On the Estimation of Aperture. By Prof. E. Able. 411 



proportion of 3 : 2 linear, and the surface in the proportion of 9 : 4, 

 it consequently gives out from every square millimetre of the 

 object as much light as is given out in air from 2|- square 

 millimetres. Consequently the quantities of light conveyed by 

 equal solid cones in balsam and in air are in the proportion of 9 : 4. 



If equal angles at the radiants in both media indicated equal 

 quantities of light, the object under the glass ought to appear less 

 bright (in the proportion of 4 : 9) in hoth these experiments. 



(3) A third fact exhibits the exact converse of the preceding. 

 Suppose a surface, for instance a sheet of white paper, illuminated 

 by a source of light at a given distance. It will show a certain 

 illumination. Putting on now a hemisphere of glass, that part of 

 the paper which is near the centre of the hemisphere will show an 

 evidently brighter illumination. The visual angle of the source of 

 light from that place is certainly not changed ; the solid cones 

 which converge to every one point of the paper are exactly the 

 same still. If, nevertheless, more light is collected to every square 

 millimetre under the hemisphere, the soUd cones in glass must 

 convey more than equal cones in air. 



The concentration of the incident rays at the centre of a 

 hemisphere, is, of course, fully accounted for on the ordinary 

 dioptrical principles — ^just as the amplification of an object at the 

 centre is. There is nothing mysterious in these observations, but 

 the dioptrical explanation does not alter the fact, that there is an 

 unequal quantity of light corresponding to equal cones in difierent 

 media. 



VII. — Belation of the Aperture-equivalent to the general 

 " Delineating Power " of the Microscope. 



The notions of " more " and " less " in regard to the number 

 of rays admitted to different systems, and the conclusions based 

 thereon, are, it will be seen, quite independent of (and much more 

 general than) mere photometrical estimations of quantities of light, 

 which of course would relate only to a difference of brightness in 

 microscopical images. ISTor are these conclusions in any way de- 

 pendent upon the author's theory of microscopical vision, though the 

 phenomena of diffraction have been adduced above as one illustration 

 and experimental support of the general principle. This prin- 

 ciple has no essential connection either with any particular physical 

 process from which the radiation of microscopical objects may result, 

 or with the laws on which the delineation of the microscopical image 

 may depend. The question so far has not been, whence come and 

 how do those surplus rays act, which are utilized by means of a given 

 balsam-angle, in comparison with an equal air-angle, but whether 

 there is such a surplus. When this is once settled, the preponderance 

 of the former angle over the latter is settled also. For it will 



