Read Ebook: The Gyroscopic Compass: A Non-Mathematical Treatment by Chalmers T W Thomas Wightman

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It is also to be noted that while the amplitudes are decreased in the manner indicated the periods of the swings are not being made less. In an ordinary pendulum the period, as we have said, depends solely upon the length and--within quite wide limits at least--remains the same whatever be the angle to which we originally deflect the bob. We should therefore expect that if the swings are "damped" in the way shown at B , the period of each swing would be the same and equal to that of the undamped swings represented at A. Actually the period of a damped vibration is always somewhat greater than that of the same system vibrating freely, for by robbing the pendulum of some of its velocity at each swing we are virtually causing the bob to pass through the resting position with the velocity of a free swinging pendulum of greater length and therefore of increased period. The increase in the period of the damped pendulum over the same pendulum when undamped is determined by the strength of the damping means employed, or, in other words, by the percentage by which we reduce the velocity at each swing.

In the early Ansch?tz compass the period of vibration at the equator without damping was, as we have stated already, about 61 minutes. With its damping device in action the period of the compass at the equator became approximately 70 minutes. In later designs of gyro-compasses the period of the damped vibration is deliberately made 85 minutes or thereabouts. A practical advantage--to be explained later--is secured by adopting this particular value. It is the period which a simple pendulum would have if its length were equal to the radius of the earth--4000 miles or so.

The damping force required is, as we have said, one which at all times is proportional in magnitude to the velocity of the bob--or what is the same thing, to the angular velocity of the pendulum as a whole--and which at all times acts to oppose the motion of the bob. Metallic friction--say, at the supporting axis of the pendulum--it would bring the motion to rest sooner or later, would not provide a satisfactory damping force, for solid friction is independent of the rubbing velocity, at least at low speeds such as we are here concerned with. The damping force provided by it being constant, would not be automatically adjusted to the velocity of the bob. It would vanish, it is true, when the bob was at rest, but as soon as the slightest vibration set in it would spring up to its full value straight away and would preserve the same value throughout a large swing as throughout a small one. In any event the presence of metallic or other solid friction at the point in the gyro-compass corresponding to the axis of the pendulum--namely, at the bearings of the vertical axis H J--cannot be permitted, and must be eliminated to the utmost possible degree if the directive force is to be sufficient to control the movement of the sensitive element.

Fluid friction, on the other hand, would provide a satisfactory damping force, for fluid friction is proportional to the velocity, at least at low speeds. A pendulum vibrating with its bob in a vessel of water or the floating card of an ordinary magnetic compass is satisfactorily damped by fluid friction. In the gyro-compass, however, the motion to be damped is, as we have seen, an exceedingly slow one, slower in fact than the small hand of a watch if the deflection of the axle from the meridian is initially less than 11 1/2 deg. east or west. A fluid damping force would be proportionately low, so that without making the damping elements of enormous size the force derived would be insignificant and next to useless for practical purposes. As an illustration of this statement it may be remarked that in the early Ansch?tz compass the sensitive element was virtually floated in a bowl of mercury. Yet the drag of the mercury, the velocity of the vibration being so small, did not measurably reduce the amplitudes of the vibration during observation extending over several hours. This example is not quite a good one, however, for the friction at the surface of a body immersed in mercury would appear to be not of the fluid description, but of the solid type.

Solid and fluid friction being thus ruled out, at least as direct means of providing the required damping force, we have to find some other method of applying it. It is, or should be, clear that in whatever way the damping force is applied it should originate within the sensitive element itself. If it originates outside, then its transmission to the sensitive element cannot, in view of the fact that its origination, growth, and decay are to be controlled by the motion of the element, be effected in any conceivable way without the introduction of some material connection between the element and the outside source of the force. Such a connection can only be made frictionless if the outside source moves in exact unison with the sensitive element. If it does so move it clearly ceases to be an outside source and becomes really part of the sensitive element itself. This consideration suggests generating and applying the damping force gyroscopically by the exertion of some suitable action on the spinning wheel itself.

THE DAMPING SYSTEM OF THE ANSCH?TZ COMPASS

In the preceding chapter we demonstrated the necessity for damping the horizontal oscillatory movement of the gyro-compass axle and discussed the nature of damped vibrations in general. We now turn to describe the damping means provided in each of the practical forms of gyro-compass so far evolved.

The wheel, running at 20,000 revolutions per minute, although it is quite plain, has a powerful blower-like action. On one side of the casing an orifice D is formed for the inlet of air, and on the periphery below an outlet duct K, directing the air blast tangentially away from the casing, is provided. The exact value of the pressure of the blast in the early Ansch?tz compass is not known to us, but in the Brown compass, wherein a similar blast is developed, the wheel, running at 15,000 revolutions per minute, gives an air pressure equal to some 3 in. of water.

The mouth of the outlet duct K is partially closed by a plate L fixed at the end of a pendulum arm suspended frictionlessly, or practically so, from some convenient point on the casing, so that when the casing turns on the vertical axis H J the arm and plate turn with it. The pendulum arm is carefully balanced in such a way that when the axle of the spinning wheel is horizontal the plate L exactly divides the orifice K, leaving equal passages for the air blast on each side. In this condition the two passages M N being equal in area, the air blast is divided by the plate into two streams of equal volume and momentum, so that if their free discharge is not influenced by surrounding objects their reactions on the casing, one on the one side of the vertical axis H J, the other on the opposite side, will be equal.

Let the compass be deflected until its axle points east and west, the end B being towards the east. Then, as we have seen, the tendency of the axle to remain parallel with its original position, combined with the rotation of the earth, will cause the axle to assume an inclined position relatively to the earth's horizontal surface. Gravity acting on the pendulous weight S as thus displaced from the plumb line will, as we know, set up a precession about the vertical axis H J, so as to cause the end B of the axle to move towards the north. When, however, the axle tilts in this manner about the horizontal axis E F, the pendulum plate L, hanging freely, remains in the plumb line. Consequently the equal areas M N become unequal, as at P Q, the larger P being towards that end of the axle which has tilted upwards, namely, the north-seeking end B. The reaction on the casing of the portion of the air blast issuing from P is now greater than that of the portion emitted through Q. This inequality results in the application to the sensitive element of a force acting about the vertical axis H J. The reaction of a jet of air or water or other fluid being opposed to the direction in which the jet is issuing, the force applied to the casing is such as to drive P into the plane of the paper and to bring Q out of it--that is to say, to tend to rotate the casing on the vertical axis in the direction of the arrow R.

The reaction applied to the sensitive element by the air blast thus fulfils one requirement of a satisfactory damping force; its effect at all times is opposed in direction to the direction in which the axle is moving. The second requirement is that the magnitude of its effect should always be proportional to the velocity with which the axle is moving.

The assumption here made is, we believe, substantially justified if the angle of tilt is never very great. In actual practice it is always small. Various considerations, however, suggest that the reactions of the two jets P Q are not equivalent strictly to the reaction of a single jet through an orifice R of constant area. Thus from geometrical considerations we can show that the sum of the areas P Q is not equal to the sum of the areas M N. Again, the total weight of air drawn in per minute through the orifice D may be constant, and therefore the total weight of air delivered per minute through the combined openings P Q may be unaffected by the tilt. But the ratio in which the total volume divides itself between the two openings P Q and the velocity through each certainly vary with the tilt. A peculiar practical phenomenon also has to be considered in this connection. In the 1910 form of Ansch?tz compass the peripheral speed of the spinning wheel was 500 ft. per second, or 340 miles an hour. The air friction at this speed was so very great that after the wheel had been run a few thousand hours its surface was found to be noticeably smoother than it was when the wheel left the grinding machine on which it was finished. As a result of this polishing effect, we should expect that even though the speed of the wheel remained perfectly constant, its blower-like action would decrease somewhat until the compass had been in use for a certain length of time. If the blower action does so decrease the magnitude of the air blast reaction on the sensitive element at any given angle of tilt must diminish with time. We do not know whether the diminution would be sufficiently great to introduce a serious error in the reading of the compass.

Taking the assumption to be correct, at least for small angles of tilt, we have next to study how the angle of tilt varies as the axle swings from the east side of the meridian over to the west and back again.

An actual curve taken from an Ansch?tz compass while it was settling down on the meridian after the gyro-axle had been deflected nearly 45 deg. to one side is given in Fig. 18. The crests A B C occur at 70-minute intervals--the period of vibration of the system when damped, as we have already stated. The oscillations are, it will be seen, damped down very effectively, being entirely eliminated in less than three hours in the course of the third complete vibration. It follows that if the wheel of a gyro-compass is started spinning with the axle pointing elsewhere than due north, several hours must be allowed to elapse before readings are taken from the card. During the period of settling down, and especially during the later portions, the movement of the axle towards its resting position is extremely slow, and cannot be detected by direct observation. It can, however, be inferred from the readings of a spirit level placed on the card, for, as we have seen, the oscillations are accompanied by a tilting of the wheel case on its horizontal axis.

THE DAMPING SYSTEM OF THE SPERRY COMPASS

In the Sperry gyro-compass the damping system adopted is mechanically of a very different nature from that used in the early Ansch?tz, although the theoretical principle of action in both cases is the same. The Sperry method rules out the employment of air or other fluid in any shape or form as a means of generating, applying, or transmitting the damping force, the reason being that if air or other fluid is relied upon, the damping force--or so the Sperry Company holds--will not act in strict unison with the oscillations, but will invariably lag behind.

The details of the Sperry method are indicated in a diagrammatic manner in Fig. 19. As in the Ansch?tz compass, the spinning wheel revolves in a casing which, being provided with trunnions E F, takes the place of the inner horizontal supporting ring of our elementary gyroscope. Since no blowing action is required of the wheel in this compass the casing, in order to reduce the expenditure of power required to drive the wheel, is exhausted of air until a vacuum of not less than 26 in. is registered on a gauge which forms a permanent fixture on the casing. The exhaustion is effected by attaching a hand-operated vacuum pump to a nipple on the casing. The vacuum produced at one exhaustion remains effective for at least a month under proper treatment. That it is very well worth while exhausting the casing, if the general design of the compass permits it, is shown by the fact that in the 1910 Ansch?tz compass over 95 per cent. of the work done by the motor driving the spinning wheel was spent against windage and air friction.

The outer ring G within which the casing is carried is, as before, mounted on a vertical axis H J. A second outer ring K--or "phantom ring," as it is called--surrounds the ring G, and is mounted co-axially with it. While the ring G, as before, moves along with the wheel and its casing relatively to the square frame under the influence of the directive force, the ring K is caused to follow it up in exact agreement by means of a small electric motor, the pinion of which engages with a gear wheel L on the upper trunnion, the current to the motor being automatically controlled by the movement of the ring G. The compass card may be regarded as attached directly to the top face of the gear wheel. A second pinion gearing with the wheel L can be arranged to transmit the reading of the card to any number of repeater compasses stationed elsewhere.

So far the arrangement of parts is exactly similar to that which would be obtained in our simple gyro-pendulum system if the stirrup of the pendulous weight were not fixed rigidly to the inner horizontal ring, but were swung freely on the pivots E F. It can be brought into complete identity with the arrangement of our simple system if the pendulous weight S or "bail," as it is called by the makers, be provided with a pin at its mid point to engage with a hole in the periphery of the casing. The system, as thus arranged, would merely be a distinctly complicated mechanical variation of our simple gyro-pendulum arrangement, and, as a compass, would be open to the same practical objection, namely, the persistence with which any oscillation of the axle, once set up, would continue. The vibrations would, in fact, be quite undamped.

The generation and application of a satisfactory damping force is accomplished in a very simple, yet beautiful and really ingenious, manner by displacing the pin connecting the bail and the casing from the mid position to some position lying eastwards of the vertical axis H J, as shown at Q.

It is to be noted that the excentric pin in the Sperry compass is displaced towards the east when the axle is resting on the meridian. If it were displaced towards the west the force applied about the vertical axis would be reversed in its effect, and would tend to increase the oscillations of the sensitive element and not to damp them, as is the intention.

THE DAMPING SYSTEM OF THE BROWN COMPASS

In both the Sperry and the early Ansch?tz compass the natural oscillation of the sensitive element about the vertical axis is damped by applying a retarding moment to the element about this same axis, the strength of the retarding moment being at all times proportional to the velocity with which the element is moving in the course of its vibration. The opposition exercised by the retarding force is not, however, a direct one. The motion of the sensitive element arises from the fact that the spinning wheel, the axle, and the pendulous weight are tilted about the horizontal axis E F. The retarding force is applied about the vertical axis, not because that is the axis on which the sensitive element is oscillating, but because a force so applied produces a movement about the horizontal axis tending to wipe out the tilt and so eliminate the cause of the oscillation.

An alternative method of damping the oscillation is possible. The effectiveness of the pendulous weight may be damped by virtually reducing the weight of the pendulum bob instead of reducing the tilt at which it is acting. In Fig. 22 the wheel of a gyro-pendulum system is shown tilted. The weight S is trying to turn the wheel on the horizontal axis E F in the direction R, and as a consequence is causing precession about the vertical axis H J in the direction T. Instead of attempting to damp this precession by applying a force about the vertical axis so as to reduce the tilt, we might virtually reduce the weight S by applying an upward force W at the end B of the axle, or, what is the same thing, a downward force V at the other end. Such a force, if it were acting alone, would tend to turn the wheel in the direction opposed to that of the arrow R, and would consequently cause the wheel to process on the vertical axis in the direction opposed to that of the arrow T. Acting in conjunction with the weight S, the force W would thus damp the natural motion by endeavouring to produce a counter precession of the wheel about the vertical axis.

This alternative method of damping the oscillations is adopted in the Brown gyro-compass. The mechanism of the Brown method is shown diagrammatically in Fig. 23. The wheel, as in the early Ansch?tz compass, runs in an enclosing case, and acts as a blower, developing a pressure of about 3 in. of water. At each side of the casing a bottle L, M is attached to the housing of the axle. A pipe N connects the bottoms of the bottles, while a second pipe P joins their upper ends. At its mid point the pipe P is interrupted, and a box Q is inserted in the gap. This box, as shown separately, is open on the underside, and is provided with a central partition. The air from the casing is delivered through the hollow trunnion F, and passes upwards into the box Q from the orifice R.

When the axle is horizontal the air blast entering the box Q is divided into two equal portions by the central partition, and exerts an equal pressure inside the bottles. These two bottles are half-filled with oil, which under the equal air pressures and the horizontal configuration of the system lies at an equal level in each bottle, and does not therefore unbalance the sensitive element on the axis E F. If, however, the axle tilts the balance is disturbed. Thus if the end B rises the box tilting with the wheel will assume some such position relatively to the nipple R--which is free of the trunnion F--as that shown at T. The central partition will divide the air jet unequally, and a greater pressure will therefore be exerted inside the bottle L than in the bottle M. Thus the oil level in L falls, while the oil level in M rises. The difference in the weights of the two bodies of oil acts as a turning moment tending to rotate the casing about the horizontal axis E F in the direction U--that is to say, in the direction opposed to that in which the pendulum weight S is trying to turn the casing. Since the pendulum weight causes precession about H J in the direction V, the weight of the unbalanced oil will cause or tend to cause precession about H J in the reverse direction.

As the excess of pressure in either bottle varies with the ratio in which the central partition of the box Q divides the air blast, and as that ratio varies with the angle of tilt, it follows that the opposition of the applied precession increases with the angle of tilt, and therefore with the rate at which the sensitive element is turning on H J under the influence of the pendulum weight S. The system therefore fulfils the requirements of a satisfactory damping method.

It may be noted that were the air blast and the box Q suppressed and the pipe P made continuous, a tilt of the axle would cause oil to flow from one bottle to the other in the endeavour of the liquid to preserve its surface horizontal. This flow might be constricted by means of a valve in the pipe N, and would then serve to damp the oscillations, for the arrangement would constitute virtually an oil dashpot. This plan would not prove satisfactory in practice, because the tilts which are attained are so small that the amount of oil flowing between the bottles would be insignificant. Further, the flow would almost certainly lag behind the movement to be damped. The application of the air blast to the surface of the oil greatly increases the rate of flow of the oil and correctly synchronises it with the tilt. The extent to which the damping effect is allowed to act on the system can be regulated by means of a needle valve in one of the bottles, which valve is made to control the orifice in the bottom of the bottle through which the pipe N enters.

THE LATITUDE ERROR

Having explained the necessity for damping the horizontal vibrations of the gyro-compass axle and how the damping force is generated and applied in the Ansch?tz, Sperry, and Brown compasses, we are now in a position to discuss the various errors to which the gyro-compass is open and how those errors are in practice eliminated, reduced, or allowed for.

The first error to which we shall turn our attention is that known as the latitude error. This error is a direct consequence of the necessity we are under of damping the horizontal vibrations of the compass axle.

It will be recalled that in any latitude other than the equator the compass rests on the north with a slight tilt up or down of the axle, the tilt increasing progressively as the poles are approached and being upwards in northern latitudes and downwards in southern. The tilt acquired in any latitude is perforce and automatically just sufficient to precess the axle westwardly or eastwardly at the rate required at that latitude to keep the axle on the north once it has found it.

Let us suppose, then, that a compass of the early Ansch?tz type is stationed in some degree of northern latitude. The axle in acquiring the appropriate tilt will clearly disturb the equilibrium between the two sections of the air blast. As the axle tilts its north end B upwards the north section of the air blast will enlarge and the southern diminish in area. Thus the tilting of the axle brings into play an air blast reaction which is applied as a moment tending to turn the sensitive element about the vertical axis H J in such a way as to make the north end move eastwardly. The actual movement produced will, in accordance with the fundamental rule, be a precession of the axle about the horizontal axis, the end B going down. Thus the tilt upwards of the axle required for the correct working of the compass is opposed. It is not allowed to acquire the full value which it should have, but instead stops at the point at which a balance is struck between the upward moving tendency of the axle resulting from the earth's rotation and the downward moving tendency caused by the uneven air blast reaction. The westerly precession of the axle about the vertical axis is now that arising from the reduced angle of tilt, and is less than the rate required to keep the end B pointing to the north. The resulting deviation is known as the latitude error. Its magnitude depends upon the latitude and upon such factors as the speed of the wheel, its efficiency as a blower and other items incidental to the particular design of the compass.

In the Sperry compass the latitude error arises from an exactly similar cause. Thus the tilt of the axle is transmitted through the excentric pin to the casing as a moment about the vertical axis H J, tending to make the north end of the axle move over to the east, and therefore causing the axle to precess vertically downwards until the position of balance is reached.

In the Brown compass, on the other hand, it is claimed that there is no latitude error. Thus when in northern latitudes the north end of the axle tilts upwards under its unsatisfied desire to set itself parallel with the earth's polar axis, the air blast is divided unequally between the two partitions of the box. Excess pressure is exerted inside the damping bottle attached to the northern face of the wheel casing, and as a result an excess of oil accumulates in the damping bottle on the south side. The weight of the excess oil applies a turning moment to the spinning wheel about the horizontal axis, and tends to lift the north end of the axle upwards in opposition to the pendulum weight, which tends to turn it downwards about the same axis. Thus in this compass the natural tilt of the axle is not interfered with by the action of the damping arrangement, for that action is applied about the horizontal axis E F, and not, as in the Ansch?tz and Sperry compasses, about the vertical axis H J. The damping action in the Brown compass is virtually equivalent to a subtraction from the weight of the pendulum bob, and is not applied, as in the other compasses, to the reduction of the tilt of the axle. It tends, therefore, to reduce the natural rate of westerly precession required at the given latitude to keep the axle on the north. Actually, however, the tilt acquired by the axle will take cognisance of the reduction in the weight of the bob caused by the weight of the excess oil. The north end of the axle will rise until the effective moment of the bob--that is, the moment due to its own actual weight less the moment due to the excess oil in the southern damping bottle--is such as will automatically generate the required rate of westerly precession for the given latitude.

In the Ansch?tz and Sperry compasses the latitude error can be allowed for by shifting the position of the lubber line relatively to the ship's longitudinal centre line in accordance with calculated tables of the error. The exact value of the error depends upon the design of the compass, but in both types it increases with the latitude. Analysis shows that--at least in the early Ansch?tz compass--the latitude error may be neglected if the change of latitude is less than 10 deg. In the Sperry compass, as we shall see presently, the movement of the lubber line to correct the latitude error is effected by a very pretty piece of mechanism, which also can control the position of the lubber line to allow for a second error to which the compass is open, to wit, the so-called "north steaming error."

In some respects as an alternative to moving the lubber line, the latitude error may be completely eliminated for a particular latitude--the latitude of most frequent use would naturally be chosen--by attaching a small weight to the north side of the wheel casing. In the early Ansch?tz compass such a weight was provided as indicated at T in Fig. 16. This weight and its position were so chosen that at 50 deg. north of the equator its moment about the horizontal axis E F, when the axle of the compass was horizontal, was just sufficient to supply to the wheel the amount of westerly precession required to keep the axle pointing to the north. The axle being horizontal in that latitude, the air blast was equally divided by the pendulum shutter, and as a result the rate of westerly precession produced by the weight T was not affected by the existence of the damping system. At other latitudes, of course, the latitude error arose, and at the equator--where ordinarily there should be no latitude error--and south of the equator, the error became worse than it would have been without the addition of the weight, unless the weight and its position were adjusted. With the compass corrected for 50 deg. N. latitude the error had the following values:

Latitude Error 60? N. .6? E. 50? N. Zero 40? N. .5? W. 20? N. 1.1? W. 0? 1.6? W. 20? S. 2.1? W. 40? S. 2.7? W. 60? S. 3.8? W.

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 , 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.

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 22 1/2 days. On these courses in either of these latitudes, therefore, the directive force would be increased or diminished respectively by about 4 per cent.

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 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 Ansch?tz 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.

It will be seen that this error is a natural one--that is to say, it is not caused by any peculiarity in the design of the compass in use. The table of deviations on various courses, at various speeds, in various latitudes, compiled for one type of compass would be equally applicable to any other design. In the case of the early type of Ansch?tz compass the "north steaming error" was corrected solely by means of such tables--that is to say, to find the exact bearing on which the ship was sailing the compass was read, and from its reading there was subtracted, or to it there was added, arithmetically, the appropriate figure taken from the tables, the uncorrected reading being a sufficiently accurate indication of the true course to permit it to be assumed as the true course for the purpose of extracting the correction from the tables.

In the Sperry design the use of similar tables in a similar way is permissible and is provided for. In addition, however, provision is made whereby the tables may be entirely dispensed with and the correction applied by moving the lubber line relatively to the ship's fore and aft direction. In the case of the early Ansch?tz compass the lubber line could be moved through 4 deg. on each side of the position in which it was parallel with the ship's fore and aft centre line. This movement was, however, for the purpose of correcting the latitude error, and not the north steaming error. In the Sperry compass provision is made for moving the lubber line so as to correct for both errors. The latitude error depends upon the design of the compass and the latitude. The north steaming error is independent of the design of the compass, and is determined by the speed of the ship, the latitude in which it is sailing, and the course which it is following. Latitude thus comes into both errors, being the sole variable causing one, and one of the three variables causing the other. It is eliminated simultaneously for both errors, by operating one dial. A second dial is set to suit the speed of the ship, while the third factor in the north steaming error, the bearing of the ship's course, is automatically brought into the movement of the lubber line by means of an inclined ring carried round with the compass card.

A diagram of the Sperry correction mechanism is given in Fig. 25. The lubber ring on which the lubber line is engraved is shown at A. The latitude corrector dial B is mounted to rotate about its centre and to read against a fixed scale. It is slotted radially to engage a pin C on a rod D E, one end of which can slide in a fixed guide F, while the other is pivoted to a link E G pinned at H to the lubber ring. If the end G of this link be imagined pivoted to some fixed point it is clear that rotation of the dial B will communicate a corresponding rotation to the lubber ring. The proportions of the parts and the positions of the pivots and pins are such that by setting the dial to the latitude in which the vessel is sailing the lubber ring is rotated through the angle by which the local latitude error causes the gyro-axle to deviate in its resting position from the true north and south direction.

If the end G of the link E G were pivoted, as we have supposed it to be, to some fixed point, then the latitude Error could be applied by itself to the lubber ring. It is not, however, so fixed, but is pivoted to a link, the end J of which carries a pin working in a curved slot extending from the centre of the speed corrector dial K to its edge. The radius of this curved slot is struck from the point G as centre. It follows, therefore, that with the speed corrector dial in the position shown the end J of the link G J may be fixed at any point in the curved slot without affecting the position of the point G. If, however, the speed corrector dial be rotated about its centre, the movement of the point G will vary in magnitude with the position at which the pin J is fixed in the curved slot. This position is set against the scale of speed in knots on the edge of the slot, but the setting is without effect until the speed corrector dial is rotated from the position shown in the diagram. When it is so rotated a corresponding movement is communicated to the lubber ring through the link G E, the end E of which is now to be regarded as the fixed fulcrum.

The two dials B K are connected by means of a link L M of length equal to the distance between the dial centres. The end L of this link is pivoted to a fixed point on the dial B, but the end M is provided with a pin which works within a slot in the dial K. Thus the setting of the dial B to any latitude will not produce rotation of the dial K, but will merely cause the pin M to slide in its slot. If, however, the link M N is moved upwards, the angle through which such movement will rotate the dial K will depend upon the exact position of the pin M in its slot--that is to say, upon the setting of the latitude dial. Thus a movement of the link M N will rotate the lubber ring by an amount proportional to the movement of M N, to the setting of the pin J in the curved slot of the speed dial, and to the setting of the latitude dial.

The link M N is pinned to a lever P Q, the end P of which is pivoted to a fixed point. The end Q carries a roller, which engages within the flanges of a ring R permanently fixed in an inclined position on the phantom ring of the compass. The higher end of this ring is situated directly above the north-seeking end of the gyro-axle, and the lower end directly above the south-seeking end, its east and west diameter being aligned horizontally.

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