330 



SUMMARY OF CURRENT RESEARCHES RELATING TO 



fore not reaching the object, there must be less illumination, unless 

 the lens could be enlarged to a complete hemisphere. 



This consideration, however, overlooks the fact that a hemisphere 

 l^roduces concentration (or condensation) of the light at its centre 

 (which does not of course exist in the case of Fig. 69). Though rays 

 which are directed to the centre are not refracted, the fact is, never- 

 theless, that the same rays which from any point (or small element) of 

 the heavens reach a circle of definite diameter 8 of the object in 

 Fig. 69, are, by the action of the sphere, collected on a circle of 



smaller diameter - in Fig. 70 (n being the refractive index of the 

 n 



lens), and consequently the original circle 8 under the sphere 



receives from every point of the heavens, between c and d, n^ times 



more light than an equal circle of the object on the plane slide. 



This may be proved by a similar dioptrical demonstration to that 



given above. 



It is thus seen that the object, in the case of Fig. 70, may obtain 



the same light from a portion of the heavens as in Fig. 69 is obtained 



from the whole. If the angle between c and cl should be 82°, the 



illumination of the object would be the same exactly. If that angle 



should be nearly 180° (in the case of a very large hemisphere and 



a very thin slide), the illumination in Fig. 70 would be n"^ times 



greater than in Fig. 69. 



(2) Illumination Fallacies. — We have called these " illumination 

 fallacies " for want of a better term, although that does not quite 

 express their true character. We give the substance, however, as it 

 has been put to us on many occasions with slight variations. 



Assume the full apertures of a dry and an immersion objective 

 to be illuminated from beneath the slide, so that we have a pencil 

 above the slide of 170° in air in the first case, and 140° in oil in the 

 second, the source of light remaining unaltered. Figs. 71 and 72 

 will then show the illumination which would be required to fill the 

 apertures of the dry and immersion objectives respectively. 



(a) When the angular aperturist recognizes that there is more 

 light in Fig. 72, he then says that the conditions of the dry and 

 immersion objectives are not the same, that the immersion objective 



Fig. 71. 



A/ff I70° 



SLIDE 



SLIDE 



I^O° 



has been " allowed to get more light " than the dry objective. If 

 it is only allowed to have a pencil of 80°, like the dry objective, its 

 aperture will be found to be not greater but only equal. 



