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This brings us at once to a practical point. It will be asked, How can such an inquiry be prosecuted? How can the amplitudes of the temples be determined?

AZIMUTH COMPASS.

Nothing is easier. An azimuth compass is all that is necessary for all but the most accurate inquiries.

SECTION OF AZIMUTH COMPASS.

A, needle and card; P, prism; SV, directrix or frame carrying a wire directed to the object and seen over the prism while the prism reflects to the eye the division of the scale underneath it.

The azimuth compass is an instrument familiar to many; it consists of a magnetic needle fastened to a card carrying a circle divided into 360°, which can be conveniently read by a prism when the instrument is turned toward any definite direction marked by a vertical wire. Its use depends upon the fact that at the same place and at the same time all magnetic needles point in the same direction, and the variation for the true north and south direction is either supposed to be known or can be found by observation.

THEODOLITE FOR DETERMINING AZIMUTH AND ALTITUDES.

A theodolite armed with a delicately hung magnetic needle, which can be rotated on a vertical axis, will do still better; it has first of all to be levelled. There is a little telescope with which we can see along the line. When we wish, for instance, to observe the amplitude of a temple, the theodolite is set up on its tripod in such a position that we can look along a temple wall or line of columns, etc., by means of the telescope. We then get a magnetic reading of the direction after having unclamped the compass; this gives the angle made between the line and the magnetic north (or south), as in the azimuth compass.

What we really do by means of such an instrument is to determine the astronomical meridian by means of a magnetic meridian. Here some definitions will not be out of place.

The meridian (meridies = midday) of any place is the great circle of the heavens which passes through the zenith (the point overhead) at that place and the poles of the celestial sphere.

The meridian line at any place is the intersection of the plane of the meridian with the plane of the horizon at that place, or, in other words, it is the line joining the north and south points. If we have the proper instruments, we can determine the meridian line astronomically at any place by one of the following methods:—

(1) If only an approximate position is required, the best means of determining it is by fixing the direction of the sun or a star when it has the greatest altitude. The instrument to be used for this purpose would be a small theodolite with both a vertical and horizontal circle, and provided also with tangent screws to give slow motion to each of the circles as required.

By using stars of both high and low altitudes, a greater exactness can be obtained, but, after all, the method only gives a first approximation, as its weakness lies in the very slow change of altitude as the meridian is approached.

(2) A much more accurate method is that of observing with an altitude and azimuth instrument the azimuth (i.e., its angular distance east or west of the north or south) of a star when at the same altitude east and west of the meridian. If the mean of the two readings given by the azimuth circle be taken, the resulting reading indicates the direction of the meridian.

If we employ the sun in place of a star, its change of declination during the interval between the observations must be taken into account.

(3) To find the meridian line by means of the pole star is a simple and accurate method, as a value can be obtained at any time at night by a simple altitude, provided the time of observation is known.[8]

If these means of directly determining the astronomical meridian line are not available, then we have to do it indirectly by using the magnetic meridian in the first instance.

If we take a magnetic needle and balance it horizontally on a vertical pivot, its ends will be directed to two points on the horizon. By drawing a great circle through these two points and the zenith point of the place, we obtain the magnetic meridian.

The magnetic meridian line is the intersection of the plane of the magnetic meridian with the plane of the horizon. The angle between the astronomical and magnetic meridian lines is called the variation, E. or W. according as the needle points to the W. or E. of true—that is, astronomical—north at any particular place at any particular time. The variation may vary from place to place, and always varies from time to time.

The bearing required has, in the first instance, to be determined by the instruments already referred to in relation to the magnetic meridian.

Having made such an observation, the next thing we have to do is to determine the astronomical or true north, which is the only thing of value.

MAGNETIC MAP OF THE BRITISH ISLES, SHOWING THE VARIATION AT DIFFERENT POINTS.

If the magnetic variation has been determined for the region, we may use a map. Such a map as that shown below gives us the lines along which in the British Isles the compass variation west of north reaches certain values. From such a map for Egypt we learn that in 1798 a magnet swung along a line extending from a little to the west of Cairo to the second cataract would have had a variation of 11½° to the west; in 1844 of 8½° to the west; and at the present time the variation is such that observations made along the same part of the Nile valley will have a variation closely approximating 4½° to the west. By means of such a map it is quite possible to get approximately the astronomical bearings of all temples which were observed by the French in 1798 or by the Germans in 1844, or which can be observed in the present day, provided always that there is no local magnetic attraction.

If we are not fortunate enough to possess such a map, the methods previously referred to for obtaining the astronomical north must be employed; observing the direction in which the sun culminates at noon will give us the south point astronomically; from observations of the pole star at night the astronomical north can also be determined. From the former of these observations the magnetic variation is obtained without any difficulty, even in the absence of accurate local time. When this is available other methods are applicable.

It is sad to think how much time is lost in the investigation of a great many of these questions for the reason that the published observations were made only with reference to the magnetic north, which is vastly different at different places, and is always varying. Few indeed have tried to get at the astronomical conditions of the problem. Had this been done with minute accuracy in all cases, either by the French or Prussian Commissions to which I have referred, it is perfectly certain that the solstitial orientation of Karnak and other temples, which I shall have to mention, would have been long ago known to all scholars.