In the Sperry compass no attempt is made to eliminate the latitude error at any particular latitude, the correction applied to the lubber line being solely relied upon to allow for it. In this compass, therefore, the latitude error is zero at the equator. At 50 deg. north or south it amounts to 2 deg., easterly and westerly respectively. A feature found in this type of gyro-compass of a connected nature calls, however, for mention at this point. This feature consists of mounting the pivots M N ([Fig. 19]), on which the bail swings, within excentric housings and graduating the edge of the housings with a scale of latitudes. In this way the pivots can be displaced to one side or the other of the vertical plane containing the axis H J by an amount proportional to the latitude. When the spinning wheel is at rest, this displacement makes the angle between the axle of the wheel and the plumb line through the centre of gravity of the bail a little less or a little more than a right angle, and in northern latitudes makes the north end of the axle dip below the horizontal and in southern latitudes rise above it. The scale is so graduated that the dip of the axle or its rise when the wheel is not running is just equal to the natural rise or dip which the axle would acquire at any given latitude with the wheel running and with the bail pivots in the mean position. As a result, when the compass is in service and the bail pivots are adjusted for the latitude of the station, the natural rise or dip of the axle leaves the axle horizontal, but deflects the bail weight from the vertical by the amount required to generate the correct degree of easterly or westerly precession.
Thus in the Sperry compass the axle, if the latitude bail correction is applied, is at all latitudes horizontal when resting on the north. Several advantages are thus secured, the chief being that the effect of any change in the speed of the spinning wheel or of a complete failure of the electric supply driving the wheel is greatly reduced or spread over a longer interval. Were the axle as well as the bail allowed to acquire the rise or dip proper to the latitude, the axle during a change of speed of the wheel would tend to deviate and develop an error which might prove misleading. If, however, the axle is not allowed to acquire the rise or dip appropriate to the latitude, the error introduced by a change in the speed of the wheel takes longer to manifest itself, and is reduced in magnitude. As it is difficult to guarantee that the voltage of the current supplied to the compass will not vary, this feature of the Sperry compass is undoubtedly of practical advantage.
CHAPTER IX
THE NORTH STEAMING ERROR
The source of error which we have just discussed affects the gyro-compass whether it is on land or on a ship. We have now to discuss certain errors which are only met with when the compass is mounted on board a moving ship.
The first of these errors to which we will refer is sometimes called the “north steaming error,” although it is equally associated with a due south course. Imagine the vessel on which the gyro-compass is fitted to be sailing due east along the equator. If its speed is, say, 20 knots it would, if it could, circumnavigate the globe in 45 days. Its velocity round the earth’s axis apart from the rotation of the earth is thus 0.000015 revolution per minute. As the speed of the earth on its polar axis is 0.0007 revolution per minute, the actual rate at which the gyro-axle is being carried round in space is 0.000715 revolution per minute. If the vessel is sailing due west its speed opposes that of the earth, so that the actual rate at which the gyro-axle is being carried round in space is 0.000685 revolution per minute. As compared with the same gyro-compass on land, the only effect of the ship’s speed on these courses is in the one case to increase the magnitude of the directive force and in the other case to reduce it, the increase and reduction both being quite small—about 2 per cent. actually. Sailing due east or west in latitude 60 deg. north or south, its speed would cause the vessel to circumnavigate the globe in 22½ days. On these courses in either of these latitudes, therefore, the directive force would be increased or diminished respectively by about 4 per cent.
Fig. 24. The North Steaming Error at 0 Deg. and 60 Deg. N.
If, now, the vessel starts at the equator and sails due north, its speed is at right angles to the speed with which the rotation of the earth is carrying the gyro-compass round in space. The speed of the ship—2026 ft. per minute—may be represented by A B ([Fig. 24]) and the speed of rotation of the earth—92,400 ft. per minute—by A C. The actual speed and direction in which the gyro-compass is being carried round in space is A D, and the actual axis about which it is being carried round is not the earth’s polar axis N S, but an axis N´ S´ at right angles to A D. The gyro-axle will settle, therefore, on the line N´ S´, and not on the true north and south meridian. The true north will be to the east of the indicated north by the angle N´ A N, which for the ship speed in question—20 knots—will be 1.25 deg. If the ship starting from the equator sails due south, the deviation will be towards the opposite side, the true north lying 1.25 deg. to the west of that indicated by the compass. If the course is neither due north or south nor due east or west, the deviation will have some intermediate value between zero and 1.25 deg., the true north lying to the east of the indicated on all courses with a northern component and to the west on all courses with a southern component.
If the ship is in latitude 60 deg. north, and is steaming north, its speed will carry it, as before, 2026 ft. northward per minute, as at E F, but, as its distance from the earth’s polar axis is now only half what it was at the equator, the earth’s rotation is carrying it round at only half the equatorial speed, namely, with a velocity E G of 46,200 ft. per minute. The compass is therefore being carried round in space with a velocity represented in magnitude and direction by E H—that is to say, it is being rotated not actually about the earth’s polar axis N S, but about an axis N´´ S´´ at right angles to the resultant velocity E H. The axle will therefore align itself parallel with N´´ S´´, and not with N´ S´. Thus in that latitude at the given speed the true north will lie 2.5 deg. eastward of that indicated by the compass. On north-easterly or north-westerly courses at 60 deg. north latitude the deviation will lie between zero and 2.5 deg., while on all courses with a southerly component the true north will be to the west of the indicated north by some amount between the same two limits. Our demonstration is not strictly accurate, for, arising from the rotundity of the earth, the speed E F of the ship is not really in the plane of the paper, but should be drawn inclined with the end F below the level of E. Accurate analysis, however, shows that the deviation arrived at by neglecting this fact is substantially correct. In the tables issued in connection with the early Anschütz compass the deviation at 20 knots due north or south in latitude 60 deg. N. is given as 2.5 deg., while those issued by the Sperry Company give it, by interpolation, as 2.41 deg.