ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 333 



composed) ? The refractive action of a plane surface affords change of 

 divergence and of position of the focus, and in the case of wide-angled 

 incident pencils introduces ample spherical aberration, but no power, 

 so that the plane-front refraction can never be an element of power in 

 a system, or compensate for loss of power anywhere else. 



Again, as to the general dioptrical principle on which is based 

 the distinction between "refraction with power," and "refraction 

 without power." Amplification does not result from the unequal 

 refraction of the rays coming from one and the same object-point ; it 

 depends solely on the unequal refraction of similar rays from different 

 object-points (by similar rays being understood those which depart 

 from different object-points in similar directions, i. e. parallel), and is 

 therefore confined essentially to curved surfaces. 



There may therefore be any large refraction of the pencils 

 emitted from an object, but nevertheless no amplification, if parallel 

 rays of any two different pencils should undergo the same refraction. 

 This is the case of the plane surface. On the other hand, there 

 may be no refraction of the pencils (the divergence of every pencil 

 and the plane of the radiant may remain unchanged), but not- 

 withstanding there may be any amount of amplification, provided 

 parallel rays from two different object-points undergo unequal re- 

 fraction. This is the case of a spherical surface in regard to an 

 object situated at the plane of the centre of the sphere. Though in 

 this case the divergence of the pencils and the plane of the focus is 

 not changed by the refraction of the rays, there is an amplification 

 of the object (as we have seen in the ratio of 1 : n), because there is 

 an unequal refraction of any two parallel rays from different points of 

 the object. 



Once more, what can the angle of the incident pencil have to do 

 with power ? If any lens or lens surface can refract a given pencil of, 

 say, 82° to a conjugate focus with any given amplification (say, two 

 diameters), the same lens, i. e. the same curvature in the same position, 

 will bring any larger pencil (140°) to the same conjugate focus with 

 the same amplification. No increase in the 

 power of the spherical surface is required, but ^^' 



only greater diameter of the lens to admit the 

 larger cone. 



The front surface of a dry objective has, of 

 course, the effect of reducing an incident pencil 

 in air of 180° to a pencil of 82° in glass, but 

 without contributing to the power of the ob- \-''„ 



jective. As is shown by Fig. 74, the same pencil ^° 



which in air is emitted under an angle of 170° is emitted in oil under 

 an angle of 80°, and thus does not require the reducing effect of 

 a plane refracting surface, and therefore no compensation is necessary 

 for the absence of such a refraction. The rays are in such case 

 identical before they reach the spherical surface, which cannot there- 

 fore require any alteration. 



(4) The Diagram Fallacy {The Stolces Immersion and the ShadboU 

 Dry Objectives). — The diagrams drawn by Mr. Shadbolt in support 

 Ser. 2.— Vol. I. 2 A 



