56 VISION WITH THE COMPOUND MICROSCOPE 



objective in consequence of total reflection, yet the remainder (80) 

 which does reach it is the exact equivalent of the air-pencil of fig. 37, 

 the two air-pencils of 170 being in all respects identical. 



The immersion objective, therefore, which is able to receive the 

 whole balsam pencil of 170 (dotted lines in fig. 38), takes up ;i 

 greater quantity of light than the air pencil of fig. 37, and so not 

 merely equals the dry objective but surpasses it. 



Let it be specially noted that in dealing with the quantity of 

 light in connection with aperture, the idea has not been that we have 

 been engaged with what is in any sense essential, but to remove a 

 difficulty felt by many. It must be clear to all that if a greater 

 aperture signified nothing more than a greater quantity of light, that 

 is to say, if there were no such specific difference of the rays which 

 can be utilised by different apertures, as we have demonstrated 

 above, the whole question would be of quite subordinate interest. 



Another subject requiring some further elucidation here is the 

 ' different angular distribution of the rays in different media.' The 

 essence of the idea of 'aperture' is relative opening. However 

 defined, its significance can only be appreciated by taking into 

 account the image-forming pencil emergent from the objective, and 

 the change in its diameter consequent upon the admission of different 

 cones of light. This diameter affords a visible indication of the 

 number of rays (not mere quantity of light photometrically, which 

 can be readily varied) which are collected to a given area of the 

 image, and which must have been gathered in by the lens from the 

 conjugate area of the object. If the diameter of the emergent pencil 

 is seen to be increased, whilst the amplification of the image and the 

 focal length are unchanged, it is clear that the objective must have 

 admitted more rays from every element of the object because it has 

 collected more to every element of an equally enlarged image. Mani- 

 festly we get an accurate measure of what is admitted into an objective 

 by being able to estimate what it emits. It is physically impossible 

 that a system of lenses should emit more light than it has taken in. 



Hence * aperture ' means the greater or less capacity of objectives 

 for gather ing-in rays from luminous objects. 



When the admitted pencil is in the same medium, we see the 

 additional portions of the solid cone from the radiant, which corre- 

 spond to the additional portions of the enlarging opening. But if in 

 any other case (e.g. where the medium is different) we see that a 

 certain solid cone, A, from a radiant is transmitted through a certain 

 opening, a, and that another solid cone of rays, B, cannot be trans- 

 mitted through the same opening, a, but requires a wider one, /?, 

 whilst all other circumstances, except those of the radiant, have 

 remained the same, we can only conclude that the pencil B must 

 contain rays which are not contained in A, even if the admitted cone 

 is not increased in size. For the additional portion (ft a) of the 

 wider opening, /3 conveys rays to the image w r hich are certainly not 

 conveyed by the smaller opening a. From the radiant only can this 

 surplus come, and the pencil B which requires the additional opening 

 must embrace more rays, even if it should not be of greater angle. 



A given objective may, in fact, collect the rays from a radiant in 



