merely arrive at corresponding results through a circuitous blind method.

Secondly, as regards the parallax of the moon, which varies with the position of the observer. The compression of the earth at any latitude is not absolutely known by formula, the earth being an irregular spheroid; but a close approximation may be used in the reduction of the parallax.

Thirdly, with respect to semi-diameters in inclination, the limit before mentioned regarding difference of altitudes can be generally adhered to, and a star may be observed in preference to the sun.

Finally, when a lunar distance is observed under favourable circumstances, so that calculated results may possibly be true to seconds of arc, seven-figure logarithms should be employed in reducing the calculation.

Under any circumstances, when a telescope can be set to an altitude or directed to the zenith, another method should be employed in preference.

3rd. Lunar Transits.-The use of a portable transit instrument, set up in the plane of the meridian, enables this more accurate method of determining longitude to be adopted on land, even if the timepiece available is rather faulty, as it merely requires the measurement of a short interval of time.

There are certain stars having nearly the same declination and right ascension as the moon, that are termed moon culminating stars, which may be seen and recognised when the sun happens not to be too near. The Nautical Almanac gives the right ascensions and declinations of these stars, also the right ascension of the moon's bright limb and the declination of her centre at the instant of their respective transits at Greenwich.

Since then we have the computed times of transit over the Greenwich meridian of both the moon and a moon culminating star, and can observe at any place with the transit instrument and a good watch the times of transit of the same two bodies, the difference between the computed Greenwich interval and the observed local interval in time is proportional to the longitude.

The moon's right ascension being discovered by observing her transit, and her position being given for each hour of mean time of the meridian of Greenwich in the Nautical Almanac, the corresponding Greenwich time may be found by a simple proportion; but as an observation would be effected on the bright limb, the right ascension recorded in sidereal time must be corrected for semi-diameter, either added or subtracted. This short period varies inversely with the distance of the moon and the cosine of her declination; but as this interval is given in the Nautical Almanac for the upper and lower transit on the Greenwich meridian, an intermediate quantity may be adopted in proportion to the approximate longitude of the place of observation.

These methods of obtaining longitude are illustrated by examples, in the next section.

The Adjustments of the Transit Instrument.

In the foregoing pages of this chapter, which are intended merely as a guide to such rough astronomical observations as may be useful on route-surveys, the use of the portable transit instrument in the plane of the meridian has been referred to as applied to the two simple cases of finding the sidereal time and observing lunar transits. The transit may, however, also be used for determining latitude by observation on the sun or a star in

the Prime Vertical, at right angles to the meridian; in this case a second stand is extremely useful, as it enables the instrument to be moved from one to the other.

In obtaining latitude by this method, a correct timepiece is unnecessary, but the approximate time is required, and the approximate longitude. At the moment that the sun or star arrives at the Prime Vertical its altitude is observed and corrected (A), its declination (D) is obtained with the help of the Nautical Almanac, and the latitude (L) is obtained by the formula:

sin L=sin D x cosec A.

Under any circumstances the transit instrument should be put in as good adjustment as possible, and even in route-survey work it is sometimes necessary to compute and apply corrections on account of defective adjustment.

First as to the adjustments themselves.

Collimation. The line of sight through the centre wire must be exactly at right angles to the turning axis of the telescope; this is checked by observing on some distant object with the centre wire, and then reversing the instrument in its Y's or supports, and repeating the observation; half the difference in the relative position of the object should be corrected by using the collimating screws.

Level. The turning axis of the telescope should be truly level. To check this, use the striding-level, whose scale is graduated usually to units equal to fifteen seconds of arc, and read the scale at both ends, then reverse the level and again read the scale at both ends, thus obtaining four readings; then the required correction to be applied by turning the levelling screw is one-fourth

of the difference between the sum of the two east readings and the sum of the two west readings.

Azimuth. The two preceding adjustments having been made, the centre wire will describe a true vertical circle when the telescope turns on its turning axis; but even if the instrument was originally set up exactly to the meridian, these adjustments have affected this, and the resulting deviation in azimuth must be adjusted by turning the azimuth screw. This requires much precision, which can only be arrived at by measuring the length of the axis of the instrument and correcting the number of threads in an inch of the screw effecting the adjustment. This will enable the observer to judge of the effect of one revolution, and to know how much to turn the screw for the amount of movement required.

It is usual to set up or fix some distant terrestrial object (a pole bearing a serrated cross-bar), in the meridional direction by observation on a circumpolar star at its eastern and western elongations. To check this, when the instrument is set up it is usual to observe the upper and lower transits of a circumpolar star. The interval of time between them should be exactly twelve hours of sidereal time; if not the observed intervals will indicate to which side the deviation in azimuth lies; as, if the western interval (i.e. that between the upper and the lower transit) be too small, the deviation is to westward of the pole, and the converse.

To obtain the actual value of the angular error in azimuth, observe the upper transit of one circumpolar star S in the attached figure, and the lower transit of another circumpolar star s, not differing very considerably from the former in declination. If then ZSs be the incorrect meridian of observation of the instrument, and

ZPH the true meridian passing through the pole P; the angle Z represents the error in azimuth, Ps, PS, are the

polar distances of the stars S and s; ZP is the colatitude, then

The value of the angle SPs in this expression varies according as the deviation is east or west; if R, r be the right ascensions, and T, t the observed times of transit of the stars S, s respectively, for the case of a deviation east,

SPs=24-{(R—r)—(T−t)}

and for the case of a deviation west,

SPs=(R-r)-(T−t);

also since the angle Z is a very small angle, and the angle SPs a very large one, their sines may be dispensed with, and the angles or supplements used instead.

These three adjustments for collimation level and azimuth can be perfected only by repeated approximation; any errors left remaining should be noted for use in applying corrections to any observations that may be taken afterwards.

The correction (c) for collimation error to be applied