11 
It appears from the expression for @ that the black annulus 
of different refracting spherules commences at various values 
of the objective aperture, readily found by the expression 
20 = 2 sin—! alee) 
’ 
» 
and no black outline can be developed at a higher angle of 
aperture. Thus, taking Sir J. Herschel’s tables for mean rays, 
the following valves of 4 being substituted, and 26 tabulated, 
the limiting apertures to correctly define spherules of the 
following substances are given in the third column. 
Substance, Index of refraction. | Objective aperture. 
Tabasheer or bamboo silica ; P 1:182 25°40! 
Water. , ; i ; : 1°336 60°16! 
Olive oil . F : ; ; P 1-470 79°18! 
Plate glass : : : : : 1500 83°36! 
Canada balsam . : : 2 ; 1:532 87°16! 
Cairngorm topaz : : d ’ 1624 100° 4.4! 
Oil of cassia. : ; ; ; 1°635 101°36' 
Blue sapphire . : : : . 1794 124°-30! 
Heavy glass (lead 2, flint 1 part) . 1-988 164°6! 
To correctly define a spherule of water the aperture should 
be reduced below 60°, for olive oil less than 80°, for oil 
of cassia less than 100°, and for a spherule of heavy glass 
the definition will bear 160° of aperture ; whilst in observ- 
ing bamboo silica spherules, no black annulus should be de- 
veloped in spherules of this substance at a greater angular 
aperture than 25°. It is evident that a coarse measure of 
the refracting index of a given spherule can be at once 
obtained by measuring the aperture at which the jet annulus 
begins to be developed. 
But as it has been the fashion to employ objectives of 
the largest attainable aperture, these nice distinctions of the 
optical definition, as depending on the relation of the refrac- 
tive index to objective aperture, have been completely over- 
looked. Precisely the same experiments may be evolved 
from observing cylindrical fibres of a refracting character. 
The kind of definition obtained is therefore frequently an un- 
known function of the aperture and refractive index of the 
substance observed. 
An interesting confirmation of this principle is to be seen 
in the behaviour of various siliceous bodies, as those found in 
sponges, the spherules and cylindricles of which display very 
different characters of a much paler definition at their inter- 
sections and at their general edges than ordinary glass 
threads, and their refractive index probably approaches the 
low value of that of tabasheer of bamboo. Apart from this 
