Immersed Aperhires. 257 



exact dimensions, with the optical conditions upon which it has 

 been carried out practically ; for unless this is done, discussion on 

 the points involved is excluded. The facts observed may do credit 

 to the ingenuity of the optician who professes to have accomphshed 

 the feat ; but the rest is utter darkness, as far as any contribution 

 to the science of optics is concerned. 



In speaking of Col. Woodward's diagram, I need not weary my 

 readers with indices of refraction, and angles innumerable, but will 

 take the outside focal point F to be a correct one, that will even- 

 tually cause the slight convergence from the back of the series 

 requisite to bring all the rays to the long conjugate focus at the 

 eye-piece, in order to form an image there. To prove his position, 

 Col. Woodward assumes another nearer focus F' with the same 

 objective, and with the ray actually emergent from the same point 

 at the posterior of the front lens, in order to show how the greater 

 angle can be obtained. But in this case, if F is considered right, 

 F' must be wrong. The first position forms a posterior focus — the 

 second does not, for the rays will be so divergent that they will be 

 dispersed, and not collected at all, so no image can be formed. . 



Let us extend Col. Woodward's demonstration, and consider all 

 points from F up to the surface of front lens when in balsam. As 

 you approach nearer, a ray is still transmitted (up to 180° if you 

 please). Where they will all go to scarcely requires consideration. 

 The practicable limit Col. Woodward has yet to demonstrate, for 

 the present diagram is inadequate to prove his position. Can he 

 show us the passage of the rays through one of the object-glasses 

 such as he advocates in a diagram of correctly enlarged dimensions ? 

 I shall then have tangible material before me, and will enter upon 

 the consideration with enthusiasm. If this is not in his power, I 

 may, perhaps, help the inquiry by another question. In the exter- 

 nal angle that he has given from outer focus F the incidence on 

 front surface is within 41°, or the limits of the total internal re- 

 flexion that must confine the emergent or internal angle to within 

 82°. That this inner angle in the body of the front of a dry lens 

 cannot he exceeded will, I think, not be disputed by anyone at all 

 conversant with optics. Now, rays making the inner angle that he 

 has shown from focus F', having a more oblique incidence in the 

 material of a dry lens, will be totally reflected back into the body 

 of the glass, rendering such an angle impossible in this case. There- 

 fore, as total reflexion must limit the internal angle to within 82°, 

 like a circular stop, I will ask Col. Woodward if in any of the extra 

 object-glasses he speaks of for obtaining larger immersion apertures 

 he has observed any such limit, when dry, to be exceeded when the 

 front is immersed ? The capability of taking in a few extra rays 

 may depend upon the form and size of the back lenses. With an 

 additional front, the utmost limit may be secured, as by myself proved 



