4 
196 4 Method for ascertaining Latitude and Time. 
The advantange that could be found by it is, that for two 
given stars the are of distance D is almost constant, as 
well as its continuation E, and the angle A on the equator. 
These three quantities vary but slowly by the procession, 
aberration, and nutation, which are a little different in the 
two stars. 
Tables of them could, therefore, be made which would save 
about 16 logarithms, or half the work. These tables could, 
without sensible error, be used for some weeks; but this 
advantage would be lost, if the problem was restored to its 
original form, by not taking the first altitude at the same 
moment as the second. Then, instead of (At — A’, 
(A — AY — m) must be employed. 
The distance D would no longer be the real distance 
between the two stars. The remainder of the solution 
would not be altered; but as it is simple and natural, it 
would be better to substitute our formule. 
For the ascertaining the value of the error that is to be 
apprehended in the latitude g, Mr. Calkoen gives the same 
formula as Mr. Gauss; he does not give the one for the 
horary angle. ; 
Mr. Gauss’s method was no more than the vulgar me- 
thod expressed and demonstrated by analysis simply: Mr. 
Calkoen’s is solely founded on a geometrical construction, 
which we have reduced to general formula. Dr. Moll- 
weyde has just given in Mr. de Zach’s Journal of June | 
1609, p. 545, a purely analytical method, which has no 
relation with the trigonometrical solution. 
Like Mr. Gauss, he commences by the equation sin h = 
sin } sin g + cosé cos cos A; and sin fh’ =, &c. 
— 
He makes x = tang (45° — 3 ¢) sin ¢ Tear, Pees 
a3 he substitutes those values, and uniting all the known 
quantities which he designs by M, N, M’, N’, he derives 
the two equations M + Nz* = x cosa 
M’ + N’x* = x cos (A—4); he cuts 
M' N—M’'N’ 
off 2* and finds % = —7Ga sin A—(N'—Neeos cosa? 
cos % (i! + 0) cos 5 (h’ — 8) cos 3 
cos 3 (A + 4) sin 5 (h — 8) cos é 
ang 
Tang (45° + A’) = 
