Royal Society. 141 



from which it follows that 



1 sin a: . d£ 



Jo 

 tana=- 



I 



2tt 



cos a' . dK 



The author remarks, that for the integrals in this formula are to 

 be substituted, in practice, the algebraical sums of the sines and 

 cosines respectively, of the apparent magnetic bearings of the distant 

 object, observed with the ship's head successively on the sixteen 

 principal points of the compass (or on eight principal points, as the 

 case may be). He considers that this method may prove useful in 

 magnetic surveys of the ocean. 



Additional remarks to the foregoing paper. 



In consequence of a suggestion of Professor William Thomson, 

 the author here investigates the modifications required in the formulae 

 of the previous part of his paper, when the compass-needle produces 

 by induction a sensible effect on the mutual magnetic action of the 

 earth and the ship. 



Let A, as in Mr. Archibald Smith's formulae, represent the mean 

 of the sines of the deviations of the compass-needle observed during a 

 complete revolution of the ship. As there is reason to believe that 

 this quantity does not vary for a given ship in different parts of the 

 earth so long as the quantity and distribution of her iron are un- 

 changed, it may be determined, once for all, while in port, in the 

 usual way. 



When the ship is out of reach of land, let 5 be the mean of the 

 sines, and c the mean of the cosines, of the apparent magnetic azi- 

 muths of a distant object observed during a complete revolution of 

 the ship. Then the sine of the true magnetic azimuth of the object 

 is given by the formula 



sV(c 2 +^_ A 2 )— cA 

 sina= —5 



When A=0, this formula becomes 



s 

 tana= — > 

 c 



being identical with that of the previous part of this paper. 



May 12. — A paper was read, entitled "A few Remarks on Cur- 

 rents in the Arctic Seas." By P. C. Sutherland, M.D. 



The author states that, during a voyage lately made in the Arctic 

 seas, his attention was arrested by the power exerted by refrigera- 

 tion and congelation in separating from water any saline ingredients 

 it may contain, and of thus causing disturbances in the mean density 

 of the waters of the ocean, which, after being influenced by cur- 

 rents, can be overcome only by subsequent intermixture with water 

 from other localities where the disturbance in the equilibrium is of 

 an opposite character. He considers that evaporation, which is 

 so active within the tropical and temperate zones, obviously renders 

 the sea more dense by depressing its surface, and thus gives rise to 



