Schlagintweit, Hermann von; Schlagintweit, Adolf; Schlagintweit, Robert von: Results of a scientific mission to India and High Asia: undertaken between the years MDCCCLIV and MDCCCLVIII, by order of the court of directors of the hon. East India Company (Band 1): Astronomical determinations of latitudes and longitudes and magnetic observations: during a scientific mission to India and High Asia (Leipzig, 1861)

METHOD OF EQUATIONS OF CONDITION.

125

Observations 1. — 0*3

2. —

0-1

Observations 4. + O'l
5. + 0-1

3. + 0-5

The final correction is not very considerable, as the observations have already been
very well represented by the first approximation.

We limit ourselves to showing, in a general way, the application of this method
also to longitude. The method can be successfully applied only, when there are two
variables.

For the latitude, these two variables were dcp and dt. For the longitude, 9 and
T are considered to be exactly known, the variables being here, S = the declination,
and B.A. — the right ascension of the moon.

The longitudes are then calculated in the same way as the latitudes, but instead
of the equation (-4 a)

cos li dh = (sin cp sin S cotan 9 — cos cp cos 5 cos t tan <p) dtp — cos cp cos 8 cos t tan t dt,
the following, formed according to the same principles, is used:

On the supposition of great correctness in the observations, the resulting values
of dt and dh will both give the same differential of longitude, thus allowing of a very
minute control of the observations.

Besides this, it would be possible to express the differential of longitude in
functions of time; but this operation is best reserved for the numeric process.

b. CALCULATION OF THE LONGITUDE BY EQUATIONS OF CONDITION.

cos h dh = (sin cp sin 8 cotan 8 — cos cp cos 5 cos t tan t) dh
— cos cp cos 8 cos t tan t, dt.