Ursæ Minoris alone, which is a star generally known, and of easy recognition. The chronometer time of the star's Eastern or Western elongation (as the case may be) being deduced, two pairs of angles may be taken before, and two pairs after that event, as described at pp. 687, 688. The corrections to these angles being computed by the approximate process, and applied, we shall have the angles at the star's maximum position. When these angles are combined with the star's computed azimuth, there will result the required azimuths of the Referring Mark.

Type of Computation by the Approximate Process.

Take the observations made at Kaliana, on the 5th October 1836, given at p. 689.

A from the following Computation applied to the Observed Angles.

Variation of the needle.

The azimuth of the Referring Mark having been deduced by any of the preceding methods, a simple observation with any magnetic instrument is only necessary, to ascertain at once the variation of the needle, by accurately fixing the theodolite over the station dot, and taking a series of magnetic bearings to the Referring Mark. The difference between the mean of such Readings and the computed azimuth, is the required variation, which will be East or West according as the true azimuth is greater or less than the magnetic, supposing the azimuth is reckoned from North by East. Hence to obtain the true azimuth when the variation is East, add it to the magnetic bearing, and if West, subtract it. It is unnecessary to enter further into this subject beyond what is required for practical purposes. All the chief works on navigation treat of the variation of the compass in different parts of the world, and to such works the reader is referred for further information. In this country the magnetic variation is about 24 degrees East.

CHAPTER VIII.

ON THE METHODS OF DETERMINING THE LATITUDE OF A PLACE.

IN the methods of computation which have already been treated of in the preceding chapters, for the determination of the error of the chronometer and of the azimuth of the Referring Mark, the latitude of the station of observation is supposed to be given. If this element can be derived from the Great Trigonometrical Survey, the best thing which the Surveyor can do, is to use it at once, as it would be superior to any determination, which he is likely to effect for himself with the limited means at his disposal. On the other hand, instances will frequently occur of the Trigonometrical Survey not having extended to those districts, which are being traversed over by a revenue or topographical operation: in such cases the required latitudes of places, must be derived from observation alone. It is the object of this chapter to explain the method of making and computing such observations.

With this view we will suppose that on a fine clear morning the Surveyor has arrived at the origin of his operation, furnished with a theodolite, possessing a complete vertical circle, together with a chronometer and a Nautical Almanac, and that he is ignorant of the geographical position of the place where he is standing, as also of the direction of the meridian, and the error of the chronometer. Under these circumstances, the first thing he will have to execute is to put up the theodolite and make an observation upon the sun as directed in Chapter II.,

and then taking out the latitude and longitude of the place from the best map which may be within his reach, he will compute the error of the chronometer and the chronometer time of the apparent noon. This deduction will not be of a very rigorous character. This however is a circumstance which will entail no inconvenience, as the object of this process is only to ascertain the approximate time of the sun's passage over the meridian.

About quarter of an hour before the chronometer time computed as mentioned above of the apparent noon, the Surveyor will intersect the sun's upper or lower limb as may be convenient. As the apparent noon has not yet occurred, the sun will be ascending, he will therefore follow up the intersection of the selected limb until it reaches the highest elevation. When an observation has been obtained at that limit, he will read off the vertical circle of the theodolite.

This vertical reading will be the meridional altitude of the observed limb of the sun. It is however taken on one face, and will therefore be impregnated with the index error of the Instrument. The amount of this error may be determined in this way. Take any fixed well-defined and high terrestrial object and observe its elevation on both faces of the theodolite, half the difference between these elevations is the required index error, additive to the face which gives the lower, and subtractive from that which furnishes the higher altitude. The Index error of the instrument may be determined before or after the sun's observation as may be convenient.

When the observed altitude has been cleared of the Index error, the next corrections to be applied thereto, are refraction and parallax, the mode of computing which will be found in the appendix. After the observed altitude has been freed from the Index error refraction and parallax, it may now be reduced to the sun's centre. This reduction is thus performed. Increase or diminish the observed altitude corrected as described above by the sun's semi-diameter according as the