5th. The last and most difficult of all the adjustments, is that by which the instrument is placed in the plane of the meridian of the place of observation. There are many modes of accomplishing this, both by direct and indirect means; but the most convenient and most generally practised are those in which a circumpolar star is employed; or in which two circumpolar stars, differing little in declination, but nearly twelve hours in right ascension; or in which two stars, differing considerably in altitude, and but little in right ascension, are, successively observed; but in whatever way the adjustment may be made, the clock that gives the times of transit must have its rate previously well determined.

The approximate position of the instrument may be ascertained by calculating the solar time of the pole star's passage over the meridian for any given day; and then the telescope levelled and pointed at it, at the computed time, will require but little adjustment. Subsequent observations of circumpolar, or of high and low stars, will gradually rectify the position, provided all the adjustments previously directed, continue unaltered for a sufficient length of time; and a meridian mark, capable of adjustment, may be placed at a convenient distance north or south, until their places are definitely fixed by some of the following methods. At 95-49 yards from the object end of the telescope, one inch will subtend l' or 60", and a scale may be made accordingly, varying of course inversely as the distances; so that when the transit is found to be any number of seconds, say thirty, too much to the east or west, a corresponding distance on the scale shows how much the instrument is to be moved in azimuth, by the proper screws, to effect the correction required.

Method 1st.-By a circumpolar star.

Where a

cotand

azimuthal deviation in seconds at the horizon,

t the time at upper transit,

tat lower passage,

L= the latitude,

the declination :

by multiplying by 15, a is converted into space if required.

If the western semicircle is passed through in less time than the eastern, the object end of the telescope points to the west of the true meridian. The clock must be a good one for this method, as it supposes no change of rate for twelve hours.

Method 2nd.-By a pair of circumpolar stars.

a=

(t−t−12)–(T−T−12h) sin Asin A’
c cos L-sin (▲'— ▲)

where ▲ and A', the star's polar distances, L = the latitude, t and t the times of the first star's upper and lower passages, T and T' the times of the contrary passages of the second star, following the other at an interval of nearly 12 hours in right ascension; or this formula, omitting the 12 hours,

when (t-t-121) is a greater interval than (r—r' — 121) the horizontal deviation a will be towards the east, and vice versâ; or when (t'r') is greater than (t—r) the deviation is also to the east. Method 3rd.-By high and low stars.

Where D

cos L sin (d)

(tt) the difference of the observed times of passage, and D'= (Ra-Ra') the difference of the apparent right ascension of the two given stars, the declination of the higher star, and that of the lower. The stars for this method ought to be removed from each other at least 40° in declination. When (D — D′) is positive, the horizontal deviation is to the east of the south point in northern latitudes; and the contrary when negative. Tables are formed to facilitate the computation of the above formulæ. The times are all supposed to be sidereal; if, therefore, solar time is used in the observations, the acceleration must be added.

The following example is given of the last method, in which, if the difference of the times of the observed passages be exactly equal to the difference of the computed right ascensions of the two stars, the instrument will necessarily be already in the plane of the meridian.

On June 20, 1838, in latitude 51° 23′ 40′′, the transits of a Corona Borealis, and of Antares, were observed.

The above is one of the sets of observations made by Major Robinson at St. Helen's Island, Upper Canada, in 1845. Reference was always made to the particular transit and chronometer used; stating also if the error of collimation had been determined, and the transit levelled immediately before the observation, and whether the east or west end of the axis was illuminated.

In the transit books used on this occasion, made of four or five quires of letter paper bound up in a strong cover, the right-hand page was printed in the above form, leaving the other blank for recording levels, calculating the azimuthal errors, &c., &c.

The form for registering transit observations in a permanent Observatory, is of course different from the above: that at present in use at the Royal Engineer Observatory at Chatham, taken from the "Corps Papers," is given as an example.