308 Transactions of the Society. 



wide-angled low-power lenses, which he admires as brilliant 

 specimens of optical art. For those, however, who work with the 

 Microscope, the economy of labour to which they are obliged will 

 be expressed by the rule : — 



Never use wider apertures than are necessary for the 

 effectiveness of the power, because excess of aperture is 

 always waste of time and labour, 



5. A few remarks about another point of practical interest. 

 By those who plead in favour of large apertures in all eases, it has 

 been sometimes suggested as a rational plan for reconciling opposite 

 demands, to have all objectives constructed with relatively wide 

 angles, and to reduce them by stops or diaphragms when smaller 

 angles are desired. The greater penetration and insensibility of 

 the low apertures may of course be attained thereby : but never- 

 theless this device is only a makeshift^ and the result is inferior to 

 that obtained by objectives originally arranged for a lower aperture. 

 It is not merely that the stops cannot increase the working 

 distance (which will always remain at the point corresponding 

 to the full aperture of the lens), but that the low-angled lens 

 which is made out of a good wide-angled one by means of a stop, 

 is in optical respects a relatively bad objective — not nearly as well 

 corrected as the same power would be if carefully adjusted for the 

 lower angle. The reason will be readily understood from the 

 following consideration. 



The best correction of an objective of given aperture depends 

 on the proper distribution of a certain amount of residuary aberra- 

 tion, which cannot be eliminated with our present means. The 

 greater the aperture the more aberration must be intentionally left 

 at the central part of the system in order to prevent an obnoxious 

 accumulation in the marginal zone. It is obvious, therefore, that 

 with an aperture-angle of say 90° the inmost cone of 45° cannot 

 be so well corrected as it might be if the marginal zone could be 

 left out of account. The effect is by no means inconsiderable, 

 particularly in regard to the colour corrections. Owing to the 

 chromatic difference of the spherical aberration the central portion 

 of a somewhat wide aperture must always, even in a well-arranged 

 objective, be perceptibly under-corrected chromatically, and in 

 using this central part alone (the compensating influence of the 

 over-corrected marginal zone being done away with), we have the 

 performance of an inferior lens. In point of fact, no intelligent 

 optician would ever make an objective of 30° aperture on the 

 same formula as one of 60°, or one of 60° on the same formula as 

 another of 100°, though this could be done by merely reducing 

 the clear diameter of the lenses. 



There cannot, therefore, be a reconciliation between the pleasure 

 of exhibiting mere optical accomplishment and the interests of the 



