 

 one looks into an objective with the front system toward the 

 eye: the dot was barely one-third the diameter of the exposed 

 flat surface of the lens : indeed, it looked ridiculously small . 

 The objective was now attached to the tube of the microscope. 

 Xot a ray of light, except what came through the ink, could 

 be obtained, neither axially or b)' oblique illumination. 

 It was next put on the sector, as in measuring the angle the 

 old way, and as soon as the arm was swung around suffi- 

 ciently, lo, the light gleamed brightly, and continued visible 

 until the sector arm read 179' I All this was from light out- 

 side the boundan,- of the little ink dot, within the area of 

 which was comprehended all that was available of the 

 objective front for work. As an immersion (and truly 

 measured, as I shall presently show, both on my own plan 

 and that of Dr. Abbe) this objective gave me 87' as the 

 angular aperture, or balsam (glass) angle, and as this is 5" 

 more than twice the critical angle, the maker might have 

 concluded, as many have done, that the equivalent air angle 

 of this objective was 180 -f. or in other words, that there 

 would be nothing absurd in marking the objective 180 . 

 Xow the true air angle, at the same closed point, as I shall 

 presently show, the angle of a triangle whose apex is the focal 

 point, and whose base is the diameter of the spot of ink 

 which just stopped all the light, is only 144'. This objective, 

 made some time ago, was actually marked, in good faith, 170", 

 which was far within what it would measure the old way at 

 the same closed point; but the angle 170^. if we compute from 

 it a balsam angle, gives one much less than the objective 

 would pass, and j^et for air angle, it is 26^ too much. It is 

 evident that the old system of marking is all wrong, telling a 

 false storv in either case, drv or immersion. 



