402 Transactions of the Society. 



The preceding figure (89) shows diagrammatically the course of 

 two beams — one axial and the other oblique — through a compound 

 Microscope. Both, after focussing in the image plane, spread out 

 in divergent beams and fall upon the eye-lens by which they are 

 brought into the condition of parallel beams of light fit to convey 

 to the eye a picture of the object on the stage. In the plane 

 behind the eye-lens which coincides with its principal focal plane, 

 these beams of parallel light from the instrumental image blend 

 with one another, and all such beams from all points of the image 

 plane here pass through the optical projection of the axial beam. 

 They thus form a very brightly illuminated field which is, in fact, 

 a focussed image of the principal plane of the objective, and can 

 be seen as an external object by drawing the head back to a suitable 

 distance behind the instrument and looking along its optical axis. 

 In like manner it can be seen by a magnifying lens and measured 

 by a micrometer, or a dynamometer, as the astronomers call a 

 micrometer adapted to this purpose.* 



Now, Helmholtz' solution of the problem of diffraction in the 

 Microscope is this. Treat the Eamsden circle as if it were a hole 

 in a card or diaphragm and the image in the focal plane of the 

 instrument as if it were an object of the same size as the image 

 situated in the focal plane of the instrument. Then the loss of 

 resolution due to diffraction will be exactly the same as if that 

 supposed object were actually viewed through that supposed 

 aperture. You will, I imagine, agree that this is a most charm- 

 ingly simple solution of a most formidable problem and that the 

 proof of it must be worth following up even at some cost of mental 

 labour. But in truth the mental labour involved is not serious, 

 so elegant is the proof, and when I took the liberty in the opening 

 part of this paper of summarising the theory of diffraction, I dealt 

 with what is by far the most difficult part of the whole inquiry. 



The Proof of Helmholtz' Proposition. 



Coming now to the proof of this proposition. It is at once 

 obvious that diffraction to this extent at least must be a disturbing 

 influence in the final image which is pictured upon the retina. 

 For these beams of light must give off diffracted beams and the 

 diffracted light so given off must enter the eye and be focussed by 

 it in the same way as the principal beams themselves. To this 

 extent, therefore, the proposition must be true and the object seen 

 must be at least as badly resolved as if it were viewed through a 

 narrow aperture having the diameter of the Eamsden circle. The 



* On this point eee Mr. Nelson's paper in the Journal Royal Microscopical 

 Society vol. for 1901, p. 212. 



