1883.J 



135 



April 12, 1883. 



THE PRESIDENT in the Chair. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



The following Papers were read : — 



I. '* The Principal Cause of the Large Errors at present exist- 

 ing between the Positions of the Moon deduced from 

 Hansen's Tables and Observation : and the Cause of an 

 Apparent Increase in the Secular Acceleration in the Moon's 

 Mean Motion required by Hansen's Tables, or of an Appa- 

 rent Change in the Time of the Earth's Rotation." By E. 

 J. Stone, F.R.S., Director of the Radcliffe Observatory, 

 Oxford. Received April 3, 1883. 



(Abstract.) 



The errors in the Lnnar Theory have been traced to the effects of 

 changes in the unit of time, which have, apparently unconscionsly, 

 been introduced from time to time into astronomy, with changes in 

 the adopted data. 



The argument is clearly seen by a consideration of the different 

 expressions for the longitudes of, what may be called, the mean sun, 

 which have been adopted for the determination of the sidereal times 

 at mean noon. 



If B, H, and Y denote the longitudes of the mean sun, according 

 to Bessel, Hansen, and Le Yerrier, we have for 1850, January 1, 

 Paris mean noon, t. 



B = 280° 46' 36"T2 + 1296027-618184 . £+0;000122180* . /*, 

 H=280° W 43"-20 4- 1296027*674055 . t + 0-0001106850 . f-\ 

 Y=280° 46' 43 /r -51 + 1296027-678400 . f+ 0-0001107300 . P. 



In all these expressions the unit of time has been supposed to be a 

 Julian year of 365*25 mean solar days. 



The constant differences 7"'08 and 7''*39 in B — H and B— Y are 

 not unimportant, for they introduce abrupt changes in the record of 

 time ; but the differences in the coefficients of t and show that the 

 same unit of time cannot have been adopted in these expressions. 



