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mences with those at Fort Reliance, which was the first winter station 

 of the expedition ; and where the dip was determined by observations 

 of the needle, both with direct and also with inverted poles. The author 

 then enters upon an investigation of formulas for the determination of 

 the dip by means of a needle, in which the value of a certain angle, 

 denoted by the symbol y, determining the position of the centre of 

 gravity, has been ascertained ; and, conversely, for the determination 

 of the value of the same angle, or, which is equivalent to it, the posi- 

 tion of the centre of gravity of the needle, when the dip at the place 

 of observation is given. He next inquires whether any tests can be 

 applied to the observations under discussion, which may indicate the 

 extent of the errors by which the results deduced from them may be 

 affected j and he employs for this purpose the values of the terrestrial 

 magnetic intensity furnished by certain equations obtained in the pre- 

 ceding investigation ; making the proper allowances, first, for the 

 needles used being ill adapted to this method of determining the re- 

 lative intensities j secondly, for errors of observation in determining 

 the times of vibration of the needle j and thirdly, for disturbing causes 

 which might affect the observations. Considerable differences were 

 found to exist in the results obtained by the two methods, at New 

 York, Montreal, Fort Alexander, Montreal Island, and Fort Ogle ; 

 differences which can be accounted for only by errors in the assumed 

 magnitude of the angle y, and which, consequently, indicate the want 

 of permanence in that angle. It was necessary, therefore, to inquire 

 what changes in the angle y will account for these discrepancies, and 

 how far the value of the dip, thus obtained, may be affected by them. 

 Formulae are then deduced by which these changes may be deter- 

 mined. 



From a comparison of the observed and computed values of the 

 angles involved in these investigations, the author infers that the dif- 

 ferences between those of one of these angles are, with a few excep- 

 tions, contained within the limits of the errors incident to dip obser- 

 vations : but with respect to the other angle, they in general exceed 

 those limits. Upon the whole, he concludes that the discrepancies 

 which appear between the values of the terrestrial intensity, as de- 

 duced from the times of vibration of the needle, and from the observed 

 angles of inclination to the horizon, are principally attributable to a 

 want of absolute permanence in its axis of motion. In the present 

 case, the centre of gravity of the needle being nearly coincident with 

 the axis, a very minute derangement in that axis would cause a con- 

 siderable change in the value of the angle y : so that the existence 

 of differences in the values of this angle do not warrant the inference 

 that the needle itself received any serious injury during the expedi- 

 tion ; to which, indeed, from the care taken of it by Captain Back, 

 it could not well have been liable. 



The second part of the paper relates to the observations of the va- 

 riation of the magnetic needle, which are already published in Capt. 

 Back's narrative, and which are here introduced for the purpose of 

 applying them, in conjunction with the observations of the dip, detailed 



2 h 2 



