514 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
tion in tenths of the following ring interval is made. A central portion 
of the silvering is removed and illumination by a mirror used in order 
to make the mark on the cover-glass visible. For the illumination of 
the rings, however, a white paper screen above the objective, and set 
obliquely to the incident light, is sufficient. The rings then appear 
dark on a white ground, and it is not necessary to have light incident 
from a mirror below. When an immersion system is to be tested, the 
observation is made in the same way except that, in this case, a drop of 
the liquid is first inserted between lens and cover-glass. To fix the 
diameter of the rings of this apparatus before they are actually scratched 
on the plate, a determination of the exact thickness of the glass plate 
and its refractive index must first be made. As found by the micro- 
scopical method, the first was 6*13 mm., the second = 1*525. The 
rings are arranged at intervals of 5/100 of the numerical aperture. 
The data, for example, for an aperture of 0*80 are as follows : — 
0*80 = 1*525 sin x , 
whence the angle in the glass x = 31° 38', but 
tan * = 6T8‘ 
from which is deduced the radius of the ring in question r = 3*777. 
The angle of divergence a in air, since 
is 
n sin x = sin a 
a = 53° 7'. 
The double amount 106° is therefore the angle of aperture cor- 
responding to the numerical aperture 0*80 mm. The radii for the 
numerical apertures up to 1 would be as follows : — 
0*80 3*777 mm. 
0*85 4*115 
0*90 4*481 
0*95 4*881 
1*00 5*324. 
The plate contains in this 
the aperture 
1*40 
way rings increasing in diameter up to 
18*820 mm. 
For greater distinctness, at certain intervals, two circles close 
together are drawn instead of one. 
In testing the oil-immersion system previously referred to, the fifth 
reckoned from the ring corresponding to the aperture 0 * 80 fell on the edge 
of the field of view. It has, therefore, at most, the numerical aperture 
1 * 00, whereas in the price list of the firm it was called 1 * 25. This was 
a great discrepancy, for if the system had really possessed the latter 
aperture, five more rings ought to have been seen. The numerical 
apertures necessary for the resolution of different diatoms are given in 
Dippel’s text-book of general microscopy in the tables of comparison 
which have been established by exact scientific observations. On 
