142 Royal Society : — The Astronomer Royal on a supposed 



two days, no sensible error would be introduced by interpolating be- 

 tween the numbers for the days immediately preceding and following 

 the omitted days. 



The years selected for this examination were 1850, 1851, 1852, 

 18()8, 1869, 1870 ; and the beginning of the first period in each ye^r 

 after the first was thus found : — Fourteen periods of 26-1- (Jays each 

 amount to 368| days. For convenience, after completion of the an- 

 nual winter adjustments, the first period in 1850 was made to com- 

 mence on January 17 ; therefore the first period in 1851 v/as com- 

 menced on January 21, and that in 1852 on January 25. Similarly, 

 the first periods in 1868, 1869, 1870 commenced on January 1, 4, 

 and 8 respectively ; and the beginnings in the three later years are 

 not unconnected with those in the three earlier years : for, from 1852, 

 January 25, to 1868, January 1, are 5820 days, and 221 periods of 

 26} days each are 5819f days; but as the years are widely sepa- 

 rated, and a small error of period would produce a large discordance, 

 it Has appeared best to exhibit the results of the two three-years' 

 groups separately. 



Some periods, in which there were unusually large interruptions, or 

 which were partly occupied with experiments, were omitted entirely. 

 The following is a complete list of periods omitted : — In 1850, that 

 beginning with December 24 for horizontal forcQ ; in 1851, that be- 

 ginning with March 14 for western dechnation, and those beginning 

 with March 14, June 28, July 24, for horizontal force; in 1852, those 

 beginning with February 20, May 9, December 6, for both elements ; 

 in 1868, those beginning with February 23 for declination, and Ja- 

 nuary 1, January 27, February 23, and December 8 for horizontal 

 force; in 1869, those beginning with October 21 and December 12 

 for both elements; and in 1870, those beginning with June 15 and 

 December 16 for declination, and that beginning with December 16 

 for horizontal force. Interpolations of three days occur only in the 

 following instances:— 1850, (dec.) Feb. 4-6, (h. f.) Feb. 9-11, 

 July 23-25; 1851, (dec.) Feb. 18-20, Oct. 20-22, (h. f.) June 

 9-11; 1852, (dec.) Feb. 7-9; 1868, (dec.) Feb. 15-17, (h. f.) 

 none; 1869, (dec.) June 6-8, (h. f.) June 6-8; 1870, (dec.) 

 Sept. 24-26, (h. f.) Sept. 24-26. 



The mean values of each element for each progressive day in 

 every period of the several years, uncorrected for the proportional 

 part of secular change through the 26 days, and omitting the imper- 

 fect 27th day, are as follows : — 



