Computatum of Apparent Places.-In computing the Apparent Places of the several stars for .... several dates of observation, I have used the formula,
Correction to Mean R.A. (in seconds of time)=Ee + Ff + Gg + Hh + L + l−300 + qt where e, f, g, h, l are the constants for each star, given in the Nine-Year Catalogue; E, F, G, H, L the "Airy's Day Numbers," given for each day in the Nautical Almanac; q the star's Annual Proper Motion in Right Ascension; and t the elapsed fraction of the year corresponding with the given date. The small correction for Daily Aberration has been neglected, a very precise knowledge of time being, as already stated, unnecessary.
Similarly, for Apparent North Polar Distance,
Correction to Mean N.P.D. (in seconds of arc)=Ee' + Ff′ + Gg′ + Hh′ + L + l′−300 + I
The Apparent Places thus found are those for Greenwich Mean Midnight of the several dates. The results, reduced to the several times of observation, are shown in Table II, further on, which exhibits the computations for latitude.
Routine of observations.-The instrument was erected on the 8th of January, and adjusted to the meridian the same evening. Observations for latitude were taken on the nights of January 9, 11, 12, 13, 15, 16, 20, 21, 23, and February 7. Clock and circumpolar stars were also observed on those nights, and the levelling of the cross-axis was carefully attended to. The times were taken with the Mean Solar Chronometer, ARNOLD and DENT, No. 1,207, kindly lent to me by Commodore CUMING, R.N. from H.M.S. Victor Emanuel. It has run pretty steadily. The use of a mean solar timekeeper for stellar observations introduces a great deal of unwelcome labour and complication into the reductions, but I had no alternative, as a chronometer rated to sidereal time could not be obtained.
The steadiness of the transit-instrument during frequent use and reversal is shown by the small change of the azimuth errors, which varied only from 6".39 W. (horizontal value) on the 9th January to 6".95 E. on the 7th February, the azimuth screws not having been touched after the first adjustment to the meridian; and it would appear from the observations that this change is mainly due to a slow progressive movement of the pier. Such steadiness of a portable instrument on a new and imperfectly isolated pier, extending over a period of 29 days, is very satisfactory.
Investigation for the latitude.--For the latitude reductions, the investigation is as follows:-
Let Z and Z' be the true meridianal zenith-distances of the south and north stars respectively, d and d' their North declinations, and L the latitude of the place; then,
L=d + Z
L = d' − Z'
L = ½ (d + d') + ½ (Z − Z').............(1)
Now, let z, z' be the (supposed) observed zenith-distances of the south and north stars; n, s the readings of the north and south ends of the level for the south star, and n', s' those for the north star; b the value of one division of the level, in seconds of arc; r the correction for refraction for the south star, and r' that for the north star. And let it be assumed that the horizontal position of the level is that which corresponds to the condition, correction for level = 0.
Then, if (as in this case) the graduation of the level proceeds continuously from one extremity towards the object end of the telescope, the central division being 40.00, and if p, p' be the reductions to the meridian in cases where the stars have been observed before or after the meridian passage, and f, f' the corrections for flexure for either star, it follows that
Z=z − b/2 (n + s −80) + r − p + f
Z' = z' − b/2 (n' + s′ — 80) + r' − p' + f'
½ (Z − Z') = ½ (z − z') + b/2 {(n' — n) + (s' − s)} + ½ (r − r') + ½ (p' − p) + ½ (f — f')................(2)
In the case of the zenith-telescope, z, z' are not measured directly, but only their difference, z-z' by means of the micrometer. To find the expression for this in terms of the micrometer; let ζ be the zenith distance corresponding to the central position of the micrometer thread; m, m' the micrometer readings for the south and north stars, in revolutions of the micrometer screw; and M the value in seconds of arc, of one revolution of the screw. Then, for that position of the instrument in which increase of micrometer readings corresponds with decrease of zenith distance, it is plain that
z = ζ + mM
z' = ζ − m'M
½ (z − z') = ½ (m' — m) M............(3)
* In practice, to avoid confusion of signs, this position was always adhered to. It corresponds with the precept to observe stars North of the zenith with Circle East, and those South of the zenith with Circle West.
Computatum of Apparent Places.-In computing the Apparent Places of the several stars for .... several dates of observation, I have used the formula,
Correction to Mean R.A. (in seconds of time)-Ee + Ff + Gg + Hh + L + 1−300 + qt where e, f, g, h, 1 are the constants for each star, given in the Nine-Year Catalogue; E, F, G, H, L thes "Airy's Day Numbers," given for each day in the Nautical Almanac; q the star's Annual Proper Motion in Right Ascension; and t the elapsed fraction of the year corresponding with the given date. The small correction for Daily Aberration has been neglected, a very precise knowledge of time being as already stated, unnecessary.
Similarly, for Apparent North Polar Distance,
R.
Correction to Mean N.P.D. (in seconds of arc)=Ee' + Ff′ + Gg′ + Hh′ + L + l′-300 + I
The Apparent Places thus found are those for Greenwich Mean Midnight of the several datesi The results, reduced to the several times of observation, are shown in Table II, further on, which exhibits the computations for latitude.
Routine of observations.-The instrument was erected on the 8th of January, and adjusted to the meridian the same evening. Observations for latitude were taken on the nights of January 9, 11, 12 13, 15, 16, 20, 21, 23, and February 7. Clock and circumpolar stars were also observed on those nights, and the levelling of the cross-axis was carefully attended to. The times were taken with the Mean Solar Chronometer, ARNOLD and DENT, No. 1,207, kindly lent to me by Commodore CUMING, R.N from H.M.S. Victor Emanuel. It has run pretty steadily. The use of a mean solar timekeeper for stellar observations introduces a great deal of unwelcome labour and complication into the reductions but I had no alternative, as a chronometer rated to sidereal time could not be obtained.
The steadiness of the transit-instrument during frequent use and reversal is shown by the small change of the azimuth errors, which varied only from 6".39 W. (horizontal value) on the 9th January to 6".95 E. on the 7th February, the azimuth screws not having been touched after the first adjust ment to the meridian; and it would appear from the observations that this change is mainly due to a slow progressive movement of the pier. Such steadiness of a portable instrument on a new and imperfectly isolated pier, extending over a period of 29 days, is very satisfactory.
Investigation for the latitude.--For the latitude reductions, the investigation is as follows:-
Let Z and Z be the true meridianal zenith-distances of the south and north stars respectively. d and d their North declinations, and L the latitude of the place; then,
L=d+ Z
L ď Z
L = ↓ (d + ď' ) + ( Z− Z ).............(1)
§
Now, let z, z' be the (supposed) observed zenith-distances of the south and north stars; n,s the readings of the north and south ends of the level for the south star, and n', s' those for the north star; b the value of one division of the level, in seconds of arc; r the correction for refraction for the south star, and that for the north star. And let it be assumed that the horizontal position of the level is that which corresponds to the condition, correction for level = o.
Then, if (as in this case) the graduation of the level proceeds continuously from one extremity towards the object end of the telescope, the central division being 40.00, and if p, p' be the reduc tions to the meridian in cases where the stars have been observed before or after the meridian passage and ƒ, f' the corrections for flexure for either star, it follows that
whence,
}
b
Z=z − (n + s −80) +r −p +f
Z' = 2'- ́ ́ ·(n' + s′ — 80) + 7' −p' +ƒ'
↓ ( z − Z ) = ↓ ( z − :') + {(n' — n) + (8' − s)} + ↓ (r−r') + 4 (p'− p) + } ( ƒ—ƒ'................(2)
}
}
In the case of the zenith-telescope, z, z' are not measured directly, but only their difference, z-g by means of the micrometer. To find the expression for this in terms of the micrometer; let the zenith distance corresponding to the central position of the micrometer thread; m, m' the micro meter readings for the south and north stars, in revolutions of the micrometer screw; and M the value in seconds of arc, of one revolution of the screw. Then, for that position of the instrument in which increase of micrometer readings corresponds with decrease of zenith distance, it is plain that
z
2':
O
m M m'M
↓ (≈2') = ↓ (m' — m) M
(3)
* In practice, to avoid confusion of signs, this position was always adhered to. It corresponds with the precept to observe stars Nort of the zenith with Circle East, and those South of the zenith with Circle West.
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