Thus far the semicircular deviation has been spoken of as if it were easy to find, unchanging, and easily corrected if so required. But unchanging it is not.

You have already been told that the earth's horizontal force is greatest near the magnetic equator, and decreases when proceeding Northward or Southward from that line; also that the dip of the needle (and hence the vertical force) is the reverse of this,— being nil on the magnetic equator and increasing when proceeding Northward and Southward in the direction of the earth's magnetic poles, and what is more, with a different pole of the needle downwards in the two hemispheres.

Now the coefficients B and C, which give the semicircular deviation, are each made up of two components, viz., (1) the subpermanent magnetism of the hard iron, and (2) the transient magnetism induced in the soft iron by the earth's vertical force. The first produces a semicircular deviation inversely proportional to the horizontal force at place; the meaning of which is that, though there is no change of name, there is decrease in amount with increase of the earth's horizontal force, and vice versa. The second produces a semicircular deviation proportional to the tangent of the dip; the meaning of which is that not only is there change of amount decrease with decrease of vertical force, and increase with increase-but, on opposite sides of the magnetic equator there must be change of name. It does not, however, follow from this that the deviation as a whole must change its name, which will depend upon the relative proportion of subpermanent to transient induced magnetism.

When B and C are uncorrected, it is easy to understand that a deviation card has but a limited value, and that the change of deviation due to change of magnetic latitude requires to be constantly checked by observations of the heavenly bodies: and this remark applies with equal force to a compass where B and C have been corrected with permanent magnets, since it is impossible that these can compensate a changing element.

A soft iron mass and horizontal soft iron exert a wholly different influence on the compass from that hitherto described.

Note the effect of a soft iron ball on the needle when carried round the compass in the same horizontal plane. See Fig. 14.

At 1 the spherical ball of soft iron lies in the magnetic meridian, and North of the compass; it therefore, according to the law of like poles repelling and unlike poles attracting, produces no deviation, but the directive force of the needle is increased.

At 2 the sphere lies in the N.E. quadrant, it therefore, since the attraction is towards the right, gives E. deviation in that quadrant, and the directive force of the needle is increased.

At 8 the sphere lies East of the compass, and at right angles to the direction of the needle, where it gives no deviation, but still increases the directive force.

At 4 the sphere lies in the N.W. quadrant, it therefore, since the attraction is towards the left, gives W. deviation in that quadrant, and the directive force of the needle is increased.

With the sphere at 1, 2, 3 and 4a, the effect on the compass must be similar to that of the respective positions 1, 2, 3, 4; that giving no deviation at South and West, E. deviation in the S.W. adrant, and W. deviation in the S.E. quadrant.

* An iron sphere is really, as already indicated, slightly magnetic in the direction of the dip; and so must be elongated iron correctors; the ill tration nevertheless holds good.

To sum up

Soft iron in the horizontal plane of the compass invariably increases the directive force of the magnetic needle.

Soft iron in the horizontal plane of the compass gives no deviation at the four cardinal points, N., E., S., and W. by compass; but the other points in each of the four quadrants are affected as follows;-if the iron lies in a direction

between N. and E., it produces Ely. deviation

Two soft iron masses on opposite sides of the compass and in the same plane affect the needle to the extent of the sum of their mass and force. Two masses situated at right angles with each other increase the directive force to the extent of the sum, and produce a deviation equivalent to the difference, of their forces.

It remains to consider the effect of soft iron extending (athwartship, and fore and aft) in a horizontal plane, parallel with that of the compass, but under or over the compass.

As the ship's head is turned in azimuth the ends of any such iron (as for instance, the deck beams) change the character of their polarities, what had been previously n or red becomes blue, and what had been s or blue becomes n or red.

Hence the following results

When the ship's head is E. or W., the soft iron beam lies under the compass, extending in each direction

beyond it, and, like the compass needle, is in the magnetic meridian; the repulsion (of like poles) occurring in the meridian produces no deviation, but the directive force of the needle is diminished. Similarly, when the ship's head is N. or S., the soft iron lies East and West, and it produces no deviation, but still diminishes the directive force of the needle. See Fig. 15.

FIG. 15

When, however, the soft iron lies N.W. and S.E., it produces E. deviation in the N.E. and S.W. quadrants, and diminishes in each case the directive force of the needle. Fig. 16 shows the ship heading N.E.; the needle is deflected to the right of the dots (cor. mag. N. and S.) by the red and blue (n and s) poles of the beam, and consequently the deviation at N.E. is Easterly; and similarly through

out the quadrant, but differing in amount on different points.

Lastly, when the soft iron lies N.E. and S.W., it produces W. deviation in the S.E. and N.W. quadrants, and, as before, diminishes in each case the directive force of the needle. Fig. 17 illustrates the ship heading S.E.; the needle is here deflected to the left, and consequently the deviation at S.E. is Westerly.

Inasmuch as B and C are called the coefficients of the semicircular deviation, since they are connected FIG. 17.-HEAD S.E. with the compass as divided into two semicircles, so here, since the horizontal soft iron of the ship acts differently in different quadrants, the resulting deviation is said to be quadrantal.

It is also well to take note of the difference, in the effect on the compass, between the sphere of soft iron and the soft iron beams, &c.; the first, with attraction, increases the directive force of the needle; the second, with repulsion, diminishes the directive force; therein lies the method of correcting the quadrantal deviation.

The late Archibald Smith neatly put the effect of horizontal on on the compass as follows:

horizontal soft iron rod placed in front of and directed

towards the compass will, when the ship's head is N., E., S., or W. produce no deviation. When N.E. and S.W. it produces a deviation to the right hand or E., and when S.E. or N.W. a deviation to the left hand or W.; it therefore produces what is called the quadrantal deviation.

"A horizontal soft iron rod directed to the compass, but placed to starboard or port, will produce an effect of exactly the opposite kind, and would correct that produced by the first rod; but if the second rod, instead of being on one side, passes, as it were, through the compass, it would produce exactly the same effect as the first rod. The two rods will then conspire to produce the quadrantal deviation.

"A quadrantal deviation of the same kind will be produced if the first rod instead of being on one side of the compass passes through it, provided always that its force is less than that of the transverse rod." Hence

The quadrantal deviation, represented in the formula p. 740 by d = D sin 2 z + E cos 2 z, arises from horizontal induction in soft iron, and, in an iron ship, it is not alone the horizontal soft iron near the compass that gives it, but all connected with the hull, keel, frame and fittings trending athwartship, fore and aft, and diagonally, over, under, and in the plane of the compass; in addition to which, in a steamer, there are the engine, screw-shaft, &c. Some of this iron gives a positive, and some a negative, quadrantal deviation, but the difference of the two is, in the majority of cases + D, it being rare to find D; and from the fact that the positive deviation is accompanied with a diminished directive force the effect of the transverse iron most probably preponderates.

The coefficient D produces the greatest error on the N.E., S.E., S.W., and N.W. points of the compass, and + D. in the formula gives or E deviation in the N.E. and S.W. quadrants, and or W. deviation in the N.W. and S.E. quadrants. Fig. 18.

D is the reverse of the foregoing, giving + or E. deviation in the N.W. and S.E. quadrants, and - or W. deviation in the N.E. and S.W. quadrants. Fig. 19.