in this place their nature and the manner of performing

them.

Those elements are of three kinds :-the Declination or, as it is generally called, the variation of the magnetized needle; the Inclination or dip of the needle, and the intensity of the earth's magnetic power.

441. The ordinary variation, or azimuth compass, is well known: the needle is supported near its centre of gravity, and is allowed to traverse horizontally on the point of a vertical pivot made of steel, and the box is furnished with plane sights, which may be placed in the direction of the meridian, or may be turned towards a terrestrial object, as the case may require. Compasses of a superior kind, like that of Colonel Beaufoy, differ from the others in having, instead of plane sights, a small transit telescope, by which the middle line of the box may, by the observed transits of stars, be placed accurately in the direction of the geographical meridian.

The usual dipping needle is a bar of steel which, before the magnetic quality is communicated to it, is balanced accurately upon its centre of gravity, where, by a horizontal axis of steel, terminating above and below in what is called a knife-edge, the needle rests, on each side, on the edge of an agate plate. With good needles there is an apparatus consisting of screws by which the centre of gravity and centre of motion are rendered coincident; this adjustment is made before the needle is magnetized by causing it to vibrate on the points of support, and observing that it comes to rest in a horizontal position; then, after reversing it on its axis, so that the uppermost edge of the needle becomes the lower, the needle is again made to vibrate, and alterations, if necessary, are made till the needle is found to settle horizontally in both situations. The needle thus prepared, and being duly magnetized, is placed in a plane coinciding with what is called the magnetic meridian (a vertical plane passing through a wellbalanced compass needle); when the position which it assumes indicates, by means of the graduated circle on whose centre it turns, the absolute inclination or dip of the needle, or the line of direction of the resultant of all the magnetic forces in the earth. On being made to vibrate like a pendulum, the number of oscillations performed in a given time affords one of the means of determining the intensity of terrestrial magnetism in the direction of that resultant.

The intensity of terrestrial magnetism in horizontal and vertical directions are resolved parts of the intensity in the

direction of the resultant, that is, in the direction assumed by the magnetic axis of the dipping needle. Thus HO being a horizontal line passing through the centre c of the needle's motion, in the plane of the magnetic meridian, and ns being the direction of the needle when subject to the force of terrestrial magnetism, so that the angle Hсn is the inclination or dip; on drawing nh perpendicularly to HO, the three lines nc, ch, nh will, respectively, represent the absolute intensity and its horizontal and vertical components: hence if f represent the absolute intensity, and d the dip, we shall have f cos. d for the horizontal intensity, and ƒ sin. d for the vertical intensity.

N

h

N'

Z

442. The dipping needle is not always so simple as that which has been described: in order to increase the facility of its vibrations, Mayer of Gottingen attached at the centre of gravity of the needle a wire perpendicular to its length, and in the plane of its vibration; this wire, which carries at its extremity a brass ball, may, by inverting the needle, be either above or below the latter, and the number of vibrations made in a given time may be observed in both positions of the needle. The intention, in separating the centre of motion from that of gravity, is to give the needle a power, resulting from the weight, to overcome the friction of the axis, and allow it, after having vibrated, to return with greater certainty to the same point on the graduated circle than if the centres of gravity and motion were coincident. In using the needle, the dip or inclination should be observed with the axis in one position, and again with the axis reversed, so that the upper edge may become the lower: and a mean of the two readings should be taken. Also, should the situation of the brass ball be such that its centre does not, when the needle is in a horizontal position, lie vertically above or below the centre of gravity of the latter, four such observations should be made, two with the poles of the needle in their existing state, and two others with the poles reversed. The reversion of the poles is effected by the usual method of magnetizing needles.

443. In order to obtain the correct dip from two observations, when the centre of gravity is alternately below and above the point of support; let ZONH be the vertical circle

in the plane of the magnetic meridian: let CN be the actual direction of the needle when a weight w is applied at the end of the wire cw perpendicularly to NC, and let cn be the direction which the needle ought to assume by the influence of terrestrial magnetism when the centre of gravity of the whole needle coincides with the point of support. Then, HO being a horizontal line, the angle HCn is the true inclination or dip (d), and HCN (=Cwb) the false dip (=d'), wb being a vertical line drawn through w to represent the weight of the ball w.

Now, an equilibrium must be supposed to exist between the weight at w and the force of magnetism acting at c (the centre of gravity of the arm NC); the former force causing the needle to turn about C towards CH, and the latter causing it to turn about c towards cz. Let the magnetic force acting at c be represented in magnitude and direction by em parallel to cn, and let fall mp perpendicularly on CN; also from 6 let fall be perpendicularly on cw. Then, by Mechanics, the force be being supposed to act at w in a direction parallel to be, and pm to act at c perpendicularly to CN,

now

and

mp (=

=cm sin. mcp=cm sin. NCn)=cm sin. (d— d'). When the needle is inverted, so that the weight w may be above it, as at w', let its position be CN': then HCn, being the true dip as before, the angle HCN' (=d") will be the false dip; and the resolution of the forces being similar in both cases, we have

- b'e' x cw' m'p' x cc' .... (B):

also b'e'w'b' sin. d'' and m'p' = c'm' sin. (d" —d).

Substituting the values in the equations (A) and (B), and cancelling the terms which by their equality destroy one another in division, there results

or sin. d cotan. d' cos. d cos. d again, dividing by sin. d, and transposing,

cotan. d" sin. d; or

cotan d'+cotan. d" 2 cotan. d:

thus, from the observed values of d' and d", that of d, the true dip, may be found.

In the " Transactions" of the Royal Society of Sciences at Gottingen for 1814, the following formula for the true dip d is investigated in the case of four observations being made with the needle and its poles in direct and reversed positions, as above mentioned.

Let d' d" be the values of the dip in a direct and a reversed position of the needle, as in the last case; and, after the poles are reversed, let d'", div be values of the dip in a direct and reversed position of the needle: then, putting

444. The place of the centre of magnetism in each arm of a balanced magnetized needle may be found precisely as the centre of gravity in any solid body would be found; and, if the needle be cylindrical or prismatical, that centre would be in the middle of the length of each arm: the centre of oscillation might also be found for a needle as it would be found for a common pendulum; and by the theory of pendulums, it may be shown that the intensities of magnetical attractions in different parts of the earth are inversely as the squares of the times in which a given number of vibrations are made, or directly as the squares of the number of vibrations made in a given time.

In making experiments with a needle, the number of vibrations made in a given time, and in an arc of a certain extent, must be reduced to the number which would be made in the same time in an arc of infinitely small extent: corrections should also be made for the buoyancy of the air; and the formulæ to be used for these purposes are similar to those which have been already given for the vibrations of pendulums by gravity.

E E

A variation of temperature affects the magnetism of a needle as well as its length; and a formula, depending on the length, similar to that which may be employed for a common pendulum, would not be sufficiently precise for the correction of the error arising from that cause. The method employed to find experimentally the co-efficient for reducing the time of making a given number of vibrations at a certain temperature to the time in which an equal number would be made at a standard temperature, consists in counting the number of vibrations performed in a given time by the needle when placed in a vessel within which the temperature of the air may be varied at pleasure. For this purpose the apparatus is placed in a vessel of earth, or a trough of wood, with a glass top; and this vessel is placed within another: between the two, cold water first, and hot water afterwards, is poured, in order to bring the temperatures to any convenient states, which may be indicated by a thermometer; care is, however, taken not to raise the temperature by the hot water higher than about 120° (Fahrenheit), lest the magnetism of the needle should thereby be permanently changed.

Now, let T, in seconds, be the time in which a needle makes any number (suppose 100) of vibrations in the vessel when the temperature is t, and T' the time of making an equal number of vibrations when the temperature is raised to ť;

then

t'-t T-T: 1° :

T-T

t-t'

and this last term is the increase, in seconds, in the time of making that number of vibrations in consequence of an increase of temperature expressed by one degree of the thermometer. If the value of this fraction be represented by m, then m (TT), in which 7' denotes a standard temperature, suppose 60° (Fahr.), and the temperature at which an observation was made, will express the increase or diminution due to the observed time of any number of vibrations, with respect to the time of making an equal number at the standard temperature. Consequently, if T be the observed time of making any number of vibrations, and T' the required time of making an equal number of vibrations at the standard temperature, we should have

T + M (T—T') = T'.

The magnetic condition of a needle ought to be ascertained at certain intervals of time, and allowance must be made for any variations which may be detected when observations at