In a communication to the Royal Society, which was honoured by publication in the Philosophical Transactions for 1868, I described the methods and gave the results of comparing the Magnetic Disturbances which might be expected as consequent on the Terrestrial Galvanic Currents recorded by the self-registering galvanometers of the Royal Observatory of Greenwich, with the Magnetic Disturbances actually registered by the self-registering magnetometers. The comparison was limited to seventeen days (1865, October 5 and 31; 1866, October 4; 1867, April 4, 5, 7, 8, 9, 11, May 4, 14, 28, 31, June 1, 2, 7, 24), various days having been omitted in consequence of a doubt on the uniformity of the clock-movement of the registering-barrel, which afterwards proved to be unfounded. The results of the comparison were exhibited in curves, engraved copies of which are given in the volume of publication. I expressed my opinion that it was impossible to doubt the general causal connexion of the Galvanic Currents with the Magnetic Disturbances, but that some points yet remained to be cleared up. As soon as circumstances permitted, I undertook the examination of the whole of the Earth-currents recorded during the establishment of the Croydon and Dartford Wires (namely from 1865 April 1 to 1867 December 31), as far as they should appear to bear upon this and similar questions. For this purpose the days of observation were divided by Mr. Glaisher into three groups. Group No. 1 contained days of considerable magnetic disturbance (or days of considerable galvanic disturbance, which are always the same), including, besides the seventeen days above-mentioned, the thirty-six days of the following list :—1865, April 15, 16, 17, 18, 19, May 14, 17, July 7,15, August 14,19, 26, September 8, 16, 28, October 4, 6, 10, 12, 14, November 1; 1866, August 11, 23, September 8, 9,12,13,17,18, 25, October 6, 7,10, 30, November 26 ; 1867, February 8; making in all fifty-three days of considerable magnetic disturbance. Group No. 2 consisted of days of moderate magnetic disturbance, and of these no further notice was taken. Group No. 3 contained the days of tranquil magnetism, and the discussion of these will form the principal part of the present Memoir.