ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 335 



fication which is obtained with them, beginning with the amplification 

 of both fronts. 



According to the law of aplanatic convergence referred to at 

 page 321, if O and O* are any two conjugate aplanatic foci (it matters 

 not whether O* is a real or a virtual focus), u and u* the semi- 

 angles of divergence of the pencils from these foci, N the linear 

 amplification of the image at 0*, and n and n* the refractive indices 

 of the medium in front and at the back of the system ; then 



n sin u 



-^^-. — X = N. 



Applying this formula to the two front lenses, »i* is = 1 for both 

 (there being air at the back), but n is = 1"525 for the Stokes front, 

 and = 1 for the Shadbolt front. Therefore, the linear amplification 

 of the former (for the conjugate foci Q, q) is 



1-525 X sin 56° 10' (z^) 

 ^ - 1 X sin 33° 0' {a*) ' ^^ ^^^^ - ^ ^3 . 



and of the latter (for the conjugate foci z, </) 



_ 1 X sin 62° 50' (m) _ „ 

 ~ 1 X sin 33° 0' (M*) ~ ' ''• 



Let M be the linear amplification (whatever it may be) of the 



posterior system which is common to both objectives, then the total 



amplification of the Stokes objective (S) will be M.N, and of the 



N 

 Shadbolt objective (Sh) M.N', which is less by ^ = 1 -42, i. e. in the 



proportion of 5 : 7 approximately. Therefore, the focal length of the 

 objective Sh must be greater than that of S in the same proportion, so 

 that Sh is a loioer power with the same bach combination. 



It has already been shown (p. 308) that, if a lower power objective 

 utilizes only the same back lens as a higher power, it will not have 

 the same, but a lower aperture. This must also be obvious instinc- 

 tively, for if it were not so, opticians would of course make their 

 J-inch of 120° aperture with the same small back lenses as are 

 sufficient for the ^-inch of 120° aperture ! 



Therefore, Mr. Shadbolt, claiming to have suggested a way to 

 obtain the pencil from q with 66° divergence from air without loss 

 of aperture, has in fact done so by a method which necessitates a 

 loss of amplification, and therefore loss of aperture ! In all cases of 

 diagrams such as these, it is not sufficient to look only at the diagram 

 on paper ; it is essential to put the question, " Have we still the same 

 system ? " — i. e. the same power. 



It may be said, however, that Mr. Shadbolt's suggestion was only 

 given as an example, and that if it is insufficient another constructioia 

 can certainly be devised for catching the pencil q with 66° angle from 

 air, and without loss of aperture. Now, "without loss of aperture" 

 can, under the conditions of the whole argument (the back combination 

 remaining unaltered), mean nothing else than " without loss of ampli- 

 fication " in the action of the front. Therefore, if it is possible by 



2 A 2 



