STATIONS NEAR THE NORTHERN BOUNDARY OF OHIO. 251 



and calling 



V = the hourly variation for argument /, we have, enclosing in 



brackets the log. co-efficient, 



V = -L (a -{- /?X + rX' -f- SX" 4- eX'" -h ^X"' -I-, &C.) 



3600 ^^ K^oo.^-, 1 



w= -^ = [3-55630] =: 



The value of V is the same as that given in the N. Almanac, viz. 

 the variation of the R. A. of the moon's bright limb in one hour of 

 longitude, and may be obtained for the argument t, as above, from the 

 values of V, for Greenwich. 



Although 1 have given several terms in the series for the value of Y, 

 three are, in all instances, sufficient for reducing moon-culminations ; 

 hence, adopting the usual notation for the argument of a series, the 

 formulae used in computing Table I. may be briefly recapitulated, / 

 being an approximate longitude, differing less than a minute from the 

 true longitude, 



a ,^^ = a-\-hX-{-cX' -\- dX" -|- eX" 



^/// 



n = n ,+, = [4-63548] ^ 



a -f- (3X -\- lyX' 



t' = / -f w (a o + t- — a o + , H- ^. ^ . 0) 



5 



=: the correction of the sidereal time of observation 



VI. 3 N 



