ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 343 



is supposed to be divided into, say, three equal parts around the 

 perpendicular, the loss of light by reflection in the second third, 

 where the rays are more oblique than in the central one, is assumed to 

 be much greater than in the latter, and the loss in the outer third, where 

 the rays are yet more oblique, as much greater still ; so that a total 

 average loss is made out to exist of not far short of 50 per cent. 



The consideration is so far sound in that it proceeds on the assump- 

 tion that the loss of light by reflection increases with the increasing 

 obliquity of the rays. The mistake, however, is in supposing that 

 Fig. 81 is a correct representation of the pencils instead of Fig. 82. 

 In the calculation of the 50 per cent., therefore, the fact was over- 

 looked that while wiLh increasing obliquity there is greater loss by 

 reflection, yet there is at the same time less light to lose. 



There is of course loss of light with a dry front, which is nearly 

 all avoided in the case of the immersion, and is so far a practical 

 benefit. This benefit, however, is very subordinate in comparison with 

 the great increase of light which is due to the greater photometrical 

 equivalent of equal cones in denser media, an immersion objective of 

 120° balsam-angle being capable of admitting more light in the ratio 

 of 9 : 4 than a dry lens of equal air-angle. 



(2) Increase of Radiation in Glass, Oil, &c. — The angular- 

 aperture theory, as we have already seen, is sometimes rested (though 

 improperly) entirely upon the question of quantity of light, and 

 involving the assumption that equal angles in air and balsam contain 

 the same amount, so that a smaller angle in balsam must contain less 

 than a larger air-angle. The notion that a balsam-angle of 100° can 

 contain more light than an air-angle of 180°, a given fixed illumina- 

 tion being supposed, is regarded as an absurdity. 



The fact of an increase in radiation with the increase in the 

 refractive index of the medium into which the emission takes place 

 has been established for many years, the case of immersion objectives 

 being hitherto the main (if not the first) practical application of it. 

 The principle may be proved theoretically and experimentally. 



Those who are interested in the tlieoretical consideration will find it 

 fully developed by Professor E. Clausius in his celebrated paper 

 " On the Concentration of Calorific and Luminous Eays." * Later, 

 a similar principle was shown by Professor Helmholtz (in his paper 

 " On the Limits of the Power of the Microscope ") to be a direct 

 deduction from that of conservation of energy. The former paper 

 was an outcome of researches which were induced by previous 

 researches of Sir W. Thomson and Professor Eankine. 



For the experimental consideration, the apparatus which we 

 exhibited at the March meeting, and for which we are indebted to 

 Professor Abbe, will be found useful for showing the different 

 photometrical equivalent of equal angles in different media. 



The apparatus (see Figs. 83, 84, 85) consists of a very thin plate 



of polished porcelain A, which (for support) is cemented with balsam 



to a disk of ordinary glass a. A block of crown glass G is also 



cemented with balsam to the polished surface of the plate A. A 



* Poggendorfif's Annalen, cxxi. (1864). 



