The Helmholtz Theory of the Microscope. By J. W. Gordon. 391 



mirrors so disposed that a mirror receives and throws back through 

 the aperture the light transmitted by the aperture from every one 

 of the lamps. Then the mirror-board will be the perfect and 

 radiant image of the lamp-board. 



It is plain that the amount of light received by each mirror 

 will be conditioned by two things : (1) the brightness of its lamp ; 

 and (2) the size of the aperture. 



Assume that all the lamps burn with the same brightness, and 

 let this factor be denoted by J. Then J X area of the aperture 

 will give us the measure that we want of the light radiated in 

 unit time by any one lamp to its mirror, and back by the mirror 

 to its lamp. 



If now the refractive system yields a perfectly correct image in 

 the mirror board rj of the lamp-board e, every lamp must send this 

 same quantity of light * to its mirror, and every mirror must stand 

 at a distance on the mirror-board from the central mirror, pro- 

 portionate to the distance of its conjugate lamp from the central 

 lamp. Thus, the lamps being by hypothesis equidistant from one 

 another, the mirrors must be equidistant also, and the common 

 distance of the mirrors from one another will have the same 

 proportion to the common distance of the lamps apart that the 

 diameter of the mirror-board has to the diameter of the lamp-board. 

 It will simplify description if we assume that the lamp-board is 

 entirely filled with lamps that fit close to one another like cells in 

 a honeycomb, and that the mirror-board is similarly filled with 

 mirrors receiving and reflecting each the light of a single lamp. 

 Then we shall know the relative dimensions of the object e and of 

 its image 77 if we can ascertain the relative sizes of one of the lamps 

 and one of the mirrors. 



The determination of this proportion will become very simple 

 if we replace the mirror by a lamp which shall be exactly 

 equivalent to it in the power of radiating light through the 

 aperture, for then we shall have a source of light that can be 

 directly compared with the original source of light on the lamp- 

 board. Let it be assumed, then, that the central mirror on the 

 mirror-board is replaced by a lamp so selected, that, seen from the 

 aperture, the lamp shall be indistinguishable from the mirror. It 

 must then burn at the same temperature as the other lamps 

 reflected in the neighbouring mirrors, Qr it would be distinguishable 

 from them by superior — or as the case might be by inferior — 

 brightness. It must be of the same size as the apparent size of 

 the reflected lamps or it would not fit into its own place. But 



* Strictly speaking this is, of course, an impossible condition because the 

 angular value of the aperture falls off as the radiant point departs from the axis. 

 All actual apertures are, therefore, to some extent astigmatic, but in small fields — 

 such as those of the Microscope — this is of no practical importance, and we may 

 fairly assume the theoretical condition to be satisfied. 



