148 NEW BOOKS, WITH SHORT NOTICES. 
collects light from a distance, but the resolving of distant points of 
light (as double stars) is more dependent upon the freedom of lenses 
from aberration than upon their size, and thus in the microscope 
likewise the capacity to “bring out” lines, points, and minute details 
of structure must be associated with similar resolving power of the 
telescope, not with its “ penetration.” * 
In seeking to determine the significance of aperture our authors 
show that the dioptric function of the lens depends just as much upon 
the aperture of pencils incident from the object (this being itself 
governed by the size of the openings in the diaphragm or screen 
which marks the boundary of the illuminating cones) as upon its own 
aperture, and that it is theoretically unimportant whether with an 
objective of 60° aperture a diaphragm opening giving 30° aperture 
of incident pencil is used, or vice versd, so that the advantage of wide- 
angled aperture does not relate to the image-forming function, except 
in so far as middle and peripheral zones of a wide-angled lens offer 
the possibility of a correction of aberrations which shall affect each 
area separately, and therefore the optician may make the peripheral 
zone work well with oblique illumination, leaving the central zone 
less perfect. The authors fully accept Professor Abbe’s demon- 
stration, that the value of aperture consists in the admission of the 
diffraction pencils which arise in objects containing details minute 
enough to cause diffraction of the illuminating pencils, and that all 
minute structure can only be transmitted as interference images by 
pencils which a small-angled objective cannot take in. The following 
extract contains an expression of opinion respecting this particular 
item of Professor Abbe’s work, which, coming from experts ranking 
amongst the highest authorities on a subject which they have made 
their own, is honourable to themselves while giving the place of 
honour to another. 
“ It may not be superfluous to note here with emphasis, that up to 
the present time the precise effect of aperture has not been established 
as a scientific fact in any work on micrography known to us, much 
less has it been explained. Nor do we find in the experiments de- 
scribed by Harting (the second edition of whose treatise has but 
lately appeared) any decisive result beyond the proof that in a given 
case (experiment with two microscopes) the peripheral zone of the 
object determined the issue. Indeed, from the time of Goring up to 
our own day the whole question of aperture and its effect has been 
altogether devoid of any satisfactory and sound basis. It is the great 
merit of Abbe that he has filled up the void by a clear and well- 
grounded exposition.” 
In concluding this notice of Professors Nageli and Schwendener’s 
Handbook we must remark that the chapters 3 3, 4, 7, 8, 9, and 10 
are worthy of the closest attention. 'The last chapter i in particular i 1s 
* The same conclusion is arrived at by Helmholtz, and the whole subject of 
delineation of the objective image by pencils of light whose aperture is regulated 
by diaphragm openings is fully demonstrated in the essay ‘On the Optical 
Capacity of the Microscope, a translation of which appeared recently in the 
‘M.M.J.’ 
