226 
Egeberg base 2025'28316 toises, 
with a probable error of 4000129, or of its 
I 
1,570,000 
length. 
Rindenleret base ... 1806°3177 toises, 
with a probable error of -+ 0'00120, or of its 
I 
1,500,000 
length. 
This is a high degree of accuracy as compared with 
older base lines (as for instance several base lines 
measured in France between 1798 and 1828, of which the 
probable errors are 
= ; but this accuracy has fre- 
0,000 
quently been attained of late years, and even surpassed, 
as, for instance, the base line of Madridejos, measured 
by General Ibafiez in 1858, with a probable error of 
I 
5,865,800. 
Part II.is the account of the connection of the Egeberg 
base with the side Toass-Kolsaas, and Part III. that of 
the connection of the Rindenleret base with the side 
Stokvola-Haarskallen of the principal triangulation. The 
observations were made during 1864-66, but owing to an 
error at one of the stations, due to the bisection of a 
wrong object, further observations were made at that 
station in 1877. 
complete, and the work is well tied in. The centres of 
the trigonometrical stations were very carefully defined | 
by letting an iron bolt into the rock, or, into a large block 
of stone; the centre of the face of this bolt, marked by a 
small hole, was the trigonometrical station. The signals, 
to which the observations were taken, consisted of an 
upright beam, to which was attached one or two boards 
about 0°75 m. square, which were painted white or 
black, and occasionally a vertical stripe o'11 m. broad 
was painted on the centre of the board. At several of 
the stations the theodolite could be placed beneath the 
signal, and at such stations the signal was placed over 
the bolt, but in several cases, owing to the nature of the 
ground, or other causes, the trigonometrical station had 
to be placed at some distance from the signal, in one case 
as much as 54 Norwegian feet. Insuch cases the correc- 
tions to be applied to the observations were obtained by | sues sae 
| length of any side is the same by whatever vou/e it is 
measuring a short base line, one end of which was the 
trigonometrical station, and the direction nearly at right | 
Ob- | 
angles to the line joining the station and the signal. 
servations were taken from the ends of this base to the 
various ‘points on the signal, which were bisected from 
the other stations, and these, together with the observed 
bearings to and from the other stations, enabled the 
necessary corrections to be made. The greatest correc- 
tion thus required was 10’ 37°34. But even at stations 
where the theodolite was placed beneath the signal, correc- 
tions were required to reduce the observations to the trigo- 
. . . | 
The connection in each case is very | : 
| taken to each station. 
NATURE 
nometrical station, because different points on the signal | 
were observed from the other stations, and these points 
were not vertically over the bolt. In these cases the cor- 
rections were computed in the following manner :—A 
piece of paper, mounted on a board, was placed horizon- 
tally on the ground over the centre of the station, and 
this centre marked on it. Then, by means of a small 
theodolite, the “traces” of the vertical planes passing 
through the various points observed to, were marked in 
pencil on the paper. The theodolite was now shifted, 
and the corresponding traces marked as before; the in- 
tersections of these traces gave a series of points verti- 
cally beneath the points on the signal to which observa- 
tions had been made. From these points, the correspond- 
ing bearings to the various stations were plotted on the 
paper ; and, lastly, perpendiculars were dropped, from the 
point representing the centre of the station, on to these 
bearings ; the length of any one of these perpendiculars 
[| Fan. 4, 1883 
divided by the approximate distance to the corresponding 
station is the tangent of the correction to be applied. 
Two instruments were used for measuring the angles ; 
a 10" universal instrument by Olsen, read by two micro- 
meter microscopes, and a 12” theodolite by Reichenback, 
read by four verniers. The errors of graduation of these 
instruments were investigated, and are given in a tabu- 
lar form in Part II. Although, owing to the numerous 
observations taken to each object starting from different 
parts of the horizontal limb, the errors of graduation 
must have been eliminated to a very large extent, yet it 
was thought advisable to apply these corrections to the 
observations, in order to obtain a more accurate idea of 
the bearings of each station. The errors of the micro- 
meter microscopes are also given in a table. The 10” 
instrument was used at all, the 12” theodolite appears to 
have only been used at two, stations. A third instru- 
ment, a 10” universal instrument by Breithaupt and Sons, 
was used for the observations of 1877. 
When observing, the instrument was first set at 0°, and 
a round of angles taken: the telescope was then reversed 
and the round taken again. The instrument was then set 
at 15° in the case of the triangulation connecting the 
Egeberg base, and at 20° (nearly) in the case of the Rin- 
denleret base triangulation, and two rounds taken as 
before. The instrument was then again moved on 15° 
and 20° respectively, and so on. Thus in the first case 
forty-eight, and in the second thirty-six observations were 
In some few instances even a 
greater number were taken. ‘The actual observations are 
not given in the Report, only the mean of four observa- 
tions—two taken in the same position of the horizontal 
limb, and two in that position increased by 180°. The 
time occupied at each station averages four days; some 
stations were completed in two days. 
The observations were compensated by the metho? 
enjoined by the Association for the measurement of 
degrees in Europe, namely, Bessel’s method. The ob- 
served angles at each station are first compensated 
amongst themselves. A correction is then applied to 
each angle thus found, subject to the condition that the 
sum of the squares of these corrections for the whole 
triangulation is a minimum, and subject further to the 
geometrical conditions that the sum of the three angles 
of a triangle = 180+ spherical excess, and that the 
calculated. The necessary calculations are very laborious, 
and in the case of the Rindenleret base require the solu- 
tion of simultaneous equations containing seventy-six 
unknowns. It is very questionable whether the result 
repays this labour; the method of compensation adopted 
for the Ordnance Survey, although perhaps not so rigid, 
compares favourably in this respect. The calculations 
for compensation are giver very fully in the Report. 
The Report is accompanied by plates showing the 
base measuring apparatus and the connecting triangula- 
tions. 
ELEMENTS OF THE GREAT COMET OF 1882 
(Communicated by Vice-Admiral Rowan, Superintendent 
U.S. Naval Observatory) 
HE following elements were computed from three 
observations made at the U.S. Naval Observatory ; 
the first and last being made with the Transit Circle, and 
the middle one compared with a known star which was 
afterwards observed on the Transit Circle :— 
Wash. M.T. App. a. App. 3. 
- m. Ss. © , “ 
Sept. 19°9697877 11 14 18°94 — 0 34 29°7 
Oct. 8°7204303 Io 28 6°63 —10 40 22°6 
Nov. 4°7009228 9 6 16°22 —27 21 26°7 
From these observations we deduce— 
