262 ON MR STONE'S EXPLANATION OF THE LARGE AND [31 



But according to Mr Stone's theory as shewn in his tabular comparisons 

 of mean solar times computed from sidereal times by means of the Nautical 

 Almanac and of those sidereal times " corrected to agree with Bessel's 

 sidereal times," the differences would be as follows : 



1865 2 8 '0 1875 16-6 



1870 9'3 1880 23-9 



and at the end of 1881 the difference would have increased to 2 6 8 ' 8 ; so 

 that the increase in five years would be 7 8 '3 instead of 8> 02 as above. 

 In fact the difference according to Mr Stone's theory is just 365 times as 

 great as it should be. 



The origin of this enormous discrepancy between Mr Stone's theory and 

 the fact is readily seen by considering that mean solar time is measured, 

 not by the Sun's mean motion in longitude, as Mr Stone's theory supposes, 

 but by the motion of the mean Sun in hour angle, which is about 365 

 times greater in amount. Hence any small error in the determination of 

 the Sun's mean motion in longitude causes a proportionate error of only 

 about a 365th part of the amount in the interval of mean solar time as 

 inferred from the interval of sidereal time. In fact, if n denote the Sun's 

 mean motion in longitude in a mean solar day, then the length of the 

 mean solar day will be to the sidereal day in the ratio of 



360 + H : 360. 



If now n + dn denote another slightly different determination of the Sun's 

 mean motion in longitude in a mean solar day, the ratio of the length 

 of a mean solar to that of a sidereal day will become 



360 + n + dn : 360. 



Hence the measure of a mean solar day when expressed in sidereal time 

 will be increased in the ratio of 



360 + n + dn : 360 + n, 

 dn 



or 



360 + n ' 



Since 360 is nearly 365 times n, this ratio will be 



1 dn 



1 + s^ - r : 1 nearl y- 



