1872.] 



26-day Period of the Earth's Magnetic Force. 



421 





1844. 



1845. 



Difference, 



Period. 



a sin (0+c). 



Max. 



a sin (0+<?). 



Max. 



1845-1844. 



d. 

 25f.. 

 26 .. 



26*.. 



22°9 sin(0 + 69°) 

 24-1 sin (0+101°) 

 2-22 sin (0+132°) 



d. 



1-5 

 25-0 

 22'9 



10-5 sin (0 + 288°) 

 10-6 sin (0 + 159°) 

 10-4 sin (0 + 252°) 



d. 



11-7 



21-0 

 157 



d. 

 + 10-2 



- 4-0 



- 7-2 



It will be seen that though the constant a varies little, it is greatest for 

 each year by the period of 26 days ; on the other hand, the constant c 

 varies considerably ; and this constant may be made the most delicate test 

 for the true mean period. By the period of 25| days, the maximum hap- 

 pens between the 1st and 2nd days in 1844, but ten days later in 1845 ; 

 by the 26-J-day period, on the other hand, it happens seven days earlier in 

 1845 than in 1844. The 26-day period shows a difference in the same 

 direction of four days. 



It will be evident that if the time employed for the calculation be less 

 than the true period, the maximum resulting from the superposition of a 

 succession of periods will be thrown later than the maximum derived from 

 the exact period ; if, on the other hand, the time employed be longer 

 than the true time, the maximum resulting from the superposition will 

 occur earlier. The difference between the epochs of maximum derived 

 from two successive series of groups will thus give an approximation to 

 the error of the period employed. If we apply this to the difference of 

 epochs in the preceding Table, remembering that 14 periods intervene 

 between the means from the two years (excepting for the 25|- days, when 

 there are 14 J periods), we shall obtain the following corrections to the 

 times employed : — -, 



10-9 



25| +™ = 26-36 



26 — -i = 2571 

 14 



2U - — = 25-82 

 6 14 



Mean = 25'96 



which is exactly the period found in my paper, already referred to, from 

 an examination of the intervals from minimum to minimum throughout 

 the two years. 



It is not unlikely, however, that this exact agreement is accidental ; the 

 constant c requires for its determination, not only an exact correction for 

 the secular change, but also for the annual period ; though any slight 

 change which this additional correction might produce would probably have 

 little effect on the final result. 



With these results in view, we may now return to the Greenwich values. 



