"7ounlL,^Syri869'^'] ^oyal Microsco^pical Society. 7 
same. Doubtless it would be more accurate to give the number of 
the hemispheres and the measure of the space between them, or the 
ratios of the diameter and the interval. 
In my own microscope, with Boss's T^ih. and a double D eye- 
piece, the diameter of the field of view at the distance of the stage 
from the eye is 12 inches, and this space represents the magnified 
image of yoVoth of a inch, on a micrometer-slide ruled by Mr. 
Waterhouse. The magnifying power is therefore 12,000 linear. 
Using this arrangement, P. Quadratum has 40 hemispheres and 
40 intervals in the diameter of the field, ^^ in 12 inches, which 
cover ToVoth of an inch on the micrometer-slide, and as each 
interval is equal to a radius of a hemisphere, the magnified diameter 
of each hemisphere covers yoths, and the interval yoth of an inch. 
Therefore, the real diameter of the hemispheres is e oio oth, and of 
each interval yWo o oth of an inch. The rows of hemispheres cross 
each other at an angle of 60°, as in P. angulatum, and are there- 
fore arranged in the order of the sides of an equilateral triangle. 
Hence, under the illusion of the common methods of illumination, 
which deal with shadows only, and under deep powers, the markings 
of these diatoms are described and figured as hexagons, with the 
sides and centre light and dark, or vice versa, and PHOToaBAPHY 
stands by as an attesting witness. But this illusion arises from 
causing either the illuminated or the shaded portions of the hemi- 
spheres to run into each other, and so to form hexagons with either 
dark or light centres. 
In a valuable paper by Dr. Wallich, " On the Development and 
Structure of the Diatom-valve," communicated to the Microscopical 
Society in March, 1860, it is stated that "in P. formosum there 
exists good evidence to prove that the interlinear spaces are occu- 
pied by elevated rhomboidal papillae, which present facetted surfaces, 
whereas in P. halHeum, instead of rhomboidal elevations, we have 
four-sided flattened pyramids, presenting, as in the former case, 
four sets of lines, of which those bounding the spaces, and not 
crossing them, are the predominant ones." No one will be more 
pleased than Dr. Wallich with the very difierent, but more truthful 
representation of these valves when illuminated by the diatom- 
prism which I will presently describe. In both valves we have 
rows of siliceous hemispheres. Those in P. formosum are at right- 
angles to each other, and meet the longitudinal division of the valve 
at an angle of 45°. In one direction there are 24 hemispheres 
and intervals in the 12-inch diameter of the field already de- 
scribed, and in the direction at right-angles to it there are 30 
diameters and intervals, so that the rows of equal hemispheres are 
rather closer together in one direction than in the other. Here, 
under the magnifying power of 12,000 linear, one hemisphere and 
interval occupy half-an-inch, the apparent diameter of the hemi- 
