1872.] 26-*% Period of the Earth's Magnetic Force. 419 



importance in the investigation, I have sought to determine it from the 

 means for the 26^-day period in each year. A consideration of the mean 

 value of the horizontal force at Greenwich will show that it varies irregu- 

 larly from year to year, and that no single value employed as a correction 

 due to a supposed uniform change from the beginning to the end of a 

 year would satisfy all the years. I adopted the following method to obtain 

 this correction (not being in possession of the Greenwich observations) : — by 

 comparing the mean value for the 1st day with that for the 14th, that of 

 the 2nd day with the mean for the loth, and so on, 13 values of the 

 change for 13 days are obtained for any gradual change, which will be ap- 

 proximately true whether there be a period of 26 days or no period what- 

 ever. This method gave the mean change during 13 days for each year as 

 follows : — 



1850. 1851. 1852. 1868. 1869. 1870. 

 + 24 -4-5 -9 —26 +7*5 -15 



the unit being in all cases '00001 of the whole horizontal force. Having 

 applied the proportional parts of these quantities with the signs changed 

 to the mean values of horizontal force for the respective years (Table, 

 p. 310, suprcT), I then calculated the values of the constants for the term 



a sin (0+ c). 



The results are as follow : — d. 



1850 6-2 sin (0+ 64°) with maximum at 1*9 



1851 5-0 sin (0 + 274°) „ 12'8 



1852 20-6 sin (0 + 266°) „ 13-2 



1868 17*2 sin (0+121°) „ 23'7 



1869 11-2 sin (0+256°) „ 14-0 



1870 43-5 sin (0 + 278°) „ 124 



Mean of group : 



1850-52 7 sin (0 + 282°) with maximum at 12-1 



1868-70 12 sin (0 + 258°) „ 13-8 



It will be seen that the four years 1851, 1852, 1869, and 1870 give, 

 within a day and half, the same epoch for the maximum. I shall return 

 to these results immediately, but shall first consider the observations 

 already referred to, made at Makerstoun in 1814 and 1845, which gave a 

 period of 25 "96 days. 



The secular change for each year was first determined as follows: — 

 the mean horizontal force for December 1843 minus the mean for De- 

 cember 1814, and the mean for January 1844 minus the mean for January 

 1845*, gave two results, the mean of which was taken as the change during 

 1844 j in a similar way the change for 1845 was found: the corrections 



* Table xxii., Trans. Eoy. Soc. Ediub. vol. xix. pt. 2, p. xxxi. 



