August 5, 1886] 
century, and has been used in determining the 
orbits of a large number of the minor planets, 
and of the comets of short period. Oppdlzer sub- 
stitutes for it in his second edition one of his own, 
which, from extensive application he has found to be 
much superior to all other methods, both as regards the 
precision of the results and the rapidity with which the 
computations may be performed. In the case of the planet 
Ceres he obtained results on a first approximation more 
exact than those given by the method of Gauss after three 
approximations. Further, it is pointed out that, where 
four observations are employed, Gauss’s method is not ap- 
plicable, except when the excentricity is small. There is a 
chapter on the modifications of Oppdélzer’s method neces- 
sary in the determination of cometary orbits ; also a nu- 
merical example for the orbit of the minor planet Ludora, 
and one for the first comet of 1866, or the comet of the 
November meteors, as well as a comparison of the new 
method with that of Gauss, by an example taken from 
the Zheorta mots. So far, three observations are em- 
ployed. Similar examples follow for the case of four 
observations. A succeeding section deals with the calcu- 
lation of circular orbits, and it is shown that an ephemeris 
deduced from a circular orbit, which admits of compara- 
tively rapid and easy calculation, may be made of service 
in following for a time a newly-discovered minor planet. In 
an appendix are collected all the formulz usually required 
in the first determinations of orbits, with reference to 
those parts of the volume where the analysis and other 
details are to be found—a résumé that possesses great 
value in so extensive a work. The tables which follow 
are on a greatly extended and refined system, more 
especially that for the calculation of the true anomaly in 
the parabola 
The great work of Oppdélzer, of which Prof. Pasquier 
has presented astronomers with so admirable a transla- 
tion, is not one suited to a beginner; but the student 
with a certain knowledge of the differential and integral 
calculus, and of analytical mechanics, may initiate him- 
self with its aid, as the translator remarks in his preface, 
“% Yun des problémes les plus hardis que se soit posés 
Vintelligence humaine.” 
LETTERS TO THE EDITOR 
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return, or to correspond with the writers of, rejected manu- 
scripts. No notice is taken of anonymous communications. 
[The Editor urgently requests correspondents to keep their letters 
as short as possible. The pressure on his space is so great 
that it is impossible otherwise to insure the appearance even 
of communications containing tnteresting and novel facts.] 
The Silver-Blue Cloudlets again 
From your last week’s issue, p. 264, it would seem that the 
silver-blue clouds and cloudlets seen at midnight low down over 
the northern horizon both in this, and last, year’s July are 
attracting much attention among your correspondents; but have 
not yet had the spectroscope directed to them. 
Now there was a remarkable display of those bright blue 
clouds on the night of Tuesday, July 27, though with some 
variations on their exact mode of appearance in the eardier part 
of the month ; but not necessarily removing them into a different 
category. The day had been cold but clear, especially in the 
northern direction, from which the wind was blowing, bar. = 
NATURE 
311 
She te! So ee 
29°60, night temp. = 48° F., depression of wet-bulb = 4”0 F 
It was therefore just such a night as at this season of the year 
and in this high latitude is certain to show a coloured twilight 
over the sun’s place beneath the northern horizon, if ordinary 
thick fogs, and low cloud-banks do not interfere. 
On issuing, then, that night, close upon twelve o’clock, from 
the Observatory computing-room, upon the Calton Hill, I was 
surprised and even startled, not at seeing a low-down coloured 
twilight in the north, but at the excessive strength, and glittering 
brightness of its colours. You might indeed have, at first 
sight, imagined that some great city, spread abroad over the 
plains of Fife was in a fierce state of extensive conflagration, so 
burning red was the first and lowest stratum extending along 
nearly 20° of the horizon. But fhat awful kind of red- 
ness passed quickly into lemon-yellow clouds in the stratum 
next above the red ; and then came the silver-blue cloudlets just 
above the lemon-yellow, and even brighter still ; but with an 
imnocence of colour and gentleness of beauty, which at once 
exorcised the horrid idea of malignant flames devouring the works 
of man ; and showed it must be something very different. 
But still what was it, that made that low level strip far away 
in the north, just then so brilliant in its light and intense in its 
colours,—that it, and it alone seemed for the time, to be 
illumining the otherwise pitchy darkness of night? At the same 
time a few stars were faintly vi-ible ; while a long streamer, 
of apparently white cirrus cloud, trailed over half the sky from 
west, to east-north-east, and passed across the Polar region at a 
considerable altitude, having the silver-blue cloudlets and their 
gorgeous red basement far below, but within, its wide-inclosing 
sweep. 
On reaching home, I got a large spectroscope to bear on the 
brightest part of the low level streak of richly coloured light, 
its red, and yellow, and light blue, both collectively, and 
separately ; but with no other decided effect than a short con- 
tinuous spectrum in the green; which, as I have elsewhere long 
ago shown, is the spectrum of ordinary twilight always. For even 
though red and yellow be present to the eye at large, these 
colours rapidly fade out in any slit-formed spectrum, leaving the 
maximum of faint twilight placed by the prism as above 
described. 
On this occasion, however, I did remark that that short 
continuous spectrum began in its citron, or commencing, region 
rather abruptly: in fact I even imagined a bright line there ; 
and after several independent measures of spectrum-place, duly 
tested by reference both to a hydrogen tube, and the micrometer 
readings,—made out, that it was in the very position of the 
aurora line; or that, in fact, aurora was at that moment assist- 
ing, though to a very small extent, in that low streak of merely, 
but yet so intensely coloured, solar and Scottish, midsummer- 
midnight, northern, twilight. 
Going next to the window, with a hand spectroscope, and 
examining the long ribbon of supposed white cirrus at some 
immense elevation, —it was startling as well as delightful to find 
it to consist of hardly anything but aurora; and to see aurora’s 
chief line thin, sharp and positively brilliant along its whole 
extent ; even appearing, if that could be, several times brighter, 
than its parent white streamer itself looked to the naked eye. 
Nor did the identification, as aurora, of this fair white arc 
(transverse to a line leading to the magnetic pole), depend on the © 
spectroscope alone: for, about ra.m., it began to form luminous, 
and rather yellowish, abutments to both its western and eastern 
terminations. Then its original singleness of curvature began to 
mould itself in the north-west into several curves of shorter 
radius; and after that, many thin arrows and shafts of light 
began to shoot out at right-angles from some parts of the great 
arc, and towards the zenith ; and then, after a few minutes, died 
away. In fact it was tothe eye a very fair auroral display, 
though the papers next morning said nothing about it. 
But luminous manifestations were by no means the whole of 
what the aurora was doing ; for presently I could conceal from 
myself no longer that the whole space below that long and high 
vaulting, white, upper arc was darkened, as compared against 
the sky elsewhere, with a brown-black hue ; which moreover 
darkened still further and deepened in obscuration as it de- 
scended, until it suddenly ended sharply above, and quite close 
to, the silver-blue cloudlets of the low coloured twilight on the 
northern horizon, 
Here then was a key at once to the apparently supernatural 
brilliance of the silver-blue cloudletsand the other colours 
below them; viz., all the broad expanse of ordinary further, 
