303 



that 5'Ou will receive the work kindly, and tell me of its fate as soon 

 as you can. 



How far advanced is the Magnetic Survey of India ? Could not 

 you get travellers to observe in Egypt, Nubia, Mesopotamia and 

 Persia ? In the Pacific we want observations, especially on Erman's 

 route : the number of facts known is too small for good inferences : 

 we want tests for Duperrey's and Freycinet's Dips, which at neigh- 

 bouring points differ 3° or 4°. Of Elliot's I know only the results 

 taken from the Proceedings of the Royal Society ; KupfFer has, I 

 see, a copy of the work itself from the Phil. Trans. Has not Rae 

 made observations on his journeys, and is anything printed ? the 

 same question as to all the expeditions in search of Franklin ? 



(Signed) 



L. M. Kamtz. 



April 28, 1853. 

 The EARL OF ROSSE, President, in the Chair. 



A paper was read, entitled " On the Application of the Law of 

 the Conservation of Energy to the Determination of the Magnetic 

 Meridian on board Ship, when out of reach or out of sight of Land." 

 By W. J. Macquorn Rankine. Communicated by Colonel Sabine, 

 R.A., Treas., V.P.R.S. &c. Received April 5, 1853. 



The author states that, assuming that when a ship is swung com- 

 pletely round, so that her head bears exactly as it did at first, the 

 magnetism of the ship, and that of the compass-needle return to 

 their original condition, the following theorem is necessarily true : — 



The mechanical poiver developed hy the mutual action of the ship and 

 of the compass -needle during a complete revolution of the ship, is equal 

 to zero. 



If ^' be the apparent magnetic azim-uth of the ship's head, east of 

 north ; a' the corresponding apparent magnetic azimuth of a distant 

 fixed terrestrial object (or w^here no such object is visible, of a star, 

 corrected by calculation f(jr its apparent diurnal motion) ; a the 

 true magnetic azimuth of the same object, so that a—cc' is the 

 westerly deviation of the compass-needle ; then the above theorem 

 is expressed symbolically thus : — 



f27r ^ r27r C27r 



= 1 sm(a — a').(/^' = sinal cos a' , a'?' — cos al sina'.rf^'; 

 Jo _ _ Jo Jo 



from which it follows that 



J^^'sina'.c?^' 



I cos a' . dt^ 



JO _ 



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

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



21'^ 



