The directions of the Local Magnetic Meridian being found at numerous points of the Earth, it is not difficult to trace through them a curve starting from any assumed point, and so drawn that in every part of its course its direction represents the direction of the Local Magnetic Meridian at that point. Such a curve may properly be called a Terrestrial Magnetic Meridian: and a number of these, at convenient intervals of

(A is the North Magnetic Pole. See Article 42.)

geographical longitude, may be advantageously used as a system of Terrestrial Magnetic Meridians. Such

a system is represented by the diverging strong lines in Figures 20 and 21, which are maps on the stereographic

(A is the South Magnetic Pole. See Article 42.)

projection. (Although this system is essentially founded on observations, collected about forty years ago, some portions of it in inaccessible regions of the Earth are supplied from a theory of Gauss's, to which we shall soon allude: some small alterations would be required to make it quite correct for the present date.) The forms of these Magnetic Meridians are very remarkable. None of them appears to be exactly a great circle.

They converge to a north pole, north of Hudson's Bay, and a south pole, in South Victoria: but these poles are not opposite. From E. longitude 70° to 150°, the northern parts agree nearly with Geographical Meridians: the same remark also applies to a large portion of the southern part in longitude 150°.

The system of Magnetic Meridians has undergone considerable changes in the times of modern accurate science. The southern point of Africa received from the Portuguese voyagers in the fifteenth century the name of L'Agulhas (the needle), because the direction of the compass-needle, or the Local Magnetic Meridian, coincided there with the Geographical Meridian it now makes with it an angle of about 30°. In the sixteenth century, the compass-needle in Britain pointed east of north it now points from 20° to 30° (in different parts of the British isles) west of north. At the present time, a change of the opposite character is going on: in 1819 the westerly declination at Greenwich was about 24° 23′, which was probably its maximum; in the last thirty years it has diminished from 231° to 20°, nearly. It is believed that the magnetic poles are rotating round the geographical poles from East to West.

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25. Imperfect method of measuring the horizontal directive force of terrestrial magnetism at any locality, by vibrations of a magnetic needle. Correction for the torsion-power of the suspending-thread.

In Article 21, it was found that the angular momentum, which the Earth's horizontal magnetic action im

presses on a suspended needle whose axis makes the angle with the Local Magnetic Meridian, is EB sin 0: and if M be the moment of inertia of the needle, the equation which determines its angular motion will be d20 EB

dt2 M

sin 0. If be very small, or if proper cor

rections be applied to the observed time of vibration (as for an ordinary pendulum) so as to reduce the time of vibration to what it would have been if the arc of vibration had been indefinitely small, we may use the equa

tion

dt2

EB

and the time

= 2π

M
EB

M

0 of which the solution is

T of a complete double vibration is

This is a single equation containing two

unknown quantities E and B, and neither of them can be determined from it.

If we repeat the experiment at a different time at the same station, or at any time at another station, where it may be presumed that the Earth's magnet

power is different, we shall have T = 2π

M

E'B'

which

still gives no information. And if there is suspicion that the magnet-power B may have changed, there is no hope of arriving at any conclusion.

There is, however, one way of using the vibrating needle, from which an imperfect result may be obtained. If the vibrations be taken at a standard place (as

Greenwich); and if the needle be carried to other stations in rapid course, so that there is little reason to fear any change in its magnet-power; and if, for confirmation, the needle be again brought to the standard place then we may obtain a certain result thus. Divide the square of the first equation above by the square of the second, and we have

Thus we obtain the proportion of the Earth's magnetpower at one station to its magnet-power at another station, at the same time. But we get no positive information on the measure of the Earth's magnet-power at either station. And as we cannot suppose that the magnet-power of the needle will be unaltered through an unlimited time, we cannot use the experiment to determine whether the Earth's magnet-power at any station has altered with the lapse of time.

The principal value of this method is for very restricted local experiments.

In all applications of the method, we ought in strictness to take account of the torsion-power of the suspension-thread as, on changing the suspension-thread, or in comparing observations where the difference of external magnetic action is great, the omission of that consideration may introduce important error. The torsion-power will be measured thus. Suppose the suspension-piece to be furnished with apparatus which admits of being turned round horizontally (as described