DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.20131#0106
86
astronomical determinations oe latitudes and longitudes.
Where observations of the sun are taken, no doubt can remain about the meaning
of cos (s -f- p) and of tan2 % (s -f- p). It is also evident that this system of equations
represents a continuous series of controls.
By differentiation of the final equations, and if we make the possible error in
time equal to the possible error in latitude (since they can both be reduced to the
altitude), and if, for giving a more simple form to the differential equations, the
azimuths are introduced after differentiation instead of the hour angles, we obtain
dh = — cos Adm —■ cos cp sin Adt
dh' — — cos A'dm — cos m sin A' dt,
or
,, cos A' ,7 cos A 77,
cos mdt =---.—j-r.-r. dh--;—t-t,--rr dh
T sin (A! —A) sin {A1—A)
, sin A1 77 sin A ,,,
dm —--:—-nr,--r- dh + —-r-77--T.dh .
T sm (A—A) sm (A'—A)
For the observer these equations show that, for obtaining results as accurate as
possible, the sun must be observed in azimuths 90 degrees distant from each other,
since sin (A' — A) is the number by which the error is divided. The details of the
observations, communicated later, will show that a similar arrangement had already
been made in most of the cases to which this method is applied.
For the calculation they show the following: If the sun has been taken in low
altitudes, viz., if A' has been nearly equal to 90°, where sin (A'—A) becomes nearly 1,
then
cos <p dt — cos A' dh — cos A dh',
and
dm = — sin A1 dh + sin A dh'.
Now if A' (for low altitudes) is nearly — ± 90°, A (for great altitudes) nearly
— 0, or 180°, we have, for dt, the influence of dh = a minimum, the influence of dh'
= a maximum, and vice versa for d<$, the influence of dh = a maximum, the in-
fluence of dh' = a minimum.
It results that, in calculating, we must use the greatest altitude for latitude, and
the lowest altitude for time.
Example for Method I.
Station No. 91. SkArdo, 1856, September 2.
Compare the detail of the observations in Section II., Group XI.
Means from the two series of the observations:
astronomical determinations oe latitudes and longitudes.
Where observations of the sun are taken, no doubt can remain about the meaning
of cos (s -f- p) and of tan2 % (s -f- p). It is also evident that this system of equations
represents a continuous series of controls.
By differentiation of the final equations, and if we make the possible error in
time equal to the possible error in latitude (since they can both be reduced to the
altitude), and if, for giving a more simple form to the differential equations, the
azimuths are introduced after differentiation instead of the hour angles, we obtain
dh = — cos Adm —■ cos cp sin Adt
dh' — — cos A'dm — cos m sin A' dt,
or
,, cos A' ,7 cos A 77,
cos mdt =---.—j-r.-r. dh--;—t-t,--rr dh
T sin (A! —A) sin {A1—A)
, sin A1 77 sin A ,,,
dm —--:—-nr,--r- dh + —-r-77--T.dh .
T sm (A—A) sm (A'—A)
For the observer these equations show that, for obtaining results as accurate as
possible, the sun must be observed in azimuths 90 degrees distant from each other,
since sin (A' — A) is the number by which the error is divided. The details of the
observations, communicated later, will show that a similar arrangement had already
been made in most of the cases to which this method is applied.
For the calculation they show the following: If the sun has been taken in low
altitudes, viz., if A' has been nearly equal to 90°, where sin (A'—A) becomes nearly 1,
then
cos <p dt — cos A' dh — cos A dh',
and
dm = — sin A1 dh + sin A dh'.
Now if A' (for low altitudes) is nearly — ± 90°, A (for great altitudes) nearly
— 0, or 180°, we have, for dt, the influence of dh = a minimum, the influence of dh'
= a maximum, and vice versa for d<$, the influence of dh = a maximum, the in-
fluence of dh' = a minimum.
It results that, in calculating, we must use the greatest altitude for latitude, and
the lowest altitude for time.
Example for Method I.
Station No. 91. SkArdo, 1856, September 2.
Compare the detail of the observations in Section II., Group XI.
Means from the two series of the observations: