a 
It is thought that the new order of facts regarding an 
accepted but transitional definition opens a very wide field 
of inquiry. The present paper is rather intended to be 
suggestive than exhaustive. 
§ I. Residuary Spherical Aberration. 
Dividing the area of the surface of a lens into concentric 
rings, it is known that, for spherical surfaces in general, each 
ring transmits its rays differently, and intersecting the axis 
at variable points. In but a few instances can each shell of 
conical rays be made to intersect at one and the same point, 
whether the rays be homogeneous or chromatic. The image 
of a window, for instance, formed by a plano-convex lens 
upon white paper, it is well known, is four times more indis- 
tinct with the plane side turned towards the light than when 
the convex surface is so turned. Spherical aberration is here 
clearly apparent. In the same way, if an objective be employed 
on the stage, and images formed by it be carefully examined 
by a microscope of excellent correction, it will be found that 
these images are more or less distinct according to the varia- 
tion of the interval regulated by the screw collar (PI. I, fig. 4). 
If a brilliant disc be thus observed, the errors of the objective, 
tested, will show a variety of characters. Irradiation, nebu- 
lous light, bright or coloured haloes, haze, yellow fog, absence 
of a decided focal point, no certain evanishment of form just 
within and without the best point of definition. Such are 
some of the more glaring appearances of either spherical or 
chromatic aberration, the yellow fog being the worst fault 
of all. In minor cases, passing muster with inaccurate 
observers, a faint mist overspreads the field; outlines appear 
considerably adumbrated, they want sharpness, decision, and 
point ; adjacent structures more or less coalesce (fig. 1 f). 
Experiments on Residuary Aberration and Aperture. 
The ordinary optical formule show that spherical aberra- 
tion for a convexo-plane lens diminishes rapidly for parallel 
rays as the aperture and focal length is smaller, and the same 
will happen with minute spherical lenses or spheres. For 
the latter the focal point of ordinary glass is placed at a 
point one fourth the diameter distant from the surface and 
without it, and the same happens with cylindrical lenses, 
supposing the refractive index be w=1°500. 
Another interesting form of lens, in some cases exceedingly 
perfect, is of accidental manufacture during the process of 
