Magnetical Observatory of Dublin during the Years 1840-43. 77 



nation increases. This movement continues until about 1 p. m., when the decU- 

 uation attains its maximum. 



n. After 1 p. m. the north pole of the magnet moves eastward, and the de- 

 clination diminishes, but at a slower rate than it had previously increased. This 

 easterly movement continues until between 9 p. m. and 11 p. m., when the decli- 

 nation is a minimum. 



III. There is a second, but much smaller, oscillation of the magnet during 

 the night and morning ; the north pole moving slowly to the west for a few 

 hours before and after midnight, and afterwards returning to the east until 

 between 6 a. m. and 8 a. m., when the decUnation is again a minimum. 



IV. In summer the westerly movement during the night becomes nearly 

 insensible. In winter, on the contrary, the easterly movement during the 

 morning nearly vanishes ; and the magnet is almost in a state of repose°from 



2 A. M. to 8 A. M. 



v. In summer the morning easterly elongation is greater than the evening 

 one ; and, consequently, the greatest range is between 7 a. m. and 1 p. m. In 

 winter, on the contrary, the evening easterly elongation is greater than the 

 morning ; and the greatest range is between 1 p. m. and 10 p. m. The total range 

 is greater in summer than in winter. 



These general characteristics of the diurnal variation may be most readily 

 understood by a reference to Plates I. and II. 



5. In order to determine the laws of the phenomenon with more precision, 

 it will be desirable to express the difference between the declination at any 

 hour, and the mean of the entire day, as a function of the time. 



If A be taken to denote this difference corresponding to any time, 



A = 2 (^i cos ir -f Bi sin iv) ; 



in which a; = n x 15", n being the number of hours, and parts of an hour, in 

 the time reckoned from the epoch of the first observation, and i any number of 

 the natural series. Then, since observation gives the values of A correspondinu- 

 to w = 0, 2, 4, &c. . . 22, we have twelve equations of condition, from which 

 twelve coefficients of the periodical function may be deduced by elimination. 

 The first of these, Jo, = ; the following are the values of the remaining 

 eleven. 



