Vll 



more than any thing else to promote the usefulness of the compass, and 

 to render its use safe throughout the British Navy. Smith's tables and 

 forms for harmonic analysis have proved exceedingly valuable in many 

 other departments of practical physics besides ships' magnetism. The 

 writer of this article found them most useful fifteen years ago in re- 

 ducing for the Royal Society of Edinburgh Forbes's observations of the 

 underground temperature of Calton Hill, the Experimental Gardens, 

 and Craigleith Quarry, in the neighbourhood of Edinburgh ; and the 

 forms, with a suitable modification of the tables, have proved equally 

 useful in the harmonic analysis of tidal observations for various parts of 

 the world, carried out by the Tidal Committee of the British Association, 

 with the assistance of sums of money granted in successive years from 

 1868 to 1872. 



2. Practical expression of the full mathematical theory. Poisson him- 

 self, in making practical application of his theory, had simplified it by 

 assuming particular conditions as to symmetry of the iron in the ship, 

 and even with these restrictions had left it in a form which seemed to 

 require further simplification before it could be rendered available for 

 general use. Airy, in taking up the problem with this object, at the 

 request of the Admiralty in the year 1839, founded his calculations on a 

 supposition that, " by the action of terrestrial magnetism every particle 

 " of iron is converted into a magnet whose direction is parallel to that of 

 " the dipping needle, and whose intensity is proportional to the intensity 

 " of terrestrial magnetism." This supposition, which is approximately 

 true only for the ideal case of the iron of the ship being all in the shape 

 of globes placed at such considerable distances from one another as 

 not to exercise mutual influence to any sensible degree, leads to a law 

 of dependence between the ship's force on the compass needle, and the 

 angular coordinates of the ship, which differs from that of the complete 

 theory, as shown afterwards by Smith, only in the want of his constant 

 term A of the harmonic development, a difference which, in ordinary 

 cases, does not vitiate sensibly the practical application. In introducing 

 the supposition, Airy correctly anticipated that it would in general lead 

 to results sufficiently accurate and complete for practical purposes. But 

 he said " it would have been desirable to make the calculations on 

 " Poisson's theory, which undoubtedly possesses greater claims on our 

 " attention (as a theory representing accurately the facts of some very 

 " peculiar cases) than any other. The difficulties, however, in the appli- 

 " cation of this theory to complicated cases are great, perhaps insuper- 

 " able." These difficulties were wholly overcome by the happy mathe- 

 matical tact of Archibald Smith, who reduced the full expression of 

 Poisson's theory, including the effect of permanent magnetism, the great 

 practical importance of which had been discovered by Airy, to a few 

 simple and easily applied formulae. [See Appendix to this notice.] These 



