ZOOLOGY AND BOTANY, MICROSCOPY, ETC, 



337 



Thus withdrawing the radiant from the vertex of the sphere 

 is increase of amplification by the spherical surface, and approaching 

 the radiant is loss of amplification —propositions the truth of which 

 may be very readily tested by an ordinary plano-convex lens. 



Now in the Shadbolt front the radiant has been brought nearer to the 

 vertex ! and there is therefore loss of amplification (cf. Figs. 75 and 76). 



This approximation is moreover a necessity, for Mr. Shadbolt so far 

 rightly saw that his emergent pencil of 66° could not be so much 

 increased within the glass as it is in the Stokes front. In the latter 

 (considering the pencil from above downwards) the 66° can be increased 

 to 113° as there is no plane surface of exit bounded by air. In the 

 dry objective, however, there is such a surface, and nothing beyond 

 82° can emerge, so that instead of being able to increase the pencil 

 from 66° to 113° it can only be increased to 82°, that is, the refraction 

 at the spherical surface must be diminished in order to have within 

 the glass a pencil not exceeding 82°. 



The notion that the refraction which is introduced by the lens at 

 the plane front surface can compensate for this loss at the spherical, is 

 one of the strangest of the aperture fallacies, as has been shown in the 

 preceding note. 



In this simple mode the fundamental mistake of Mr. Shadbolt' s 

 diagram is shown. 



(5) Fallacies in Practical Construction. — It need hardly be 

 pointed out that the better practical optician will, ccBteris paribus, be 

 he who is the best grounded in those theoretical principles which lie 

 at the root of the construction of objectives. The mistakes into which 

 the practical optician who is an angular aperturist is led, may be 

 shown by several instances: 



(1) We will take first the case of the construction of objectives of 

 high angles. An optician holding the views we have referred to, will 

 have observed that when he increased the angular aperture of his ob- 

 jective from 100° to 120° he obtained a substantially increased effect. 

 He is therefore encouraged to improve the construction and add yet 

 another 20°, making 140°, or a third 20°, making 160°, and yet 

 more until he arrives at the nearest approximation to 180°, all the 

 time supposing that with each additional 20° he had obtained the 

 same increase of effect as at first. 



The knowledge that aperture must be measured by the sines and 

 not by the degrees would, however, have shown him that the increasing 

 effect was not properly indicated by the figures 100, 120, 140, 160, 

 and 180, but by 77, 87, 94, 99, and 100 ; so that the real increase is not 

 by additions of 20, but of 10, 7, 5, and 1 only. He would see, there- 

 fore, that the difference between 140° and 180° was so slight — being 

 only 6 per cent. — as not to make it worth his while to encounter the 

 difficulties of technical construction attendant upon the extreme in- 

 crease of angle. 



(2) If the practical optician considers that aperture and angle are 

 identical, the same angle being always the same aperture whether in 

 a dry or an immersion objective, he will continue to struggle for the 

 optical perpetuum 7nobile — to construct dry systems which shall eqixaX 



