82.

Examination of the heeling-disturbance, and

remarks on the possibility of correcting it.

The quotient of the deviating force by the terrestrial directive force, on which the needle's deviation will

depend, will be (remarking that

N.cos

V

H

= tan dip)

- sin h x N. cos 24+ (R tan dip +

No simple rule can be given for the position of the ship's head which will make the bracket vanish: cos A will be determined by a quadratic equation.

The first term has for factor N. Now in examining Articles 68 and 69, it will be seen that Nis that effect of induction which puts on the appearance of a constant magnetic force parallel to the ship's keel. The correction of N by a magnet is of no avail in reference to the formation of the first term in the last article. But correction of N by a mass of iron subject to the same induction as the rest would destroy the term in the last Article. In the ordinary place of the steering-compass in a merchant-ship, it may happen that this term is negative and large, principally as affected by the magnetism of the sternpost: and the treatment of the heeling error is very unmanageable. There appears to be no way of determining the value of the bracket in different azimuths, except by inclining the ship in different azimuths. Here we see a great advantage in the use of Mr. Rundell's vertical bar in front of the compass. This,

which is subject to induction, if so adjusted as to correct N when the deck is level, will also correct Nin the heeling term: and the part depending on cos 24 will disappear. In ships where the steering compass is much nearer the middle of the ship, N will usually be small. Supposing then that N is put out of consideration, the term that remains is

Both terms of the bracket become large in high magnetic latitudes, where the dip is large and H is small. If K be positive, or tending to draw the red end downwards (as will hold in the subpermanent magnetism produced by the operations in the process of building iron ships in north latitudes), the second term, which is the larger, will be negative; and, remarking the sign of cos A, when the ship's head is north of the east-and-westline, and the ship heels to starboard, the red end of the needle will be drawn to the west: when the ship's head is southerly of that line, the red end will be drawn to the east. Both cases are included in the seaman's rule "the red end of needle deviates to the windward side." In southern magnetic latitudes, it is the blue end which so deviates.

When the ship's head is east or west, that is, when A=90° or 270°, the heeling force vanishes: it is maximum, with different signs, when the ship's head is north or south, that is, when A=0° or = 180°.

The circumstance that the deviating force is expressed

by a multiple of sin h x cos A enables us to correct it by application of a magnet. In Article 51, Figure 41, putting h for 4, that is to say placing a magnet in the ship which shall be vertical when the ship is on even beam and which will have the inclination h when the ship has the heel h, we found that its horizontal force on the red end of the needle is

When the ship's head is north, or A=0, this force acts transversely to the needle, and is wholly available (and so, with changed sign, when the ship's head is south). But in any other position of the ship's head, the force acts obliquely on the needle, and must have the factor cos A. The efficient force is therefore

This follows the same law as the force which we wish to neutralize and therefore, by proper choice of the poles of the magnet, and by sliding it up and down parallel to the ship's masts, a position may be found in which it will entirely correct the heeling-error.

Unfortunately, the terms included in the bracket both depend on geographical position, and the correction which is valid in one part of the earth will not be valid in other parts. The correction of the heeling-error deserves, more than any other point, the attention of practical magnetists.

SECTION XI.

ON THE CONTINUOUS REGISTRATION OF SMALL CHANGES IN TERRESTRIAL MAGNETISM.

83. General principle of photographic self-registration now usually adopted. Distinction of the magnetic elements which are to be registered, and appropriate positions of the recording apparatus.

The object to be attained is, to make an impression depending on the position of some part of the apparatus, without contact, or friction, or mechanical resistance of any kind. Nothing is so suitable for this purpose as photography. If from a minute source of light (as a lamp shining through a very small aperture) light falls upon a concave mirror, or upon a plane mirror assisted by a convex lens, which is firmly attached to a moving part of the apparatus; then a spot of light (the optical image of the small source of light) may be formed at a proper distance, and the motions of the moving part of the apparatus will produce corresponding motions of the

spot of light; which, if received on photographic paper, may be made to impress a permanent register of the position of the spot, from which the positions of the moving apparatus may be inferred.

It is now necessary to explain how the time is registered in combination with the register of the spotmovement. For this purpose, the photographic paper must be attached, either to a plane board which is moved by clock-work uniformly in its plane in the direction at right angles to that in which the motions of the spot occur, or to a barrel which is made to rotate uniformly and whose axis is parallel to the motions of the spot. With either of these, the motions of the spot leave on the paper a photographic curve, whose abscissa represents time at a given length for an hour, and whose ordinate represents a quantity proportional to the instrumental movement which causes the motion of the spot. If we interrupt for a short time the beam of light (which will cause an interruption in the photographic curve), noting also the clock-time, we can mark off accurately the hours, &c., on the time-scale. And if we possess any independent methods of observing the position of the moving apparatus at definite times, we can, by adjusting the scale of ordinates to the spotposition at those times, make it available for every other time.

The elements which most conveniently represent the state of terrestrial magnetism as acting at any one geographical point, and whose changes it is desirable to record, are,—the position of the free magnet, the small changes