[ si ] 
XVII. 4 Method for ascertaining Latitude and Time by 
means of Two known Stars. By M. DELAMBKE. 
Translated from the ** Connoissance des Tems”’ by Mr. 
FrrminGer, many Years Assistant Astronomer at the 
Royal Observatory, Greenwich*. 
Ps 
1 uIs problem is well known to astronomers, who resolve 
it by the plain rules of spherical trigonometry, applied to 
three connected triangles. Several geometers have thought 
it worth their while to take it into their consideration, and 
M. Gauss has just made it the subject of a dissertation, an 
extract of which has appeared in the Journal of Baron de 
Zach, Our readers. will see with pleasure the new re- 
searches of the learned professor who holds so distinguished ' 
a rank among geometers and astronomers. 
Besides endeavonring to render the solution of this useful 
problem more useful -and commodious, M. Gauss’s object 
has been to prove that, by a well understood use of analysis, 
the same results may always be obtained, as are more com- 
monly sought for by purely geometrical considerations. 
_ Iwas ever persuaded of the truth of this assertion; but 
Thave also generally found that the demonstrations are 
longer and more painful ; that a considerable degree of ad- 
dress is sometimes required to attain the end; and that 
often it is useful to know beforehand, and by another pro- 
cess, what is sought for, as otherwise we may be led into 
analytical combinations that produce nothing convenient : 
but though it may thus happen at times that trials are un- 
productive, they will also sometimes lead to unexpected 
theorems, of which much simpler synthetic demonstrations 
will afterwards be found. ; . 
The best way, in my opinion, would be not to exclude: 
any thing; to mix analysis with synthesis, to set down the 
equations of the problem in an easy construction, to avail 
ourselves of al] the formulas that an immediate inspection 
of the figure may furnish, and to endeavour afterwards, by 
analytical processes, to give those equations a form the most 
advantageous, and most applicable to the use of logarithms. 
In oider to set a proper value on the advantages of the 
analytical solution of a known problem, i is necessary 
first to compare it with the vulgar solution; but this last 
should be previously reduced to general formulas, whereby 
‘no other altention is required im the calculator but that of 
_* Supezintendant of the late Right Hon. Charles F. Greville’s Plans for 
Education at Milford, in South Wales; ‘Teacher of Astronomy, Geography, 
Navigation, and the various Branches of the Mathematics. 
Vol. 37. No. 154. Feb, 1811. F the 
