NEW BOOKS, WITH SHORT NOTICES. 147 
stereoscopic effect to pass. And, finally, say our authors, “ We must 
call attention to a fact that seems hitherto to have been overlooked. 
The idea of projections and depressions may be caused by mere dif- 
ferences of density, which, when an object is examined by transmitted 
light, must produce exactly the same optical effect. If we suppose a 
membrane equally thick throughout, but containing in its substance 
parts of greater and less density, the denser spots will appear in the 
stereoscopic picture convex, and the less dense spots concave, and 
so produce an illusory effect on the senses. For this reason we con- 
sider it more prudent, under present circumstances, to prosecute 
scientific researches with the ordinary monocular instrument.” 
2. We pass on now to another subject of general interest, upon 
which our authors have expressed a decided opinion, namely, the 
significance of aperture of objectives. 
Referring to the distinction originally made by Herschel in the 
case of the telescope between defining and penetrating power as one 
which applies equally to all optical instruments, not excepting the eye 
itself, our authors say, “ Let it not be forgotten that penetrating 
power rises or falls not with the aperture of the refracting lens, but 
with the aperture of the cones of light which proceed from the object 
to the lens. It is self-evident that when incident pencils of light 
occupy only a part of the aperture of an objective the whole of the 
unoccupied portion is inactive.” When, however, a parallel is drawn 
(as has been done by Goring and others) between penetrating power 
as understood in the telescope, and that which is termed penetrating 
power in the case of the microscope, it becomes necessary to examine 
in what sense this transference of idea is to be explained. Now in the 
telescope its entire aperture is occupied by beams of light which come 
from the object seen (as if they were self-luminous), and an increase of 
its aperture (just as the widening of the pupil of the eye) has only one 
purpose, namely, increase of light when the objects to be seen are 
weakly illuminated. If this light be too strong, wide aperture exer- 
cises only a disturbing influence, as lenses of wide aperture are mostly 
affected with serious aberration. But, say our authors, the illumination 
can be intensified at will in the case of the microscope (up to applica- 
tion of direct sunlight), so that the need of large aperture for illu- 
mination does not come into consideration. Further, it is well known 
that the cones of light admitted through the diaphragm openings are 
so small that the rays converging on the focal plane form cones which 
have not commonly a greater aperture than 23°-30°, and these, after 
undergoing a change of course in the objective, again group them- 
selves into cones which appear as if they severally came from separate 
points of the object to form an image of that object in the microscope. 
The apertures of these pencils are approximatively the same as those 
of the incident pencils. Supposing therefore an objective to have 
60° to 80° of aperture, the separate pencils only partly occupy this 
aperture, so that the sense in which penetrating power has been used 
as a term applicable to the telescope (i.e. the power of penetrating 
space gained by additional admission of light) is altogether mis- 
applied in the microscope. The large object-glass of the telescope 
