RELATION OF APERTURE AND POWER IN THE MICROSCOPE. 213 
Having already ¢settled the total amplification N, which is 
required for the utilization of a given aperture,* we need only to 
find the super-amplification v which an objective of that aperture 
will bear, without a perceptible depreciation in the quality of the 
image if objectives up to the present standard of excellence are 
N 
supposed. The quotient — will then indicate at once the normal 
Vv 
amplification [N] of the objective which is necessary in order to 
obtain the said N under the best possible conditions ; and having 
thus determined [N], the quotient —— will yield the focal length 
which an objective of the aperture in question ought to have for 
utilizing the delineating-power of that aperture in the most favour- 
able manner. (The focal length thus assigned for a given aperture 
will be expressed by millimetres or by inches, according as Z is 
taken = 250 mm. or = Io inches.) 
Though the problem in this way leads us to practical questions 
which are to be answered by observation, apart from all theory, it 
will not be useless to point out some theoretical considerations 
which may elucidate certain experimental facts, or guide the 
observer in experiments on that subject. 
(a) One fact which we may foresee in theory, is that the limit of 
useful super-amplification must depend on the aferture of the 
objectives, and that the former must diminish with increase in the 
latter. The greater the aperture the wider the range for the 
deviation of the rays from the ideal collection of the pencils to 
mathematical image-points. All technical faults of the lenses— 
slight defects of figure and of centering—must give rise to increased 
deviations, and therefore to an increased amount of their accumu- 
lated effects, because the clear diameter of the lenses which trans- 
mit the pencils bears a greater ratio to those radii of curvature 
which are required for the wider aperture. Exactly the same holds 
good with the strictly residuary aberrations which are the pre- 
dominant source of defective performance in modern objectives 
(the unavoidable technical faults being much less apparent with 
the excellence of workmanship which has now been attained).— 
Of tie ES. ; 
(Zo be continued. ) 
* See this Journal, ii. (1882) p. 463. 
