Marcu 24, 1904] 
NATURE 
497 
logues, whilst some of the rejected Struve stars have also 
been measured. 
Eighteen new pairs discovered by Burnham are also 
included. The pairs are arranged in order of R.A., and the 
coordinates (for 1880-0), the number in the original cata- 
logue, and the measures of position angle and distance are 
given. 
Orictxn oF AuRoR.—In a lengthy communication to the 
Société Francaise de Physique (Bulletin No. 3, 1903), M. Ch. 
Nordmann discusses the causes which produce aurore. 
After reviewing the various observations of the phenomena 
attending aurore, and discussing in detail the theories of 
Arrhenius and Birkeland, he formulates his own theory in 
the following words :—‘ I think that the Aurore Boreales 
are luminous phenomena produced in the upper atmosphere 
by the Hertzian waves emanating from the Sun.” 
In support of this belief he discusses each of the pheno- 
mena attending the appearance of aurora, and shows that 
the forms and orientation, the extension, the frequency, the 
height, the spectrum and the diurnal, annual and un- 
decennial periodicities may all be explained by the applica- 
tion of his theory. In discussing the relations between 
aurora, solar disturbances and magnetic storms, he states 
that the emission of the Hertzian waves becomes more 
intense in the regions of spots and facula: at the period of 
maximum solar activity, and quotes the observed fact that 
it is only the rapidly moving aurorz (1.e. those due to the 
greater disturbances) which apparently affect the magnetic 
needles. 
ASTRONOMICAL DETERMINATION OF LATITUDE AND AZIMUTH. 
—In a recent publication of the Royal Geodetic Commission 
of Italy, Prof. V. Reina gives the details and the results 
of the astronomical determination of the latitude and 
azimuth of five selected stations situated near to the meridian 
of Rome. The main object of this determination was to 
study the action of the local attraction on these two 
coordinates. A number of circum-meridian observations of 
certain fundamental stars were made at each station, and 
the results are given separately. Auwers’s correction to the 
astronomically determined position is then applied, and the 
final results are embodied in a table, which also shows the 
reduction of each position to the ‘* mean pole,’’ the effects 
of local attraction, and the differences between the results 
of the astronomical and geodetical determinations. 
THEORIES OF THE RESOLVING POWER 
OF A MICROSCOPE.: 
(GEOMETRICAL optics in its relation to instruments has 
been studied to great advantage abroad; we in 
i 
forms the basis of his work, is here reprinted, and it will 
be interesting to consider some of the points it raises. 
But first let us contrast what is now possible so far as 
achromatic correction is concerned with what was possible, 
say twenty years ago. In those days the ordinary flint 
and crown glasses only were available. In the case of a 
telescope object glass with a focal length of one metre for 
the D line, the variation in focal length will, with 
such glasses, amount to 1-4 millimetres for A’ and 2-2 
millimetres for G’. In an object glass using modern glass, 
such as that designed by Mr. H. D. Taylor, these errors 
are reduced respectively to —o-1 millimetre and +0-3 milli- 
metre. 
These figures are enough to show how much the optician 
owes to the art of the glass maker. 
Turning now to some theoretical matters connected with 
the microscope which are dealt with by Abbe in his papers, 
let us consider first the term numerical aperture in its re- 
lation to the resolving power of the instrument. We owe 
to Abbe the introduction of this term, and the realisation 
of its importance as defining, in certain circumstances, the 
resolving power of the instrument. By numerical aperture 
is meant the value of the quantity » sin a, where p is the 
refractive index of the medium in which the object is placed, 
2a the vertical angle of the cone subtended at the object 
glass by the point in which the axis of the instrument 
meets the object. Let us suppose, then, that an object is 
on the stage viewed by transmitted light, and to simplify 
matters let us suppose the source of light at some distance. 
Then, according to Abbe‘ and his followers, im consider- 
ing the image formed in the focal plane of the eye-piece 
we are not to start from the object as a self-luminous source 
and consider where the image of such a source would be if 
formed by the laws of geometrical optics; we are to 
start from the source itself, to consider its image formed 
in the focal plane of the object glass, and to treat this 
image as a self-luminous source of light in the microscope 
tube from which arises the image we see. 
If the object be small, the focal image will be modified 
by diffraction due to the object, and according to the views 
enunciated in the paper before us, it is on the nature of 
the diffraction images and the number of them which are 
| formed that the definition depends. 
We will return later to the question whether it is 
| necessary thus to consider our problem. 
|} us a 
England have of recent years somewhat neglected the sub- | 
ject, with the result that only a small share in the recent 
advance in lens construction has been ours. The books and 
papers under review tell us of the advance. 
It was in 1878, in his report on the London International | 
Exhibition of Scientific Apparatus, that Prof. Abbe first 
directed attention to the fact that the further perfection of 
the microscope as an optical instrument depended on the 
advance of the art of glass making. With the glasses 
then at their disposal it was not possible for opticians 
to get rid of the secondary spectrum of their 
object glasses; while a glass could be made achromatic 
for two wave-lengths, the differences in the relative dis- 
persion of the two ends of the spectrum were such that 
there was an outstanding amount of colour which prevented 
the attainment of the highest perfection of the image. It 
was to this fact that the establishment of the now cele- 
brated firm of Schott and Company was due, and the 
resuits of Abbe’s own work on microscope lenses are summed 
up in the first volume of his collected papers, which has 
recently appeared. 
The well-known paper, “‘ Contributions to the Theory of 
the Microscope and of Microscopic Perception,’’ which 
1 *Gesammelte Abhandlungen." Von Ernst Abbe. 
“Das Zeisswerk und die Karl Zeiss-Stiftung in Jena.” 
“Zur Theorie der Mikroskopischen Bild-erzeugung."’ By Victor | 
Grunberg. 
“ The Helmholtz Theory of the Microscope.’ By J. W. Gordon. 
“The Theorv of Optical Images."’ By Lord Rayleigh (Journal of 
Royal Microscopical Society, 1903). 
NO. 1795, VOL. 69] 
At present let us develop it and examine whether it affords 
satisfactory solution of the problem of resolving 
power. 
Suppose, now, the microscope has been focused on some 
object on the stage and then this object has been removed ; 
the parallel rays from the source are brought to a focus 
in the focal plane of the object glass, forming there a 
circular patch of light; rays diverge from each point of 
this, and reaching the eye produce the sensation of a uniform 
luminous field. 
Now let the field in the focal plane be limited by dia- 
phragms pierced with a series of small apertures. The 
distribution of light in the focal plane of the eye lens, the 
view plane, will be no longer uniform; we shall see the 
diffraction pattern formed there by the apertures. 
If, for example, there be but one aperture, a single 
narrow slit, the field will still be uniform; light diverges 
from the slit uniformly in all directions, and no structure 
| is seen. 
If we have a number of equidistant slits the view plane 
will be crossed by a series of equidistant dark and light 
bars. The distance between these bars and the distribu- 
tion of light between them will depend on the distance 
between the slits of the diaphragm and the distribution of 
luminosity among the slits. If this be known, the distribu- 
tion of light in the view plane can be calculated. If, for 
example, the distance between the slits be doubled, the 
distance between the maxima in the view plane will be 
halved, that is to say, the number of bright bars in a 
given interval will be doubled. The distribution in the 
view plane depends on that in the focal plane, and can be 
calculated from it; this is quite certain. 
1 It was stated recently by Dr. Czapski (Pec. Royal Microscopical 
Society. August, 1902, p. 569) that it would be a mistake 10 suppose that 
Prof. Abbe had merely given a grating theory of the microscope; he has 
treated the matter mcre fully. 
