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considerable intervals of time are compared together. In the "Voyage of the Beagle," it is stated that the time in which the needle performed 300 vibrations had increased in 5 years from 734.45 to 775".8. The state of a needle should not, however, be interfered with during the progress of any course of experiments for determining the intensity of terrestrial magnetism.

445. For the more delicate researches relating to terrestrial magnetism it is now found convenient, instead of the usual variation compass, to employ what is called a Declination Magnetometer; and, instead of ascertaining the intensity directly by a dipping needle, to employ horizontal force and vertical force magnetometers, by which the intensities in those directions may be determined; and, from them, the direct intensity may be deduced.

446. The Declination Magnetometer is a bar magnet from twelve to fifteen inches long, nearly one inch broad, and a quarter of an inch in thickness; this is made to rest horizontally in a stirrup of gun-metal, which is suspended, from a fixed point above, by fibres of untwisted silk nearly three feet long, and the whole is inclosed in a box to protect it from the agitations of the air. The bar is furnished with two sliding pieces, one of which carries a glass lens, and the other a scale finely graduated on glass, the scale being placed at the focus of the lens. By means of a telescope at a certain distance, the divisions on the scale may be seen through the lens (in the manner of a collimating instrument), and minute changes in the position of the axis of the magnet may therefore be detected by the divisions of the scale, which may be observed in coincidence with a fixed wire in the telescope.

In order to have the suspending threads free from torsion at the commencement of the observations, a bar of gun-metal is previously placed in the stirrup, and allowed to remain there till the threads are at rest, when a button, carrying the point of suspension, is turned horizontally so as to bring the bar into the direction of the magnetic meridian; after which the bar is removed, and the magnet is introduced in its place.

It is obvious, however, that though the threads may be free from torsion when the needle lies in the plane of the magnetic meridian, yet, as soon as by changes in the declination, the needle turns from that position, the threads will become twisted, and the apparent deviation from the mean position of the needle will be less than the true deviation. In order to

ascertain the correction due to this cause of error, the ratio of the force of torsion to the magnetic force must be found by experiment. For this purpose, NS representing the position of the suspended needle when in the magnetic meridian, let the button of the torsion circle be turned upon its centre, vertically above C, till its index has described any angle NCA;

A

(suppose a right angle), then the needle taking a position as ns and resting between the force of torsion acting horizontally from n towards A, and the force of magnetism acting horizontally from n towards N, if H represent the former force, and F the latter, we shall have by Mechanics,

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The terms in the second member of this equation being given by the experiment, the ratio of F to F +H, or of 1 to 1 + is found. Any change in the declination of the

H

F

needle, which may be observed with the instrument, is to the corresponding change, free from the error produced by torsion, as 1 is to 1 + ; and hence the observed change multiplied

H

H

F

by 1 + gives the corrected change.

F

447. In order to obtain the value of the horizontal intensity of terrestrial magnetism by the instrument, a magnetized bar, called a Deflector, is placed in a horizontal position at right angles to the magnetic meridian, and in a line imagined to be drawn through the centre of the suspended magnet. Its centre is to be placed at two different distances from the latter on this line; and, in each position, the observer is to take notice of the deflexions produced by its attraction on the declination magnet when the north end of the deflecting bar is turned successively towards the east and towards the west; half the difference of the deflexions with the north end towards the east, and afterwards towards the west, being considered as the required deflexion at each distance. The experiments are then to be repeated on the other side of the suspended magnet at equal distances from its centre, and a mean of the four deflexions, two on each side at equal distances, is to be taken

for the deflexion at each of the two distances. Now it is demonstrated by M. Gauss (Intensitas Vis Magnetica Terrestris, 1833) that if m represent the momentum of magnetism in the suspended bar, x the horizontal intensity of the earth's magnetism, R and R' the distances of the centre of the deflecting bar from that of the suspended magnet, and o, p', the means of the observed angles of deflexion at those distances,

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therefore the ratio between the horizontal force of terrestrial magnetism, and the magnetism of the bar or needle, can be found from the experiment.

Next, the declination magnet being removed, the deflecting bar is to be attached to the suspension threads, and allowed to vibrate horizontally, and the time T of one vibration is to be determined from at least 100 oscillations: then, the momentum K of the bar's inertia being calculated, we have

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From these two equations m may be eliminated and the value of x may be found.

If the value of the inclination or dip (d) be found by observation with the inclination instrument or dip circle in the plane of the magnetic meridian, the most correct method of ascertaining the vertical intensity will be to deduce it

MX
K

*Here mx expresses the momentum of the horizontal force of terrestrial magnetism by which the bar is made to vibrate; and, ê being the momentum of the bar's inertia, denotes the angular velocity of the bar; but, by the nature of the centre of oscillation, in Mechanics, 7 being the distance of that centre from the point of suspension, and g the force of gravity, mg g or or its equivalent (T=3.1416), denotes the like

ml'

ין

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-2

T2

The factor (1+) is the cor

rection of the square of the time of vibration on account of the torsion of the suspension thread, as above shown. The bar being rectangular, the momentum K of its inertia with respect to a vertical axis passing through its centre of gravity may be shown, by Mechanics, to be equal to 1⁄2 M (a+b'); in which expression a is the length, b the breath, and м the mass of the bar.

from the value X, of the horizontal intensity, found as above. It is manifest that, if ch (fig. to art. 441.) represent X, hn will represent the vertical intensity which, consequently, is equal to x tan. d. Let this be represented by Y; then the total intensity, represented by R and acting in the direction cn, may be obtained from the formula R= √(x2+Y2).

sus

448. That which is called the horizontal-force-magnetometer, and which is also employed for determining the horizontal intensity of terrestrial magnetism, is a bifilar instrument consisting of a magnetized bar or needle, pended by a slender and very flexible wire passing under a pulley (from the axle of which a stirrup carrying the magnet is suspended) and through two perforations in a small bar above the pulley; the wire is attached at its extremities to a plate at the top of the apparatus, so that the two halves of its length are parallel to one another when the needle is in the plane of the magnetic meridian.

Now, turning the plate at the top of the apparatus till the needle is made to take a position at right angles to the magnetic meridian, resting there in equilibrio between the horizontal component of magnetic attraction by which it is drawn towards that meridian, and the force of torsion by which it is turned from it; then, the force of torsion being computed, that of the magnetic component in the horizontal direction may be obtained. The same instrument is employed to determine, by the observed extent of the horizontal oscillations of the needle about its mean place, at right angles to the magnetic meridian, the ratio between the corresponding variations of the horizontal intensity, and the whole amount of that component. The formula for this purpose, as given in the "Report of the Committee of Physics," published by the Royal Society, 1840, is

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in which F represents the horizontal intensity, ▲ Fits variation, v is the angle formed by lines joining the upper extremities and the lower extremities of the suspending wires, and u, expressed in terms of radius, is the observed deviation of the magnet from its mean place.

The vertical force magnetometer is used for determining the variations in the vertical component of terrestrial magnetism. It consists of a magnetic bar or needle about 12 inches long, having a horizontal axle formed into a knife edge and resting upon two agate planes which are supported on pillars of copper. The needle is provided, on each arm, with

a screw; one of these acts as a weight to keep the needle in a horizontal position, and the other, to render the centre of gravity nearly coincident with the centre of motion. The apparatus has an azimuthal motion by which the needle may be allowed to vibrate in the plane of any verticle circle; and it is usually placed at right angles to the magnetic meridian. From the observed extent of the vertical vibrations of the needle about its mean place, in a horizontal plane, at right angles to the magnetic meridian, the ratio between the corresponding variations of the vertical intensity and the whole amount of that component may be determined.

The formula for this purpose, in the "Report" above mentioned, is,

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in which F represents the vertical intensity, ▲ F its variation, the dip or inclination, T and T' are the times in which the needle vibrates in vertical and horizontal planes respectively, and 7, expressed in parts of radius, is the observed deviation of the magnet from its mean place.

449. For the sake of regularity, in the expressions for the numerical values of the intensities of terrestrial magnetism, all measures of length, as well the linear dimensions of the magnetic bars or needles as the distances of the deflecting bars from them, should be given in feet and decimals of a foot; the mass of a bar should be denoted by its weight in grains; the times in which vibrations are performed should be expressed in seconds, and angular velocities by the decimals of a foot described in one second on the arc of movement. In

m

such terms, from the formulæ for and mx above, Lieu

X

tenants Lefroy and Riddle, in 1842, found 3.72 as an approximation to the value of the horizontal intensity at Woolwich (Phil. Trans. 1843, p. II.), at the same time the inclination, or dip, was found to be 69° 3'; therefore x tan. d, the vertical intensity, would have been expressed by 9.72, and X the total intensity, by 10.404.

cos. d'

At present the unit of absolute intensity is taken to represent the state of that element on the peripheries of two curve lines surrounding the earth, and containing between them a band of irregular breadth crossing the geographical equator. The northern limit of this band was, at one time, supposed to be the line of least intensity; and, with reference

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