Could we entirely eliminate the effects of friction that might be used as a compass, for it could be set, say with its axle pointing north and south, at the commencement of the voyage, and it would remain so despite all the evolutions through which the ship might go.
But there is a better scheme even than that, based upon the peculiar behaviour of a revolving wheel when it has only two degrees of freedom. Suppose that we dispense with the ring employed in the previous arrangement, pivoting the ends of the axle between the prongs of the fork. The wheel is then free to rotate, and its axle can slew round through a complete circle by the turning of the fork in its socket, but there can be no tilting of the axle. Being thus deprived of one of its movements the gyroscope with three degrees becomes a gyroscope with two degrees of freedom, and in that form it supplies the need for an efficient and reliable compass.
The secret of the whole thing is the curious fact that a gyroscope with two degrees of freedom exhibits a keen desire to place its axis parallel with the axis of the earth. Owing to the shape of the earth, a device such as has been described, with its fork standing up vertically, cannot possibly have its axis really parallel with that of the earth, except on the Equator. Still it gets as nearly parallel as possible. To be scientifically accurate, we ought to say that it places it own axis "in the same plane" as that of the earth.
To understand this we need to realise that all movement is relative. In ordinary language, when we say a thing is still we mean that it is still in relation to the surface of the earth, but since the earth is moving the stillest thing, apparently, is really travelling at enormous speed.
Saint Paul's Cathedral in London, or a tall sky-scraper in New York, would usually be regarded as supreme instances of immobility. It would be hard to find better examples of stationariness, as we ordinarily look at things. Each stands, firm and strong, upon a horizontal base. Yet each is really turning a somersault every twenty-four hours. The plateau upon which St Paul's stands, though it seems still and motionless beneath our feet, is continually tilting; its eastern edge is continually going downwards and its western edge upwards, as the earth performs its daily spin. It is only a north and south line which does not share in some degree this continual tilting action. Every plane, large or small, so long as it remains horizontal, is being tilted thus, down at the eastern edge and up at the western. And the plane in which the axle of a gyroscope with "two degrees" is free to move is a horizontal plane. Owing to its being held between the prongs of the fork, while it can swing round to point north, south, east or west, or towards any point between them, it cannot deviate from the horizontal plane. Therefore such axle is always being tilted by the motion of the earth, except when it happens to be lying exactly north and south.
Now for a reason which is too complex to go into here a gyroscope strongly objects to having its axle tilted in this manner. If it be compelled by superior force to submit to tilting, it tries to wrench itself round sideways. Anyone who has a gyroscope top and cares to try the experiment will feel this action quite easily. Hold the spinning-top in your hand and turn it over so as to tilt the axle, when it will, if you are not careful, twist itself out of your grasp.
So a gyroscope of the kind we are considering, when the motion of the earth tilts its axis, turns itself round in its socket until at last it reaches the north and south position, when the tilting, and therefore the twisting, ceases. Hence the axle of the gyroscope if left to itself (the rotation of the wheel being maintained the while) will place itself in a north and south direction. And, moreover, it will keep in that direction. It will take some force to slew it round into any other. And if moved into any other by some extraneous means it will restore itself to the old position again.
Hence a wheel thus arranged has all the attributes which we need for a mariner's compass. But unfortunately there are mechanical difficulties in the way of using such a simple contrivance for that purpose.
Chief of all these is the fact that it is not what engineers call "dead-beat." That means that it will not go to the proper position and then remain there quite still. Instead, it will first slightly overshoot the mark, which being followed by the reverse action, it will come back and overshoot it just as far in the opposite direction. Instead, therefore, of a steady pointing, always in the same direction precisely, it will oscillate more or less, the exact north and south line being the mean or average position, the centre of the oscillations.
It would of course be possible to damp this, to apply a break as it were, if the apparatus were to remain stationary. For example, if the whole concern were immersed in water the resistance of the liquid would restrain any quick movement of the axle, yet it would not prevent it from slowly finding its true position. Thus the oscillations would be reduced to such a small range as to be for practical purposes negligible. But the drawback to a device of that kind, applied to a gyroscope on board ship, would be that the axle would be carried round to some extent every time the ship turned. As she changed direction it would more or less carry round the water with it; that in turn would carry the gyroscope, and so the direction of the latter would be for a time untrue. It would in course of time regain its accuracy, but in the meantime it would be leading the ship astray.