68 Royal Society. 



I mentioned to you in former letters. It would follow from the ma- 

 terials which I have employed, that the horizontal force requires 

 constants which differ from those for the vertical force, and the 

 differences, although for the most part not considerable, are some- 

 times too large, as it appears to me, to be overlooked : it is for 

 observers to decide in this matter. To avoid the introduction of 

 insecure numbers I have not computed the potential, but have con- 

 tented myself with deriving the values of X, Y and Z (declination, 

 inclination, and force horizontal and total) being the quantities 

 principally used for comparison. A second calculation of the con- 

 stants for X and Y would have given rather more exact values, but 

 I think that with the existing data the result would scarcely repay 

 the labour of so extensive a calculation, for the tables would have to 

 be entirely recomputed. 



After obtaining the data from the theory, I wished to compare 

 them with observation. I could take for the inclination and force 

 the values which had served as the bases of the calculation ; there 

 are indeed several observations of inclination without our knowing 

 the force, and a few of the force without inclination ; but on the 

 other hand; there are more extensive districts where I had no declina- 

 tions, although the other two elements were well determined. Under 

 these circumstances I was obliged to have recourse to older observa- 

 tions, which indeed I had occasion to use also for secular change and 

 reduction for epoch to 1830. Thus the character of the work was 

 gradually modified. For the Atlantic Ocean I availed myself of your 

 excellent Memoir, Contributions No. IX. ; I only added the obser- 

 vations of Lutke, d'Urville, and Rumker; of older observations, I 

 took those of Abercrombie and Ekeberg, only using them however 

 in parts where they had observed the inclination, and principally 

 with the view of finding its secular change. 



In the Pacific there was more deficiency ; with the exception of 

 what has been furnished by Liitke, d'Urville, the ships of the Prus- 

 sian Merchant Service, and in the neighbourhood of the magnetic 

 equator by Duperrey, modern voyages scarcely gave me anything ; 

 for Becquerel, in his detailed table*, omits all determinations made 

 at sea. I therefore took all I could get since the voyages of Byron, 

 Carteret and Wallis, chiefly from Hansteen's great work, and reduced 

 to 1830, taking from each observer the mean of all his determina- 

 tions within a space of 5° lat. and 10° long. I did not allow myself 

 to exclude any observer, for as all have errors from the ship's iron, 

 it might easily happen that a man but little known may have given 

 values which are much nearer to the truth than those given by a 

 celebrated voyager. A selection is no less objectionable, as it 

 might easily lead to retaining observations which accord with a 

 possibly not altogether correct theory, and omitting others, other- 

 wise good, which might depart from it. Moreover, such a full com- 

 parison shows better what may be expected from the observations : 

 incomplete as are the data they afford, yet, when I arrange the re- 

 maining errors in latitude and longitude, I rarely find groups in which 

 * Electricity tome vii. 



