ing the measures at the same nominal hour by months, and taking their monthly means for each hour. As these exhibited sensible discordance, they were smoothed by taking the means of adjacent numbers, taking the means of the adjacent numbers of the new series, and so on, repeating the operation six times. The author explains the theory of this process, and the way in which it tends to degrade the periodical terms of higher orders. He then explains an easy method of resolving the numbers so smoothed into periodical terms recurring once in the day, twice in the day, thrice in the day, &c., and applies the method to the numbers for every month. When these quantities (which from month to month are perfectly independent) are brought together in tables, they present such an agreement, with gradual change accompanying the change of seasons, as leaves no doubt on their representation of a real law of the diurnal changes of the galvanic currents. They also show the existence of a constant turn towards the north (which explains the apparent increase of force to the north observed in the results for days of great disturbance), and a still larger force towards the west (which also is well marked on the days of great disturbance). No light is obtained on the origin of these terms, but they appear to be probably pure galvanic accidents, depending on the nature of the earth-connexions. The author then exhibits in curves the diurnal inequalities of magnetism which the galvanic currents must produce. The form generally consists of two parallel lobes, making with the magnetic meridian an angle of nearly 60° from the north towards the west. The greatest east-andwest difference of ordinates, in the month of April, is 0.00044 of Total Horizontal Magnetic Force; it corresponds, in the hours to which those ordinates relate, nearly with the Ordinary Diurnal Inequality. But it is much smaller than the ordinary diurnal inequality, and the daily law of the galvano-magnetic inequality differs greatly from that of diurnal inequality. For the greater part, therefore, of diurnal inequality the cause is yet to be found. II. "Monthly Magnetic Determinations, from December 1866 to May 1869 inclusive, made at the University of Coimbra." By Professor J. A. DE SOUZA, Director of the Observatory. Communicated by BALFOUR STEWART, F.R.S. Received December 16, 1869. [NOTE. These observations form the continuation of a series the results of which were communicated to the Royal Society on May 8, 1867, by the President. In both series the same instruments were used, and the method of observation was the same in both.-B. S.] Observations of Deflection and Vibration for absolute measure of H. F. d h m 10 59 7.5 8.98256 I 1'3 4 58 537 898241 10 57 37 5 898189 123 4 58 212 898194. 10 58 50°C 8.98213 4 58 487 898205 1 61 13 52 50863 9'2948 10'5955 261 23 32 161 11 19 61 12 43 161 12 26| 261 12 13 0*39548 04883 17 1 12 20 53 711 I 14 2 61 10 42 50906 92530 10.5609 I'O 20 I 12 81.6 10 56 16 2 1'3 4 57 350 898111 20 I 27 834 423589 0*39579 161 12 52 0'39580 04880 30 5 420 54 52 21 I 40 261 14 49 50979 92849 10'5923 Observations of Deflection and Vibration for absolute measure of H. F. Distances. Sept. foot h m ΙΟ 1'3 Temperature, Fahr. Deflection. Log I ΙΟ 1 15 78.1 10 49 556 897667 IO 21 I 9 13 4 54 369 897630 I 40 799 423975 0*39499 0'39460 0*39460 o 50 814 423856 039499 0.4858 3 4 10 20 39 43 2 21 1 19 822 423898 039497 0.4858 20 10 57 20 42 4922 0'39497 I 20 1 61 12 36 2 61 7 30 2 61 10 43 1 61 15 58 2 61 11 13 2 61 10 6 1 61 11 51 51063 92867 105980 I 37 2 61 II 39 1 61 13 51 51087 92930 10*6047 1 61 10 7 II 2 17 720 423729 04859 10 0 42 20 53 4412 I 34 0'39449 21 1 27 616 423883 0'39417 261 8 51 161 12 56 51040 92681 10.5805 04855 22 I 47 0*39417 Means ...... 20 43 2 2 61 10 21 5'1054 92844 105956 61 11 55 51099 9°2945 10.6066 |