152 Analyses of Books. 
VIII- A catalogue of nebulae and clusters of stars in the southern hemisphere, 
observed at Paramatta, in New South Wales , by James Dunlop, , Esq. In a letter 
addressed to Sir Thomas Makdougal Brisbane, Bart.K.C. B. late Governor ot New 
South JVa’es. Presented to the Boyal Society, by John Frederic William Herschel, 
Esq. Vice-President. 
The title is all we can afford room for of this paper. 
IX An account of trigonometrical operations in the years 1821, 1822, and 1823, 
for determining the difference of longitude between the Boyal Observatories of 
Paris and Greenwich. By Captain Henry Kater, V. P. B. S. 
In this paper, though on a subject which many will think has been almost ex- 
hausted, we meet with those original views and ingenious suggestions which dis- 
tinguish every thing that comes from the pen of Kater. W e shall endeavour to 
give our readers an idea of them. , . . . , 
In the year 1 79,1, a series of trigonometrical operations was carried on by General 
Roy, in concert with MM. De Cassini, Mechain, and Legendre, for connecting the 
observatories of Paris and Greenwich. In 1821, the Royal Academy of hemnee, and 
the Board of Longitude at Paris communicated to the Royal society of London 
their desire, that these operations should he repeated by both countries. On the 
part of England Captains Kater and Colby, and on that of France MM. Arago 
and Mathieu were appointed to conduct them. Mr. Gardner, from the ordnance 
survey of England, was alt acheil to them. , 
« The signals used for connecting the stations upon the coasts of England and 
France were lamps with compound lenses constructed under the direction of M. 
Fresnel. It will be sufficient here to mention, that the lens, composed of uunie. 
rou- pieces, was three feet in diameter, and that the light far exceeded that of any 
of our lighthouses, appearing at the distance of d 8 miles like a star of the first mag- 
nitude.” , , 
It was in the course of these operations that, the great improvement was sag- 
gested by Captain Kater of attaching numerous microscopes to a circle ; in pre- 
ference to changing the zero, when a second or ihird value of the angle was desi- 
rable f r the purpose of diminishing the errors of divisions, as had been till then 
the practice. He had four additional microscopes applied to General Roy's theodo- 
lite, which, with one of the two that belonged to it, made live*. The other was al- 
lowed to remain, for the purpose of comparing the mean of two opposite readings, 
with that of five. We had an opportunity of hearing of this great improvement at 
the t me or soon after the ingenious author suggested it ; and we thought then, as 
we do now, that it is one of the greatest steps yet made towards improving small 
instruments Nor can we refrain from expressing our astonishment, that the in- 
strument makers have not yet adopted it. Perhaps it is too searching a proof to sub- 
ject. their workmanship to ; but this is an additional reason lor the purchasers in- 
sisting on having it. Except the repeating property, we do not recollect an equally 
important improvement, and we doubt if this latter does not yield to it. 
At the station at Severndroog Castle they “ experienced considerable difficulty 
in obtaining the requsite angles with Hanger Hill, as the signal erected upon that 
tower was seen only once, inconsequence of the intervening smoke oi Loudon. At 
length Col. Colby thought of a method by which this difficulty was overcome. 
Tin plates were’ nailed to the staff upon Hanger Hill tower, the plates being dis- 
posed above each other in certain angles so as to reflect the su n s rays to Severndroog. 
This contrivance, which answers the purpose in a certain degree of the heliostat 
of Professor Gauss was perfectly successful ; each plate gave in succession a neat 
image of the sun resembling a fixed star, which was seen through a smoke so thic 
that even the hill was invisible.” . 
Of the three known methods by which small triangles on the surface of an el- 
lipsoid may be resolved ; i. e. 1. Spherical trigonometry, 2* Themethod of chords, and 
3. That of Legendre depending on the spherical excess ; the latter is adopted. We 
cannot help thinking, that the first is very undeservedly neglected in general by 
geodests. DeLambre has shown its facilities and a method of converting the loga- 
rithm of a distance in feet i nto the logarithm of a sine. The question is of course 
merely one of facilities, as they are all equally accurate; Legendre’s being perhaps 
the most elegant. 
* It requires a prime number, or, in turning the instrument half round, the 
microscopes would come on the same divisions again. 
