160 METEOROLOGY [TERRESTRIAL MAGNETISM. By these means an accurate reading of the sun s bearing may be made ; and, the position of the place and the time of observation being known, there are tables which enable the azimuth to be at once determined. 7. Lloyd s Method of Determining the Total Force. While the dip circle and the horizontal force magnetometer may be used by travellers in addition to their use as observatory instruments, the Rev. Dr Lloyd has devised a new method of determining the total force. The ordinary method of obtaining this is first to find the dip and the horizontal force, from which the total force can be at once determined by the equation, total force = horizontal force x secant dip. This method is, however, open to objection in high magnetic latitudes where the horizontal force is very small and the dip approaches 90. Now in Lloyd s method this objection is over come. Another circumstance which renders his method peculiarly convenient for high magnetic latitudes, where a traveller s equip ment must be kept as light as possible, is the fact that it only requires the addition of two needles to an ordinary dip circle in order to give the required determination. These needles must be carefully kept frorn contact with other magnets, and their poles never reversed. Here as before we have two unknown quantities to determine, the one being the magnetic moment of the magnet and the other the total force of the earth. We must, therefore, obtain two results, the one embodying the product of the earth s total force into the magnetic moment of the needle, while the other gives the ratio between these two quantities. 8. In order to determine the former of these, let the needle have a grooved wheel of radius r attached to its axle as in fig. 21, and over this wheel let an accurately known weight W be FIG. 21. Dip Circle. suspended by means of a very fine silk thread. The best way of doing this is to have a thread with two hooks of precisely equal weight at each end and then attach the preponderating weight W to one of these hooks. When this is done a new position of equili brium will be taken by the needle. If we suppose that m denotes the magnetic moment of the needle, that i is the angle of dip at the place, and that t denotes the angle which the needle in its deflected position makes with the horizon, the weighting being so made that TJ shall be less than i, then it is clear that the needle has been deflected out of its position of equilibrium through an angle i - TJ. If we call this angle u and designate by R the total force at the place, we obtain the following equation of equilibrium : ?nRsinM = Wr (1), on the supposition (which is very nearly but not strictly correct) that W denotes a constant force at all latitudes. 9. Next, in order to determine the ratio between this needle s force and that of the earth, let it be removed and employed to deflect another substituted in its place. When using it thus as a deflector it should be laid in a frame in an invariable position as in fig. 21. This frame is at right angles to the line between the two microscopes, and as both pieces move together the best plan is to turn the whole round until the deflected needle is visible in the centre of the field of the microscopes, in which position it is of course perpendicular to the deflecting needle. By always keeping to this arrangement we secure an invariable distance between the poles of the two needles. Suppose therefore that we have employed the needle as a deflector in the above manner, and that the deflected needle has thus been made to assume a position denoting an angle TJ with the horizon. It has therefore been deflected from its position of equilibrium by an angle i - TJ (i denot ing the dip as before); calling this angle of deflexion u , we obtain the following equation of equilibrium: Rsinw = mU ....... (2), U being a function depending upon the distance of the needles and on the distribution of free magnetism in them. 10. If we multiply together equations (1) and (2), we obtain ...... (3), in which u, u are determined by observation, while W and r may be regarded as constants. U is, as we have said, a function de pending upon the distance of the two needles and upon the distri bution of free magnetism in them. The magnetic moment of these needles is of course liable to altera tion, but if they are carefully guarded from contact with magnets we may imagine that while their intensity alters, becoming weaker for instance, this nevertheless does not sensibly affect the distribu tion of the free magnetism within them, in which case the function U may be regarded as a constant quantity. The results obtained by this method of Lloyd s fully confirm this hypothesis regarding U ; but it is essential that the two additional needles, the deflector and the deflected needle, should have their poles at no time either reversed or disturbed. Assuming therefore the constancy of the quantity U, its value may be easily determined at any ba.se station where the total force has been determined independently by the ordinary method. 11. Having thus determined the value of U, or at once of UWr (which we may call c), let us carry our instrument to a different station and make the requisite observations. We thus obtain R = vs sin u sin u As this method is specially adapted for high latitudes, the dip circle employed (fig. 21) ought to be one for which the agate supports are horizontal, so as to admit of the needle being visible when the dip is nearly equal to 90. It will also be noticed that, if the deflecting needle have the same temperature when it is used in equation (1) which it has when used in equation (2), then m in the one case is strictly equal to m in the other, and thus no temperature correction is rendered necessary. 12. A slight modification of the method now described is some times adopted. Instead of employing separate weights, which may be easily lost, two small holes are bored in the deflecting needle near each end. The one of these is filled with a suitably heavy brass peg when the observations are to be made in the higher magnetic latitudes of the northern hemisphere, and the other is filled in a similar manner when the observations are to be made near the southern pole. In this case therefore we must readjust the instrument as we pass from the one hemisphere to the other. A slight change must be made in the formula when this method is adopted, for it is clear that the weight will not now act always at the same constant leverage. If the weight be called W and its leverage when the needle is horizontal r, we shall have to modify equation (1) as follows: mR sin w = Wr COST; (5). Equation (2) will, however, remain unaltered, and hence equation (3) will become If the quantity UWr be determined at the base station and called c , we shall have C COSTJ ^_ / A/ V amusinu (7) Instruments adapted for Travellers by Sea. 13. Azimuth Compass. At sea the declination is generally observed by means of an azimuth compass invented by Kater. This is exhibited in fig. 22. It consists of a magnet with a graduated compass card attached to it. At the side of the instru ment opposite the eye there is a frame which projects upwards from the plane of the instrument in a nearly vertical direction, and this frame contains a wide rectangular slit cut into two parts by a wire extending lengthwise. The eye-piece is opposite this frame,
and the observer is supposed to point the instrument in such a