the object. The more obliquely the rays enter the atmosphere, the more they will be bent out of their rectilinear course, and hence the greater the refraction: consequently, refraction is greatest at the horizon, and ceases at the zenith. Refraction is always to be subtracted from the apparent altitude of an object, because the effect of refraction is to cause bodies to appear higher than they really are; so much so that the sun, stars, &c., may actually be below the horizon, when they appear above it. In nautical and astronomical works, tables of refraction are usually given. For terrestrial refraction, see Levelling.

TO FIND THE VARIATION OF THE NEEDLE.

The following method of finding the variation is sufficiently exact for ordinary purposes, but not accurate enough for fixing a true meridian, owing to the uncertainty of the refraction; but, if the sun ascends or descends with little obliquity, the error will not then be very considerable.

When the sun's lower edge or limb is a semidiameter above the horizon (at which time its centre is really about on the horizon, although it is apparently elevated, on account of the refraction of the atmosphere), take the bearing of its centre from the N. or S., whichever it is nearest, with an azimuth compass. The prismatic surveying compass will do, if provided with what is termed an azimuth. The thread is made to bisect the sun's disc, and the observed bearing subtracted from 90° will be the sun's magnetic amplitude, or distance from the E. or W. points by the needle.

Next calculate the sun's true amplitude for that day, thus:

To the log. secant of the latitude, rejecting the index, add the log. sine of the sun's declination, corrected for the time

and place of observation, from a table for that purpose; their sum will be the log. sine of the true amplitude.

another rule:

Or by

As the cosine of the latitude is to the radius, so is the sine of the sun's declination at setting or rising to the sine of its amplitude from the W. or E. To be reckoned from the east in the morning, or the west in the afternoon, and it will be N. or S., as the sun's declination is N. or S.; and the distance in degrees and minutes between the true E. or W. and the magnetic is the variation of the needle.

Observe, if the true and magnetic amplitudes be both north or both south, their difference is the variation; but if one be north and the other south, their sum is the variation and, to know whether it be easterly or westerly, suppose the observer looking towards that point of the compass representing the magnetic amplitude; then, if the true amplitude be to the right hand of the magnetic, the variation is east, but if to the left hand, it is west.

EXAMPLE I.

Required the sun's true amplitude on November 6th, 1828, in latitude 48° 21'.

Latitude

48° 21' . . . Secant 0.17745 Declination. . . 16 4 S. . Sine. 9.44210

True amplitude 24 37

. . Sine . 961955

Hence the sun rose 24° 37′ south of E., and set 24° 37' south of W.

EXAMPLE II.

July 3rd, 1828, in latitude 9° 36' S., the sun was observed to rise 12° 42′ north of E.: required the variation of the needle.

September 24th, 1828, in latitude 26° 32′ N., and longitude 43° W., the sun's centre was observed to set 6° 15′ S. of W. about 6 p. m.: required the variation of the needle. Sun's declination. . 0° 33' S.

An excellent way of preventing mistakes, which inexperienced observers are subject to, is to draw a rough diagram, thus: first, a circle to represent the visible boundary of the horizon, and on it to draw such lines as are necessary to render the figure complete; then it will at

* The necessary tables for the declination and corrections are given in the "Nautical Almanac," and in most works on navigation; some of them are also contained in "White's Ephemeris." This latter, with the addition of a few more tables, would be very useful to military men, and travellers generally, being so portable.

once appear how the variation is to be found, whether by addition or subtraction, and on which side of the north it lies. For example:

We will suppose the variation to be sought at sun-setting. Draw a circle, N. W. S. E., to represent the visible horizon; in the middle of it mark the

point, C, for your station; from C draw the line, CW, to represent the o

true west; then on the north or south w side of that line, according as the sun sets north or south of the true west,

draw the line, CO, representing the

E

direction of the sun's centre at setting; and another line, Cw, for the magnetic west, either on the north or south side of O, as it was observed to be, and at its judged distance. Then, by observing the situation of these lines, it will easily be seen whether the magnetic amplitude and true amplitude are to be added or subtracted to give the variation; and on which side of the true north the variation lies. In the present supposition w is the magnetic amplitude, and C W the true amplitude: W, therefore, must be subtracted from Ow, to give w W, the distance of one from the other; and n, the magnetic N, 90° from w, must be westward of N, the true north.

SECTION XXII.

LATITUDE AND LONGITUDE.

WAR is the great pioneer of geography. Travellers, incited by motives of curiosity or science, may traverse distant lands, and impart to us much useful information respecting their natural phenomena, productions, and inhabitants; but, till countries have been actually surveyed for military purposes, they must remain but imperfectly known. All history bears witness to the truth of this observation, from the period of Alexander's conquests up to the time of our recent expedition into the Chinese empire.

There is no doubt that, with reference to most parts of the globe, lines of coast generally, together with remarkable points situated thereon, are traced upon maps and charts with tolerable accuracy, owing to the professional exertions of our naval brethren; but, beyond the confines of Europe, we have reason to believe that the courses of some of the greatest rivers, as well as the positions of many cities and towns, have been laid down on very loose authority.

Now, it must be admitted that officers, both of the Royal Army and East India Company's service, have greater opportunities than most persons of observing and correcting the errors of maps, and otherwise contributing to scientific knowledge, whether their wanderings into remote regions are occasioned by the calls of professional duty, or proceed from that spirit of enterprise so prevalent amongst them, which impels many to travel: and, in order that they may be able to avail themselves fully of such opportunities, it is highly desirable that they should make themselves