550 Royal Society. 



pendent determination of the magnetic intensity with Hansteen's 

 apparatus, derived from the data furnished by Captain Belcher's ob- 

 servations, the author shows the extreme improbability that the 

 differences in the results obtained at Otaheite by Messrs. Erman, 

 FitzRoy and Belcher, should be occasioned by instrumental or ob- 

 servational error. They are also far greater than can, with any de- 

 gree of probability, be ascribed to periodical or accidental variations 

 in the magnetic force from its mean value. The only known cause 

 adequate to their explanation is what may with propriety be termed 

 Station error ; that is, local disturbing influences, in an island com- 

 posed chiefly of volcanic rocks, and where the spot of observation 

 selected by the different observers may not have been precisely the 

 same. 



By a reference to the magnetic survey of the British Islands, the 

 occurrence of station error is shown to be frequent in countries of 

 far less decided igneous character than Otaheite ; and that its exist- 

 ence may always be apprehended where rocks of that nature approach 

 to, or rise through, the superficial soil. The absolute determinations 

 of fixed observatories are as liable to station error as those of the mag- 

 netic traveller, since no continuance or repetition of the observations 

 can lead to an elimination of the error ; it consequently presents a 

 practical difficulty to the proposed determination of the elements 

 of the theory from exact observation at only a few selected positions 

 on the globe. The remedy is to be found in the combination of 

 fixed observatories and magnetic surveys : the observations of the 

 survey, being made in concert with, and based on those of the fixed 

 observatory, will be furnished thereby with corrections for the se- 

 cular, periodical, and accidental variations of the elements, and will 

 consequently determine mean values : and a proper combination of 

 the mean values thus determined, over a space sufficiently extensive 

 to neutralize district anomalies, as well as those of a more strictly 

 local character, will furnish, in their turn, a correction for the sta- 

 tion error, if any, of the fixed observatory. 



A paper was also read, entitled, " On the Calculation of Attrac- 

 tions, and the Figure of the Earth." By C. J. Hargreave, B.A., 

 of University College. Communicated by John T. Graves, M.A., 

 F.R.S., Professor of Jurisprudence, University College, London. 



The principal object of the calculations contained in this paper 

 is to investigate the figure which a fluid, consisting of portions, 

 varying in density according to any given law, would assume, when 

 every particle is acted upon by the attraction of every other, and by 

 a centrifugal force arising from rotatory motion. That such has 

 been the original condition of the earth has been assumed as the 

 foundation of most of the mathematical calculations connected with 

 this inquiry ; although the hypothesis itself may admit of doubt. 

 The principal difficulty of this problem consists in the computation 

 of the attraction of a body of any given figure, and composed of 

 strata varying in their densities according to any given law. In sol- 

 ving it, the author follows the steps of Laplace as far as the point 

 where the equation, known by his name, first appears. It has, 

 however, since been discovered by Mr. Ivory, that the theorem of 



