To appreciate the significance of this vertical rise of the north end B of the axle, let us consider the condition of the compass as it is passing through the even keel position. The elevation of the end B out of the horizontal plane causes the weight S to swing forward towards the north, and therefore to apply a turning moment to the spinning wheel about the axis E F. This turning moment will tend to bring the end B down again to the horizontal, but, as we know, the actual motion produced will be a precession about the axis H J, the end B moving westwards. Looking at [Fig. 34], it will thus be seen that the net effect of the rolling of the ship is to deviate the axle of the compass in the direction shown at V—that is to say, in the direction required to set the plane of the spinning wheel parallel with the plane of the rolling by the shortest possible course—in our example by a rotation westward through 45 deg. With the axle so deflected the earth’s rotation, of course, calls a directive force into play, tending to restore the axle to the north and south line, but if the ship is rolling violently the deviating force will be much stronger than the directive force until a very considerable angle of deflection is reached. When the balance is struck, the axle settles down with a steady deviation towards the west, which will remain constant as long as the rolling is maintained. In practice the violence of the rolling varies almost from roll to roll, for it represents a conflict between the natural period of rolling of the ship and the period of the waves. As a consequence, the deviation of the compass varies somewhat during the rolling, but it is always westwardly if the course is in the north-west quadrant.
A little consideration will show that if the ship is steaming towards the north-east the additional kick on the weight S ([Fig. 33]) at the port out position will be towards the north and at the starboard out position towards the south. The end B of the axle is therefore precessed vertically downwards instead of upwards, and as a result the deviation of the axle is eastwardly. In general, if the ship is steaming on any course in the north-west or south-east quadrant, the deviation caused by her rolling will be towards the west. It will be towards the east if the course is in the north-east or south-west quadrant. The effect of pitching on a quadrantal course is to cause a deviation of the axle in the direction opposed to that of the deviation caused by rolling, so that if the vessel be both rolling and pitching, the deviation is somewhat less than it would be if rolling only had to be considered.
It may perhaps be thought that the quadrantal error is an effect produced by the double gimbal mounting of the compass, and that had we adhered to our simple model, as shown in [Fig. 32], it would not arise. This is not so. If [Fig. 32] be taken as representing, after the manner of [Fig. 33], the north view of the compass on a ship steaming due north-west, it will be seen that the southern kick at the port out position causes the axle to precess in the direction K and the northern kick at the starboard out position in the direction L. Resolving these movements as before, we see that, while the horizontal components N Q again cancel, the vertical components M P are, as in [Fig. 33], cumulative in effect, but this time they result in the end B of the axle moving downwards, and therefore finally cause it to precess eastwards instead of westwards, as before. The quadrantal error is therefore not eliminated, but merely reversed in direction by adopting the simpler mounting for the compass.
CHAPTER XII
THE ELIMINATION OF THE QUADRANTAL ERROR
From our description of the cause of the quadrantal error it should be clear that it is of a variable erratic nature, or at least that, unlike the latitude and north steaming errors, its magnitude cannot be forecast from a knowledge of the ship’s speed, course, latitude, or other factors. Its direction is determined by the direction of the ship’s course, but its amount is settled by the violence of the rolling and pitching, and cannot therefore be calculated and tabulated in a practically useful way. It follows, therefore, that to get rid of the upsetting influence of the quadrantal error we cannot resort to “correcting” the compass readings for it, but must entirely eliminate it.
In the early (1910) Anschütz compass there were no means of eliminating the quadrantal error, for the existence of the error, or at least the importance to be attached to it, was not at first recognised. The compass, we believe, showed errors from this cause of as much as 20 deg. to 40 deg. As a result, within a very short time the design was discarded, and what amounted to an entirely different compass was substituted for it. The 1912 Anschütz compass will be briefly described later on, but here it may be said that the quadrantal error in it is eliminated by adding two more gyro-wheels to the sensitive element. The theory of this compass is not very easy to understand, so that it will be best if we explain first how the quadrantal error is eliminated in the Sperry and the Brown compasses.
The early Sperry, like the early Anschütz compass, was open to the full action of the quadrantal error. In the form now in use, however, it is prevented from taking effect by controlling automatically the position of the excentric pin connecting the weight or “bail” to the gyro casing. In the Sperry compass, as we know, the weight S ([Fig. 35]) is not hung from the inner supporting ring or its equivalent, but from the follow-up or phantom ring, its pendulous effect being communicated to the casing and thence to the spinning wheel through the excentric pin A. The kicks of the weight at the out positions during the rolling of the ship are also transmitted through the pin to the casing and wheel inside it.
Fig. 35. Sperry Compass on N.W. course.