Measurement of Immersed Apertures. 11 



air, water, and balsam apertures were measnred, and the relative 

 loss due to tlieir refractive powers ascertained. Had I played with 

 extra thick covers instead of those used for the slides of diatom- 

 aceous objects usually sold, then I might have laid myself open to a 

 suspicion of trickery on either side. I trust that this now concludes 

 the main point of the controversy, which rests, not upon little 

 questions of manipulation, but upon one of optical law and theory 

 with which Col. Woodward's measurements agree. 



The next consideration is that in which an object-glass does 

 apparently give a greater angle than I had assigned as the limit. 

 Here, again, I consider that I am fortunate in Col. Woodward's hands ; 

 had the measurements merely been certified by credible witnesses, 

 without any knowledge or description of construction, I should 

 perhaps have doubted them as much as they could have misunder- 

 stood myself — a most unsatisfactory end to any discussion. I have 

 therefore to thank Col. Woodward for the following precautionary 

 explanation. " Now in the first place I must remark that the ob- 

 jective was certainly an exceptional one, and apparently put together 

 with a view to this controversy. Instead of three combinations I 

 found it to be constructed with four ; the posterior two resembled 

 those of other fifths of Mr. Tolles, and were together moved by the 

 screw collar, the anterior two remaining stationary." Near twenty 

 years ago I explained the loss of aperture consequent upon fluid 

 mounting ; till recently this has not been controverted. I showed 

 the reduced aperture the following way : — A thick piece of polished 

 plate glass had one surface smeared with beeswax. Various object- 

 glasses, set to proper air-apertures, were focussed on to the clean 

 surface. A light was then set behind, and the diameter of the 

 well-defined circular disk on the wax marked with a needle-point. 

 The cone, from front to back, taken in the proportion of the known 

 thickness of the plate by a protractor, gave the loss or aperture 

 from air to glass, and by inference, on balsam-mounted objects. 



Now arose the question of a means of obtaining the full aperture 

 on objects in balsam or fluid. It at once appeared that if the 

 object was set in the centre of a sphere (or hemisphere) that all 

 rays from the central point must continue their course without 

 deviation, and that in such a case neither the length of radius of 

 the glass hemisphere, or the refractive power of the material, would 

 influence the results. I therefore made a number of minute plano- 

 convex lenses of various radii ; some less than the y^oth part of an 

 inch. Such of these as turned out to be hemispheres were set 

 exactly over a single selected diatom and balsam let in. Before the 

 balsam was admitted for a well-known optical law, the object could 

 not be seen. When a ^th or other object-glass was brought over 

 this lens, the arrangement might be termed a four-system one, 

 though the optical efiect of the hemisphere as a lens was nil, 



