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514 pass diminished together, as nearly in equal proportions as the accuracy of our observed variations could be depended on; and I therefore considered the connexion between them to be so far certain, as to make the dip one datum in reducing the observed to the true variations.

Another point of equal importance remained to be known: the compass stood right in both hemispheres when the ship's head was at North or South, and erred most on one side when the head was West and on the other when it was at East; but what was the proportion of error at the intermediate points, between the magnetic meridian and East and West? Unfortunately, the direction of the ship's head when observations were taken, had not been particularly marked in the first part of the voyage, nor always in the latter part; and in gathering it from the courses steered when under way, and from the direction of the winds and tides when at anchor, there was often a good deal of uncertainty; but it was evident, that the quantity of error increased as the angle between the ship's head and the magnetic meridian became greater. After some consideration, it appeared to me that the magnetism of the earth and the attraction forward in the ship must act upon the needle in the nature of a compound force; and that the errors produced by the attraction should be proportionate to the sines of the angles between the ship's head and the magnetic meridian. I tried this upon many observations where the direction of the head was least doubtful, and found the differences to correspond as nearly as could be expected, and sometimes exactly; it therefore seemed probable that the error produced at any direction of the ship's head, would be to the error at East or West, at the same dip; as the sine of the angle between the ship's head and magnetic meridian, was to the sine of eight points, or radius. According to this, when the error was ascertained at any given direction, more especially at East or West where it was greatest, it might be found at any direction required, by inspection in the Traverse Table.

Soon after my arrival in England, application was made to the Lords Commissioners of the Admiralty to have experiments tried on board some of His Majesty's ships, that this law might be verified; and they were pleased to order them at Sheerness, Portsmouth, and Plymouth. I was present at the two first ports, when a series of observations were made in