136 



Stone. Errors in Lunar Theory. 



[Apr. 12, 



The measure of time must be continuous, let, therefore, 1 and (l + x) 

 be the units in B and H, 



then 1296027-618184 . * + 0*0001221805 . & 



= 1296027-674055 . t(l + x) + 0-0001106850 . f(l + x y. 



If, therefore, ™=1296027'674055, 



0-055871 , 0-000114955 . t 

 x — — + . 



t n n 



To reconcile B and H, therefore, x must contain a variable term. 

 Similar remarks apply to the difference between B and V. 



Now, let N be the moon's mean motion referred to 1 as the unit of 

 time, and + the moon's mean motion referred to (l + x) as 

 the unit of time, 



then (N + 8N)(l + a?)=N, 



and 



t . aN=— {0-055871 . £-0-0000114955 . 0}=O"747 . t-V''$4— Y- 

 n 1 ; V1007 



But Hansen determined his mean motion of the moon so as to 

 force an agreement between his theory and observations reduced with 

 Bessel's unit 1 ; and his tables, therefore, represented the observations 

 well for many years whilst 1 was adopted as the unit of time ; but 

 directly the unit of time was changed by the adoption either of H or 

 V, then the effects of the erroneous determination of the moon's mean 

 motion by Hansen became apparent. The change of error in longi- 

 tude of Hansen's Lunar Tables between 1864, when Le Yerrier's 

 Solar Tables were adopted in the Nautical Almanac, and 1880 

 amounts to more than 10". 



The effect of the change of unit is also shown in the comparison of 

 Le Verrier's Solar Tables with observation, but, of course, only to 

 about the thirteenth part of the amount shown by the Lunar Tables. 



The necessity of adopting some definite unit of time, by fixing the 

 constants in the expression for the longitude of the mean sun, is 

 insisted upon. 



If L + n i + s £ 2 is the expression adopted for the longitude of the 

 mean sun, the quantities L , n Ql s must never be changed. The 

 correction ch, which from time to time may appear necessary to 

 obtain the mean longitude of the sun from the longitude of the mean 

 sun, must not be allowed to change the adopted values of L , n Qi and 

 Sq. The true longitude of the sun will then 



= L + n t -f + ^L + Periodic terms. 

 It would appear that speculations respecting changes in the time of 



