400 Transactions of the Society. 



as is obvious from the diagram. It throws into the eye the same 

 quantity of light only as eye-piece No. 2, and as it produces a 

 larger image, the brightness of that image must suffer in proportion. 

 We now see that N.M.P. represents a definite limit in the 

 capabilities of an objective. For magnifications less than M the 

 lens gives images of full brightness. But beyond this point the 

 brightness of the magnified image begins to fall off. The total 

 light is still the same in amount, but the light collected on a 

 given point of the super-amplified image is only a fraction of 

 that which comes from its object-point. And the fraction rapidly 

 comes to be a very small one. The diagram shows that it is pro- 

 portioned as area of pupil to area of emergent beam, that is to say, 



/MA 2 

 as ( tTT ) if M g be written for the degree of magnification of the 



super-amplified image. In this sense, therefore, N.M.P. is the 

 point at which the image begins to deteriorate. 



JEntojrtie and Ocular Shadows. 



The next point is again a matter of practical importance con- 

 nected with this diminution in diameter of the beam received by 

 the eye which accompanies high magnifying power. Helmholtz 

 points out that when these beams become very narrow, we have 

 precisely the conditions which cause shadows of objects within the 

 eye to be thrown with sharp definition upon the retina and so to 

 blend with and impair the visible image. This is explained by 

 Helmholtz in a passage which I will take the liberty of quoting 

 textually. After describing the Eamsden circle of the Microscope, 

 (see fig. 89 below), he says : — 



" Here, however, we meet with other difficulties arising from 

 the very small divergence angle of the emergent beam, as is shown 

 in the case of great amplification by equation (12).* 



" First there are the shadows in the eye, of entoptic objects 

 which crowd more and more into the field of view in proportion as 

 the above-mentioned ocular image of the objective becomes smaller. 

 This image is the source of illumination to the retina ; all the light 

 which enters the eye comes from it. It is at the same time the 

 base of the complete beam containing all the pencils of light which 

 connect the several points of the object with their retinal images, 

 and its diameter diminishes as is above shown, for high magnifica- 

 tions, in proportion as the magnification increases. But the known 

 condition which must be fulfilled in order to produce strong sharp 

 shadows of entoptic objects is precisely this, that the intromitted 

 light should reach the eye from a very small surface. Anyone 



* Equation (4) alove. 



