formula) are now in regular use in the Compass Department of ihe 

 Admiralty, for the practical deduction of rigorous results from the har- 

 monic analysis already referred to. In fact the full expression of the 

 unrestricted theory, as given by Archibald Smith in Part III. of the 

 ' Admiralty Manual/ is even simpler and more ready for ordinary use 

 than the partial and restricted expressions which Poisson and Airy had 

 given for practical application of the theory. 



3. Heeling error, Poisson's general formula) express three rectangular 

 components of the resultant force at the point where the compass is 

 placed, due to the magnetism induced in the ship by the terrestrial 

 magnetic force. To these Airy added the components of force due to 

 permanent magnetism of the ship's iron, which, though not ignored by 

 Poisson, had been omitted by him, because, considering the probability 

 of scattered directions of the magnetic axes of permanent magnetism in 

 the isolated masses of iron existing in wooden ships and their arma- 

 ments, he justly judged that permanent magnetism could not seriously 

 disturb a properly placed compass in a wooden ship ; and iron ships were 

 scarcely contemplated in those days. This general theory of Poisson and 

 Airy expresses the resultant force in terms of three angular coordinates, 

 specifying the position of the ship. In the practical application these 

 coordinates are most conveniently taken as: (1) the ship's "magnetic 

 course," defined above ; (2) the inclination of the longitudinal axis of 

 the ship to the horizon ; (3) the inclination to the horizon of a plane 

 drawn through this line perpendicular to the deck. The second co- 

 ordinate has no name and is of no importance in the compass problem ; 

 for under steam, or even under sail, the average inclination of the longi- 

 tudinal axis (chosen as horizontal for the ship in still water) is never so 

 great as to produce any sensible effect on the compass disturbance, and 

 the magnetic effects of pitching in the heaviest sea are not probably ever 

 <so great as to produce any seriously inconvenient degrees of oscillation in 

 the compass card. The third coordinate is called the "heel ;" and its mag- 

 netic effect on the compass is called " the heeling error." The heeling 

 error was investigated by Airy in his earliest work on the compass disturb- 

 ance ; but at that time, when iron sailing ships were comparatively rare, 

 he confined his ordinary practical correction of compass error to the case 

 of a ship in different azimuths on even keel. Since that time the heeling 

 error has come to be of very serious practical importance, on account of 

 the great number of iron sailing ships, and of screw steamers admitting 

 of being pressed by sail to very considerable degrees of " heeL" Archibald 

 Smith took up the question with characteristic mathematical tact and 

 practical ability, and gave the method for correcting the heeling error 

 which is now, I believe, universally adopted in the Navy, and too fre- 

 quently omitted (without the substitution of any other method) in the 

 mercantile marine. 



