426 Transactions of the Society. 



understood by reference to the annexed diagram (fig. 119). Here the 

 optical system of the Microscope is represented by its Gauss planes. 

 Now let us suppose that for the due delineation of a particular 

 feature in the object it is necessary to throw the light-source 

 slightly out of focus with the object. Then, the image of the 

 light-source, being focused, say at Px - 2 ] in. short of the object, 

 another image, conjugate to this, will be formed at the point 

 marked P 2 in the diagram, which lies at about -^fa in.* behind 

 the eye-point E of the instrument, it being assumed that the 

 Microscope as a whole has a magnifying power of 1000. It will, 

 of course, follow that this image of the source of light will be 

 interposed between the eye-lens of the Microscope and the retina 

 •of the observer ; and therefore, upon the principle first explained 

 by Helmholtz, the effect upon the image, so far as diffraction is 

 concerned, will be the same as if a diaphragm were interposed at 

 that point in front of the observer's eye, having an aperture of the 

 same form and dimensions as the image of the flame. Those 



Fig. 119. 



dimensions are easily calculable. But as it is only the breadth 

 which now concerns us, it will suffice to obtain a notion of the 

 breadth of this post-ocular image of the lamp-flame. Assuming 

 the original lamp-flame to have a breadth of j 1 ^ in., its image at 

 P x would, with a £-in. condenser, have a breadth of about one- 

 thirtieth of that quantity, amounting, say, to ^^ in. The second 

 image, formed at P 2 , may be supposed to have a breadth of about 

 one-quarter of this amount, so that the image of the lamp-flame 

 formed over the eye-lens of the instrument would have a dia- 

 meter of about 50V0 ^ n - It ^ s we ^ known that the diffraction 

 produced by an aperture of such dimensions is very serious, and 

 in fact it is found quite impossible to obtain a well-resolved 

 image of fine detail under these conditions. Experience has shown 

 that what is known as " critical illumination " is necessary , that is 

 to say, the edge of the flame must be accurately focused in the 

 plane of the object, so that its image may everywhere coincide with 

 the image of the object and there may be no diffracting aperture 

 interposed between the eye-lens and the observer's retina. Hence 

 it is in practice found impossible to use a lamp-flame for critical 



* This, perhaps, is stated too rigorously, the position and dimensions of the 

 image being variable within comparatively wide limits in different optical systems. 

 But as the case actually put is one that might very well occur in practice, it may 

 serve the purpose of illustration. 



