the motions of the pendulum BC will not be indicated correctly by the pendulum CD; yet this is exactly a parallel case to that when a pendulum or clinometer is trusted to indicate the angles of inclination to the vertical of a ship rolling amongst waves. Pendulum indications, under these circumstances, usually err in excess, and in some cases the error is proportionately very great, as the following examples will show. The figures are taken from published returns of rolling for her Majesty's ships.

Many similar examples could be given, but they appear unnecessary; the correct angles stated in the table were observed in all cases with the accurate batten instruments which are now the service fitting.

The misleading character of pendulum observations has been for many years acknowledged; and they are no longer made in ships of the Royal Navy, except in special cases. When the horizon is obscured, or at night, batten observations cannot be made, while pendulum observations can; and it is ordered that under these circumstances the rolling indicated by the pendulums shall be noted. To enable the results so obtained to be afterwards corrected, simultaneous observations are made, when circumstances permit, of the indications of these same pendulums hung in the same positions, and of the indications of batten instruments.

In concluding these remarks on pendulum observations, it may be proper to add that any other devices, such as spiritlevels, depending for their action on the directive force of gravity or statical conditions, are affected by the motion of a ship much as the pendulum has been shown to be affected.

Suppose a spirit-level to be placed in the best possible position in a ship, at the height of the centre of gravity; in accordance with the principles previously explained, when its indications would lead an observer to think it exactly horizontal, it would really be parallel to the effective wave slope. Many persons who admit the faultiness of the pendulum are disposed to cling to the use of the level; but on reflection it will be seen that both instruments are open to similar objections. Moreover, the extreme sensitiveness and rapid motions of the spirit-level make it ill adapted for any observations in a seaway.

Several kinds of gyroscopic instruments have been devised for the purpose of measuring rolling and pitching motions, all of them being based upon the well-known principle—ex emplified in the toy gyroscope-that a delicately balanced heavy-rimmed wheel spinning rapidly will maintain the plane of rotation in which it is set spinning, until its speed of rotation is considerably diminished. One of the earliest and best instruments of the kind is illustrated by Fig. 74. It was devised and tried at sea nearly twenty years ago by Professor Piazzi Smyth, Astronomer Royal of Scotland, and can be used to measure"yawing" motions as well as rolling and pitching. It consists of a fly-wheel A, the axis of which forms a diameter of the gymbal-ring B; this is carried by a second gymbal-ring, C, the pivots of which rest on the frame F; and the whole is mounted in an outer frame, enabling it to be easily carried or placed in position. Suppose the pivots of the ring C to be placed athwartships in a ship, the instrument standing on the deck or on a table: then for transverse oscillations the line-of-centres of the pivots will remain parallel to the deck-that is to say, so far as rolling is concerned, the ring C must move with the ship. But it is free to oscillate about its pivots as the ship pitches.

* See the description given by the inventor in vol. iv. of the Transactions of the Institution of

Naval Architects, from which the drawing is taken.

R

When the fly-wheel A is spinning rapidly and maintaining its plane of rotation, it is practically uninfluenced by the motions of the ship which so largely affect the pendulum ; and as its axis is carried by the ring B, that ring also must

maintain its position. This maintenance of position by B further involves the non-performance of any oscillations by C except in the transverse sense. In other words, neither A nor B changes the direction of its plane, while the ship rolls and pitches, so long as A spins rapidly; while C can accompany the rolling motion, but not the pitching

motion. Hence the graduated semicircle E, shown fixed upon and across C, moves relatively to B as the, ship rolls; and the pointer attached to the upper edge of B sweeps over an arc on the semicircle equal to the arc through which the ship is oscillating. On the left-hand side of the diagram there is shown a graduated circle G, which has its centre coincident with one of the pivots of C, and is fixed to the frame F. As the ship pitches, therefore, the frame F moves with her, and oscillates about the ring C, which is prevented from accompanying the pitching in the manner described. Pointers marked p are attached to the under side of C, and the arcs they sweep over upon the graduated circle G indicate the arcs through which the ship pitches. By this ingenious arrangement the simultaneous rolling and pitching motions can be read off by observers with the greatest ease.

One point of disadvantage attaching to this as well as to all other gyroscopic instruments should, however, be noted; viz. that there is no separate indication of the angles of inclination. attained on either side of the vertical. When the wheel A is set spinning, if it were truly horizontal, then B would be vertical, and this disadvantage would disappear. But a ship in a seaway changes its position rapidly, and it is practically impossible to secure this condition of initial horizontality; hence the observer must be content to note the total arcs of oscillation. No doubt, in most cases, the rolling of a ship not under sail approaches equal inclinations on either side of the vertical, the roll to leeward being somewhat in excess of that to windward; but in a ship under sail the rolling takes place about an inclined position, and in any case it is a great advantage to be able to ascertain the extreme inclination on either side of the vertical.

Professor Smyth fully appreciated this defect of all gyroscopic instruments, observing that they had "no power "of determining absolute inclination, or angular position with "reference to horizon or meridian;" but he was unacquainted with any other instrument which did not have its records

affected by the accelerating forces due to the motion of the ship, and so preferred the gyroscopic clinometer. Now we have other means of measurement free from the objections belonging to pendulums or spirit-levels, and can therefore afford to dispense with the gyroscope.

It has been mentioned that the maintenance of the plane of rotation by a fly-wheel depends upon the maintenance of its speed; this is well illustrated in the common toy, which droops as the speed decreases. The practical difficulties attending the use of these instruments arise, therefore, from the extreme care required in suspending the fly-wheels in order that friction or other causes may have the least effect in hindering free rotation, and in the difficulty of maintaining continuous rotation. The instrument shown in Fig. 74 is said to have been so well designed that, when once carefully adjusted, it did not require readjustment for some time; but from the few records of its use that have been published, it would appear that Professor Smyth limited any single series of observations to a very brief period. When a considerable time is occupied in making the observations, there is a danger of the gyroscopic action being somewhat interfered with by the loss of speed of rotation.*

On this point some interesting facts have been stated by Admiral Paris, of the French navy, who produced a gyroscopic clinometer ten years ago, which automatically recorded the rolling of a ship. The gyroscopic wheel in this instrument formed the body of a top, the lower end of the axis about which it spun being wrought to a sharp point, and resting on an agate bearing in order to diminish friction. To spin this top, a string was wound round the upper part of the axis, and drawn off gradually, giving a gradually accelerated motion of rotation. It was found that this top would revolve steadily

It may be interesting to add that, when the instrument illustrated in Fig. 74 was used to measure "yawing," it was placed with the pivots of the ring C in a vertical

line; the frame lying on its side instead of its bottom, and the wheel B being horizontal. The angles of "yawing" could then be read off on the graduated circle G.