212 ON THE LONGITUDE OF WASHINGTON. 



by Mr. S. C. Walker in Vol. V. Transactions Amer. Phil. Soc, new scries, with a simple 

 modification in the value of -JTas there given ; that used in the computations, whose results 

 follow, being the coefficient of t, whilst in the published paper referred to, it is the co- 

 efficient of {t — 6 h 00 m 00 s ). 



The formula is thus explained by Mr. Walker: 



" The computed increase of the right ascension of the moon's bright limb in passing 

 from an eastern to a western meridian is obtained after Bessel's modification of Newton's 

 formula for interpolation, from the moon-culminating series in the Nautical Almanac. 



"The observed increase is derived from the series of corresponding observed culmina- 

 tions by Gauss' formula. 

 " The computed increase, 



I' = b X + c X' + d X" + e A'" 

 where 



t = assumed longitude in time, west from Greenwich, 



A' = [5. 3645163]. t 



X' = [5.06348] . (t— 12 h 00 m 00 s ) A. 



A" = [4.8874] . (t — 6" 00-" 00 s ) . A' 



A" = [9.6498] . (t + 12 h 00™ 00»). (t — 24i> 00- 00 9 ) . A' 



b = first difference of the moon-culminating series. 



c = second (mean) 



d = third 



e = fourth (mean). 



Also for the computed increase I a , let us call, 



D and 3) ' = the clock time of the culmination of the moon's bright limb at the eastern and western stations 

 respectively. 



>)< and ■%■' = the same quantities for the star, corrected for rate in the intervals (3 — ^) and ( D ' — >(;') respect- 

 ively. 



H and n' = the number of wires at which the moon's limb was observed at the two stations respectively. 



% 



and >*' = the numbers for the stars. 

 _ ^ V-' 



/*■+!*■ 



v v 



v -j- v 



[ ] Gauss' symbol for the aggregate of similar quantities enclosed, 

 n = — _ = 1 -=- seconds of increase of R. A. of the moon's bright limb. 



A=nD'—D 



„_ [>(» — *')1 



w 



whence the 



observed increase I a = A + B. 



Again, let, 



e = *r—/ ? 



* When the eastern observatory is not Greenwich, the value of T is the sum or difference of the two computed 

 increases, according as they do or do not enclose its meridian in the shortest parallel between them. 



