The Helmholtz Theory of the Microscope. By J. W. Gordon. 387 



maximum value. However much the surface be extended it can- 

 not radiate along the axis a . . a any greater quantity of light 

 than passes through the small aperture A . . A. 



It is evident that this maximum aperture — or rather maximum 

 aperture value — stands in some definite relation to the length of 

 a wave of light, and without elaborating the mathematics of it in 

 this place it will be interesting to note down one or two instances 

 of the maximum amount of visible radiation which can be dif- 

 fracted off at one or two selected angles from a beam of parallel 

 light. We will assume green light from the most luminous part 

 of the spectrum having the wave-length X = yo^ooo m - Then 

 the utmost amount of light that can be so diffracted off from such 

 a beam — whatever its aperture — at 45° would pass through a chink 

 rather less than yooVoo ^ n - ^ n diameter and in length equal to the 

 breadth of the aperture, and even the light so passing would not be 

 uniphasal. The quantity of light which an aperture of this breadth, 

 and of any ordinary dimensions as to length, can transmit, must 

 be quite inconsiderable, and for ordinary purposes not distinguish- 

 able from zero or absolute darkness. 



Of course an angle of 45° is a large angle : suppose we take 

 a small one, say an angle of 1° equal to (say) a rise of a foot in 

 20 yards. The maximum aperture value of light diffracted 

 along this axis calculated in the same way will be a little less 

 than yoooo ^ n - Again, for ordinary purposes we may treat the 

 light that can pass through a chink less than ^sW ^ n - ^ n breadth 

 as being the equivalent of darkness or full shadow, and we thus 

 see incidentally how it is that the undulatory theory of Light 

 explains the propagation of shadows along what are visibly 

 straight lines. But we also see what is even more important for 

 our present purpose, namely, how the amount of light diffracted 

 along any given axis can be increased and rendered visible. To 

 this point we may now proceed. 



Suppose that our aperture is a square aperture having a dia- 

 meter of £ in., and that it transmits a beam of parallel light. 

 We know now that the aperture value of that beam of light along 

 an axis inclined only 1° to its own axis will be less than half of 

 ijyQQ in. Therefore, leaving out of account a small correction and 

 treating the aperture as equal to its own projection on the poly- 

 phase front which is inclined to it, at this small angle of 1°, we 

 may say that this £-in. aperture contains upwards of 500 zones 

 each of which is capable of radiating as much light as the full 

 aperture itself in this direction. Suppose then that we divide up 

 its face into 500 facets each 20W ^ n * ^ n breadth. Suppose further- 

 more that we block up alternate facets, say the facets which 

 contain what at a given instant might be identified as the 

 negative half series of phases. Then the facets that are left will 

 shine without hindrance along our 1° axis, and if we bring their 



