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This is evident from the figure below, ES, ES', and QS" being the respective declinations of the objects S, S', and S"; and PO or ZE the latitude of the
Perhaps the rule given by Professor Young for the two first cases is more simply expressed thus:-Call the zenith distance. north or south, according as the zenith is north or south of the object. If it is of the same name with the declination, their sum will be the latitude; if of different names, their difference; the latitude being of the same name as the greater.
On April 25, 1838, longitude 2m 30s east, the meridional double altitude of the sun's upper limb was observed with a sextant 104° 3′ 57′′; index error 1′52′′; thermometer 56°; barometer 29-04. Required the latitude of the place of observation.
On March 31, 1838, at 5h 12m 57s by chronometer, the meridian altitude of the moon's upper limb was observed 67° 1′ 5′′; the index error of instrument being 1' 0"; barometer 30 1 inc.; thermometer 51°; the approximate north latitude was estimated 52°, and longitude 2m 21′ 5′′ E. Required the latitude *.
Apparent altitude ▷
* The number of corrections required, and the necessary dependence upon Lunar tables,
render an altitude of the moon less calculated for determining the latitude than one either of the sun or a star.
An observer not furnished with a mural circle, or other instrument fixed in the plane of the meridian with which to measure meridional altitudes, can obtain his latitude more correctly than by observing a single approximate meridional altitude with a sextant or other reflecting instrument, by taking a number of altitudes of the sun or a star near to, or on each side of the meridian, and from thence determining the correct altitude of the object at the time of its culmination.
This method, termed that of “circum-meridian altitudes,” to the mean of which altitudes is to be applied a correction for its "reduction to the meridian," is susceptible of great accuracy; and the repeating circle, already described, is peculiarly adapted for these observations, on account of the rapidity with which they can be taken. The distance of the sun or star from the meridian (in time) is noted at the moment of each observation, by a chronometer when the former is the object, and by a sidereal clock (if there is one) when the latter, to save the conversion of one denomination of time into the other. The formula given by Mr. Baily, freed from the second part of the equation which it is seldom necessary to notice, is
represents the required correction in seconds.
L, the latitude (known approximately).
D, the declination (minus when south).
Z, the meridional zenith distance, also known approximately
from the above.
A, a quantity depending upon the horizontal angle of the object, and given in the 13th table, page 240, under the head of "Reduc
tion to the meridian," being =
2 sin2 P
where P the horary
angle at the pole, as shown by a well-regulated clock; which angle will change its sign after the meridional passage of the star.
Among the instructions drawn up by Mr. Airy for the guidance of the officers employed upon the survey of the North American Boundary, this method of determining the latitude with the altitude and azimuth instrument is recommended, and was constantly practised with stars near the meridian. The axis of the instrument is to be adjusted nearly vertical, and the cross axis nearly horizontal (great accuracy is not required), the telescope made to bisect the star upon its middle horizontal wire, and the time noted. Then read the large divisions with the pointer, and the two microscopes A and B; read also the level right hand and left hand.
Turn the instrument 180° in azimuth, and repeat these observations-revert to the first position, and continue this process as often as may be thought necessary-note the barometer and thermometer-then add together
Reading of A.
And equivalent for left-hand level.
Subtract equivalent for right-hand level.
Divide the remainder by 2, and apply the pointer reading of A for the uncorrected circle reading for the first observation.
The same process is repeated for the second and all the other observations.
For each observation correct the chronometer time for rate and error, and convert this into (if not already showing) sidereal time; take the difference between the sidereal time and the star's right ascension for the star's hour angle, which reduce to seconds of time and call p.
Then compute for each observation the number
(225 sin 1")
cos Lat. X cos Star's Declination
which is the correction in seconds of arc to the observed zenith distance to bring it to the true meridian zenith distance, and is always subtractive, except the star is below the pole. In applying