ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
087 
As before, the image will correspond accurately with the object 
when v is very great, so that the series iucludes a large number of terms. 
As v diminishes the higher terms fall out, until when v is less than 2 7 r 
the series is reduced to its constant term, and the field becomes uniform. 
The resolving power in this case is therefore only half as great as when 
the object is self-luminous. 
These conclusions accord with Abbe’s theory. The first term of 
the series represents the central image, the sec md term the two spectra 
of the first order, and so on. Resolution fails when the spectra of the 
first order cease to co-operate. 
The more complex case when the incident plane waves are inclined 
to the grating is next taken. Calculation shows that the image of the 
grating or row of points can be represented by the sum of terms 
it I v [e imu -f- e' : (" l + s i)“ -f -f- e i (- m + t ^ u -f . . . 
where = 2 ir / v, s 2 = 4 ir / v, &c. 
Each of these terms corresponds to a spectrum of Abbe’s theory. 
With this the author concludes the discussion of the theory of a 
rectangular aperture. The consideration of a circular aperture for the 
case of parallel waves and perpendicular incidence leads to results similar 
to those obtained in the case of a rectangular apeiturc, with one important 
difference. In this last case the spectra do not enter suddenly and 
with their full effect, as in the case of a rectangular aperture, but the 
effect of a spectrum which has just entered is infinitely small. 
The author concludes with a general method of investigation, 
in which the form of the aperture is supposed to remain symmetrical 
with respect to both axes, but is otherwise kept open, the integration with 
respect to x being postponed. In the case where the illumination is 
such that each point of the row or of the grating radiates independently, 
the limit to resolution is shown to depend only on the width of the 
aperture, and thus to be the same for all forms of aperture as for the 
case of tho rectangular aperture previously considered. 
(6) Miscellaneous. 
Microchemical Reaction for Nitric Acid.*— Prof. R. Brauns re- 
commends the use of barium chloride as a microchemical test for nitric 
acid, since barium nitrate is soluble with difficulty. A drop of barium 
chloride is added to a drop of the solution to be tested, and warmed over 
the water-bath. On cooling, sharp colourless octahedra of barium nitrate 
separate out of a solution which contains a nitrate. 
Sublimation and the Determination of Melting-Points in Micro- 
chemical Investigations.t — Prof. H. Behrens, in his introduction to the 
microchemical analysis of the most important organic compounds, 
describes a simple heating arrangement for experiments on sublimation 
and the determination of melting-points under the Microscope. In 
fig. 107 the apparatus is seen in natural size. Beneath the Microscope 
* Zeitschr. f. wiss. Mikr, xiii. (1896) pp. 207-8. 
t Zeitschr. f. aug Mikr., ii. (18 J6) pp. 161-4. 
