244 Elements of the Solar Eclipse. 



For the purpose of facilitating the objects last mentioned, the 

 elements of the eclipse which forms the subject of this paper, were 

 calculated with great care, the value of each equation having been 

 obtained within the nearest thousandth of a second. The solar 

 tables used, were those of Delambre, to which were applied the 

 corrections indicated by Bessel. The lunar tables, both of Dam- 

 oiseau and Burckhardt, have been employed, in the hope that ob- 

 servations may be made at those places in our country, whose lon- 

 gitude has been previously determined, and thus the number of 

 tests, by which their respective merits must be ascertained, be 

 somewhat increased. On the importance of these, it is deemed 

 unnecessary to insist. It is proper to state, that the first and two 

 last longitudes derived from Damoiseau's tables, as stated in the 

 elements, were obtained by applying the hourly motion computed 

 for the second period, and the last but one respectively. 



From the elements as now presented, their values for any inter- 

 mediate period of time, may be readily deduced by the application 

 of simple proportion and the equations of second and third differen- 



and d'" the second and third differences. The factor x ( x — 1 ) CO r- 

 2 



respondent to every hundredth of the interval, will be found in 

 the first of the tables, subjoined to the elements of the general 

 eclipse, and the factor x ^ x ~ 1 ^ fcl^ for every twentieth, in the 

 second. The first of these has been used in the computation of 

 the equations, wherever the accuracy of the tables admitted of its 

 application. The Nutation of Bcsscl has been employed in the 

 computation, both of the solar and lunar elements, and in accord- 

 ance therewith the epoch of the lunar tables has been diminished 

 by 0" 455 of the sexagesimal division of the circle. 



In the computation of the sun's horizontal parallax, 8"605M has 



