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plane, a series of bright points would result from the accumulation 

 of the light falling on each lens. If the plane of vision be next made 

 to coincide with the surfaces of the lenses, these points would ap- 

 pear dark, in consequence of the rays being refracted towards points 

 now out of focus. Lastly, if the plane of vision be made to coincide 

 with the plane beneath the lenses that contains their several foci, so 

 that each lens may be, as it were, combined with the object-glass, 

 then a second series of bright points will result from the accumula- 

 tion of the rays transmitted at those points. Moreover, as all rays 

 capable of entering the object-glass are concerned in the formation 

 of the second series of bright focal points, whereas the first series 

 are formed by the rays of a conical shell of light only, it is evident 

 that the circle of least confusion must be much less, and therefore 

 the bright points better defined, in the first than in the last series. 



If the supposed lenses were of small convexity, it is evident that 

 the course of the more oblique rays only would be sensibly in- 

 fluenced ; hence probably the structure of P. angulatum is recognized 

 only by object-glasses of large angular apertures, which are capable 

 of admitting very oblique rays. 



The writer has recently, in an address to the members of the 

 Royal Institution, proposed to explain the extreme darkness of the 

 dots, under certain conditions of focus and illumination, by the hy- 

 pothesis that some of the oblique rays are thrown out of the field by 

 internal reflexion, being incident at the upper surface at an angle 

 too large for emergence ; but this does not appear to invalidate the 

 present hypothesis respecting the course of the transmitted rays. 



It does not appear to be desirable that objects should be illumi- 

 nated by an entire, or, as it may be termed, a solid cone of light of 

 much larger angle than that of the object-glass. The extinction of an 

 object by excess of illumination may be well illustrated by viewing 

 with a one-inch object-glass the Isthmia illuminated by Gillett's 

 condenser. When this is in focus, and its full aperture open, the 

 markings above described are wholly invisible ; but as the aperture 

 is successively diminished by the revolving diaphragm, the object be- 

 comes more and more distinct, and is perfectly defined when the 

 aperture of the illuminating pencil is reduced to about 20. The 

 same point may be attained, although with much sacrifice of defini- 

 tion, by gradually depressing the condenser, so that the rays may 



