Yet may the latitude be now deduced, with fully suf ficient accuracy for that purpose, by observing the pas sage of any one known star over the meridian, and read ing off its altitude and zenith distance. 'fle pole star, or any star of the first or second magnitude, will be found visible in the day-time with the telescope of this instru ment ; and the latitude being-, though roughly, deduced from it, the correction for time may be sought in the usual way. That required for azimuth may as easily be investigated by this very simple formula, which the late Air \Vales constructed for this purpose." Take the daily variation of the sun's declination from the Nautical Almanac. Then say, as 24h is to half the interval between the observations, so is the daily change in the declination to its change in that half interval. Turn the half interval into degrees, minutes, and seconds ; and reduce the change in that half interval to seconds. Then to the log. of the change so found add log. co-secant of half intervals -I- log. secant of the latitude of the sta tion, the sum will be the log. of the correction in azimuth in seconds to be airplied to the middle point. 'fills will fall to the west of the true south point when the sun is advancing towards the north pole, and vice versa cast when he is receding from it.
44 1-lav ing calculated the necessary correction, you may then apply it to the azimuth before deduced, from a mean ()I' the observations; and shift the instrument just that quantity, as shown on the azimilth circle. Then clamp ing it firmly there with both of the side clamps, you may trust to its remaining in that position as far as the instru ment itself is concerned ; for WIIC11 Once those clamps are set, the tangent-screw for adjustment has 110 1)0 \ I Over it.
'Thus it becomes, to all intents and purposes, so far as its situation and size permit, a transit circle ; placed very nearly, if not quite truly, in the meridian, from one clay's observation alone ; and ready for making some observa tions in that first evening.
Tile chronometer hat jug been let go down, may lint e alturcd its rate, which as yet will be uncertain ; though if the watch be good, that rate will not be unsteady. Its error at noon was known from the corresponding alti tudes; and any observations of the evening may after wards be reduced to the real time, when the rate becomes known. The passage of stirs over the meridian, CVell in this first evening, will therefore be valuable; and if the • moon should be among the number, an observation of her passage, and a comparison of it with that of a star nearly of the same declination, will already give great in sight into the longitude of the station. 'clic error of the instrument in collimation of altitude must be known, be fore the exact latitude can be ascertained ; but as that error is not apt to vary even by carriage, the latitude may he confided in, within 16", from the observations of the same evening.
By repeating the same process, either in whole or in part, as lie may judge necessary, the next (lay, he will vcrifv his meridian, or bring it still more near to the truth. Ile will obtain the rate of his time-keeper, and begin to feel a degree of confidence. For when once he has a mark in the meridian to which to re-adjust his tele scope, he may, if he finds occasion, release the instru ment, and turn it in any direction for other observations, know ing that he can replace it at pleasure. Vet must it be said, that in all instruments, the less they are moved out of any position, and their adjustments disturbed, the better they will always perform what is expected from them.
Another method there is, which has not often been practised, though it was found very convenient to Gene ral Roy in his trigonometrical measurements; the calcu lating of the exact time and distance of the pole star from the meridian, when it is at its greatest elongation cast or west ; and by adjusting the instrument to it at that time, reading off the azimuth on its circle. After this, cor recting the distance of the star from the pole by the co sine of the latitude of the station, you \VIII have the true azimuth of the star ; the difference of which, from the azimuth observed on your circle, will give you the de viation of it from the true meridian. This does not re quire the time to be known or attended to with very great precision; because the motion of the star in azimuth is very slow indeed. And since it conies both to the east and west of the meridian in the space of every twelve hours, two opportunities of this kind offer every day.
Another method, where you have the time sufficiently correct, is, to calculate the meridian passage of the pole star above or below the pole. This occurs nearly six hours after the other ; pointing the telescope of the instrument to the star, and following it in its slow motion, covered or bisected by the meridian wire, till the exact instant it is to come on the meridian, then clamping the instrument there, it will be found very nearly in the meridian indeed. If all the adjustments of your instrument are right, you will probably find it err hut a few tenths of a second of time in respect of stars observed afterwards within the tropics.
These are methods of finding a meridian, which seem best to be recommended with such an instrument ; which, describing true verticals and horizontals, and giving the angles of elevation in the one and azimuths in the other, has all the requisites for such a purpose ; and is itself a transit instrument encompassed by a circle, or a small portable transit circle, ready for meridional observations as soon as its true position is ascertained.