

31] INCREASING ERRORS OF HANSEN'S LUNAR TABLES. 261 



In 1864 the error of Bessel's formula amounted to rather more than 

 half a second of time, and accordingly in that and subsequent years the 

 sidereal time at mean noon was deduced from Le Terrier's Solar Tables, 

 which gave much more accurate results. 



Now it is contended by Mr Stone that by the change thus introduced 

 into the Nautical Almanac the unit of mean solar time was practically 

 altered to such a degree that at the end of 1881 the difference in the 

 count of mean solar time amounted to nearly 27 seconds, and that the 

 difference is increasing at the rate of about 1'46 seconds per annum. 



It is clear, therefore, that if no such change had been made in the 

 Nautical Almanac that is, if Bessel's formula had continued to be employed 

 no such change of the unit of time would have taken place. 



Let us see then, what difference this would have made in the count 

 of mean solar time as derived from sidereal time when compared with the 

 count found by means of our present Nautical Almanac. 



Bessel's formula for the sidereal time at Greenwich mean noon of Jan. 1 

 in any year is given in the prefaces to the Nautical Almanacs from 1834 

 to 1863 inclusive. In 1864 and subsequent years the sidereal time at 

 Greenwich mean noon is derived from Le Verrier's tables. 



The following little table shews the sidereal time at Greenwich mean 

 noon of Jan. 1 as calculated for every fifth year from 1860 to 1885 by 

 Bessel's formula, and as taken from the several Nautical Almanacs: 



By Bessel's From pjg 



Formula. Nautical Almanac. 



h. m. a. h. m. s. s. 



1860 18 41 28-87 18 41 28'87 Bessel's formulae employed O'OO 



1865 18 44 35-36 18 44 35"92 Le Verrier's Tables employed 0'56 



1870 18 43 43-87 18 43 44'44 0'57 



1875 18 42 54-47 18 42 55'06 0'59 



1880 18 42 5-95 18 42 6'56 0"61 



1885 18 45 1173 18 45 12'37 0"64 



Hence we see that the difference of sidereal times at mean noon in 

 consequence of the change from Bessel's formula to Le Verrier's Tables, 

 which amounted to 8< 56 in 1865, had increased to 8 '64 in 1885. That 

 is, the difference increases at the rate of 8> 08 in twenty years, or of 

 8 '02 in five years. 



