In this, the XIII.th Number of the “Contributions to Terrestrial Magnetism,” I have the pleasure of presenting to the Royal Society the Magnetic Survey of the North Polar Regions of the Globe, in a suitable form and arrangement to entitle it to be regarded as a companion to the Magnetic Survey of the South Polar Regions, presented to the Society in 1868; constituting, with the present contribution, a moiety of the Magnetic Survey of the Globe corresponding to the general epoch 1840 to 1845. The area comprised in the present communication is coextensive with that of the South Polar Survey, and the epochs are the same, viz. 1840 to 1845, or more simply 1842.5; the chief distinction between the two surveys being, that the South Polar Survey is the work of a single nation,—executed by the authority of its Government and at the national expense in the brief interval comprised between the years 1840 and 1845, and thus requiring no corrections to be introduced for secular change, a troublesome and not very certain operation; whilst its companion, the present communication, comprehends the cooperative labours of many European and American contributors, acting for the most part independently of each other, within the limits of about twenty years preceding, and twenty years following, the mean epoch of 1842.5: the results, therefore, when brought together, require the introduction of “ corrections for secular change,” where these are practicable, and where they can be made with safety.