188 CORRESPONDENCE, 



new, having been pointed out long ago by others, himself among the 

 number. 



To the second part — that the more oblique rays can enter with 

 the water — he replies, true they can enter the front lens ; but to what 

 purpose ? From this lens they emerge too oblique to enter the back 

 combinations, and therefore they do not reach the eye. If the reader 

 will tm-n back to the upper of the two figui-es in Plate LX., this will 

 be very plain. Take one of the more oblique rays, e. g. that nmn- 

 bered 6 or 7, and produce it straight on (there is no change here by 

 refraction), then it is at once seen that such a ray will pass outside 

 the back combinations and be lost. 



This is, as we might say, checkmate, — in one move. Dr. Pigott 

 committed the oversight of forgetting that the back lenses must be 

 taken account of. Having seen his rays safely into the front glass, 

 he takes no thought for the rest of their journey, assuming that if 

 they can enter the front they will also enter the eye. 



In strictness, no more is required so far as Dr. Pigott's discovery 

 is concerned. His theory is shown to fail in its proof, and this quite 

 independently of anything that may be put in its place. Mr. Wenham, 

 however, goes farther than this. He supplies a correct figure, with 

 the rays projected through a real object-glass, to take the place of 

 Dr. Pigott's imaginary one ; and he points out how to determine pre- 

 cisely the limit of the aperture which the immersion lens does admit 

 of. The reasoning by which he fixes this, which is somewhat close 

 and concentrated in form, is given in the second paragraph of p. 17, 

 and may require some slight attention from the reader to follow it. 

 It may be paraphrased as follows : — Taking a dry object-glass, the 

 pencil issuing from the object cannot exceed 180°. This being re- 

 fracted by the flat surface, is converged to a pencil, which cannot 

 exceed 82^. This is again refracted at the second sm-face of the front 

 to a narrower pencil, whose angle determines the figure of the back 

 lenses and the pencil iliey admit. Eemove now the dry front, and 

 substitute the immersion, other things the same. To find the extreme 

 ray of our new objective, we must begin to trace its course in the place 

 where it is known ; that is, we trace it inversely from the back com- 

 binations, for which we have already fixed the maximum limit. This 

 we have found to be such that, tracing inversely to the inside of the 

 front, the rays will there be found converging at an angle not exceed- 

 ing 82°. These we trace thence into the balsam (without change) till 

 they converge at the focus, thus determining a maximum aperture of 

 82°, the same precisely as for the dry lens. 



Unfortunately, Dr. Pigott has omitted to read this, or else has 

 failed to understand it. That something is wi-ong in his diagram he 

 has indeed become conscious after seeing Mr. Wenham's figm-es ; and 

 in a foot-note to p. 70 he admits that his o^^^l diagram will not work, 

 but curiously he regards this as of no consequence. He accounts for the 

 mistake, and expects it should be allowed to pass on the very remark- 

 able plea that when he made it he was thinking only of the front. 

 Precisely so ; his mistake was that he thought only of the front when 

 he ought to have thought of the rest as well. The aperture of an 



