422 



Mr. J. A. Broun on the 



[June 20, 



If we suppose, as the above calculations indicate, that the interval from 

 maximum to maximum is somewhat less than 26 3 days, we obtain from 

 the differences of the epochs for 1852-1850 and 1870-1868 the following 

 values of the period : — 



1852 minus 1850. . 26'33 - ^ 26 ' 33 + ^ ~~ 13 ' 2 = 2579 days. 



1870 minus 1868. . 26'33 — ^ = 25*90 „ 



28 



The result from 1870 and 1868 is that which merits the greatest value, 

 owing to the largeness of the coefficient a for these two years. If we as- 

 sume, then, that the true period is 26 days, we may, by applying a correc- 

 tion to the epochs of maximum for 1870 and 1852 of + AJ days = 4-f, 

 find the epochs for 1869 and 1851 : these would be for 1869, 17*1 days, or 

 three days later than results from the calculation ; and for 1851, 17' 9 days, 

 five days later than from the calculation ; and the smallness of the coeffi- 

 cient for 1851 would show that an error of this amount is quite possible. 



We have still, however, another means of determining which of the 

 values, 26 or 26^, is the most probable. The two best-marked results 

 from the Greenwich observations are those for 1852 and 1870; we may 

 ' compare the epochs of maximum from these years with that derived from 

 the Makerstoun observations for 1844. The terms for these three years 

 having the largest value of the constant a are (in 100,000ths of the force) : — 



1844. . .... 337 sin (0+101°) max. 25 days. 



1852 20-6 sin (0 + 266°) max. 13 



1870 43*5 sin (0 + 2/8°) max. 12'4 „ 



Now as the period began in 1844 with the 1st of January, the first 

 maximum in that year corresponded to the 25th January. In 1852 (the 

 first day of the period being the 31st December, 1851) the maximum 

 happened on the 12th January, 1852. In 1870 the first day of the period 

 was the 8th January, and the maximum occurred on the 20| January, 

 1870 *; and we have for the epochs of maximum, with the intervals in 

 days, as follow :— 



Intervals. 



1844, Jan. 25 to 1852, Jan. 12 . . 2909 days = 112 x 26 - 3 days. 

 1852, Jan. 12 to 1870, Jan. 20 . . 6583 days = 253 x 26 + 5 „ 

 1844 to 1870. 9492 days = 365 x 26 + 2 „ 



If, however, we assume the period to be 26^- days, we should have 



for 2909 days = 1 10 x 26^ + 12 days. 

 6583 days = 250 X 26^ + „ 

 9492 days = 360 x 26§ + 12 „ 



* This is also the date, obtained by Dr. Hornstein from the declination observations 

 for 1870. 



