The author, having been consulted by Captain Back, previous to the departure of the latter, in 1833, with the expedition for the relief of Captain Ross, respecting the nature of the magnetical observations which it might be desirable to make in the regions he was about to visit, and considering that, with a view to the attainment of the principal object of the expedition, the greatest economy of time in making these observations was of the first importance, limited his suggestions, in the first instance, to the methods proper to be employed for determining the direction and the dip of the needle, but more especially the latter. Captain Back, immediately on his return, placed all his magnetical observations at the disposal of Mr. Christie, who having since completed their reduction, gives, in the present paper, the results of his labours. The. first part of the paper relates to the observations of the Dip of the magnetic needle. With a view to economize as much as possible the time consumed in making each observation, the process of inverting the poles of the needle, which is usually resorted to in each instance, was here dispensed with. But in order that the dip may be determined independently of this operation, it is necessary not only that the position of the centre of gravity of the needle employed should be ascertained, but that it should be pertnanent. In giving an account of the observations made to verify this condition, the author commences 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 formulæ for the determination of the dip by means of a needle, in which the value of a certain angle, denoted by the symbol γ, 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 position 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; and he employs for this purpose the values of the terrestrial magnetic intensity furnished by certain equations obtained in the preceding investigation; making the proper allowances, first, for the needles used being ill adapted to this method of determining the relative intensities; secondly, for errors of observation in determining the times of vibration of the needle; 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 γ, and which, consequently, indicate the want of permanence in that angle. It was necessary, therefore, to inquire what changes in the angle γ will account for these discrepancies, and how far the value of the dip, thus obtained, may be affected by them. Formulæ are then deduced by which these changes may be determined.