364 Sir William Thomson on the Perturbations of the 



bearing-point were carried by the ship uniformly in a straight 

 line. They are nearly enough realized in a large ship to render 

 inconsiderable the errors due to want of perfect uniformity of 

 the motion of the bearing-point, if this point is placed anywhere 

 in the " axis of rolling"* ; for in a large ship the compass, how- 

 ever placed, is not considerably disturbed by pitching, or by the 

 inequalities of the longitudinal translatory motion caused by waves. 

 Hence, supposing the compass placed in the axis of rolling, the 

 perturbation produced in it by the rolling will be solely that due 

 to the variation of the horizontal component of the ship's magnetic 

 force. Such a position of the compass would have one great 

 advantage — that the application of proper magnetic correctors 

 adjusted by trial to do away with the rolling- error, would per- 

 fectly correct the heeling-error. To set off against this advan- 

 tage there are two practical disadvantages : — one, that the axis of 

 rolling (being always below deck) would not be a convenient 

 position for the ordinary modes of using the compass ; the other 

 (far more serious), that, at all events in ships with iron decks, 

 the magnetic disturbance produced by the iron of the ship would 

 probably be so much greater at any point of the axis of rolling, 

 than at suitably chosen positions above deck, as to more than 

 counterbalance the grand kinetic advantage of the axial position. 

 But careful trials in ships of various classes ought to be made ; 

 and it may be found that in some cases the compass may, with 

 preponderating advantage, be placed at the axis of rolling. 

 Hitherto, however, this position for the compass has not been 

 used in ships of any class, and, as we have seen, it is not pro- 

 bable that it can ever be generally adopted for ships of all classes. 

 It is therefore an interesting and important practical problem 

 to determine the perturbations of the compass produced by oscil- 

 lations or other non-uniform motions of the bearing-point. 



The general kinetic problem of the compass is to determine 

 the position at any instant of a rigid body consisting of the 

 needles, framework, and fly-card, which for brevity will be called 

 simply the compass, movable on a bearing-point, when this point 

 moves with any given motion. Let the bearing-point experience 

 at any instant a given acceleration «, in any given direction. 

 Let W be the mass (or weight) of the compass, and gW the 

 force of gravity upon it, reckoned in kinetic units. The position 

 of kinetic equilibrium of the compass at that instant is the posi- 



* One way, probably the best in practice, of finding by observation the 

 position of the axis of rolling is to hang pendulums from points at differ- 

 ent levels in the plane through the keel perpendicular to the deck, till one 

 is found which indicates the same degrees of rolling as those found geo- 

 metrically by observing a graduated scale (or " batten ") seen against the 

 horizon. 



