OF THE HORIZONTAL FORCE. 



9 



Ae difference between any single period and the mean epoch. 

 A< " " any temperature and the mean temperature. 



The formula was first applied to the monthly means resulting from five years of 

 observation ; it gave y = + 1.0 scale division ; but the remaining differences showed 

 that the irregular changes between June and July, and December and January, of 

 the years 1840-41, had an undue effect on the result, the first year's observations 

 were, therefore, omitted, and the process repeated for the remaining four years. 

 The twelve conditional equations gave the normal equations : 



+ 2143.15 = + 143a; 200.4 y. 

 2549.73 = 200.4x+ 71 1.1 y. 

 whence x= monthly effect of the progression = + 16.5 scale divisions. 



y temperature correction for 1 Fahr. = + 1.8 " " 



An examination of the observed and computed values showed that the introduc- 

 tion of a term Ae 2 2 Avould improve the agreement, solving the three normal equa- 

 tions we found 



x= + 17.6 

 y= + 1.62 

 -- 0.31 



The following table shows the comparison of the observed and computed monthly 

 mean readings of the bifilar : 



Adding + 3.5 scale divisions to the mean value of B m the above differences will 

 balance. According to the above results, the annual progressive change is + 17.6 x 

 12= 211.2 scale divisions, and the change in magnetic moment of the bar for a 

 change of 1 Fahr. in the temperature, or q = + 1.62 x 0.0000365 = 0.0000591. 

 This agrees with the best direct determination, being the one in which the observa- 

 tory was alternately heated and cooled. 



To test these results, a combination of the six warmest months with the six 

 coldest months, by alternate means furnished several values for q depending 

 merely on the assumption of a gradual regular progressive change during each year 

 and a half, for which separate results were deduced ; this series commences with 

 May, 1841, and ends with April, 1845, and contains, therefore, the same number 

 of months as the first combination, excluding at the same time the two defective 

 portions noticed above. This combination also possesses the advantage of showing 

 the variations in the values of q. 



