(1) 



STATIONS NEAR THE NORTHERN BOUNDARY OF OHIO. 249 

 , t-\-l.t.t—l.t — 2. , ^4-1.^.^—1./ — 2./—^ ^ 



-f — ! e -4- — ^ H f 



^ 1 .2.3.4 ^ 1.2.3.4.5 "^ 



/4-2./4-I ./.^— 1.^ — 2./ — 3 

 "^ 1.2.3.4.5.6 ^ 



Also the variation of the function for the unit of interval at the 

 rate for the arrangement t, being the first differential quotient of the 

 above formula. 



6, 2^ — 1 , 3f — 3^4-^, 



r= _-^ c -4- ! — 2 d 



1 ^ 1.2 ' 1.2.3 



W 



4f_6f— 2^+2 5^—10/^4-5^— 1 



"^ 1.2.3.4 ^~^ 1.2.3.4.5 '>' 



6 /^ — 15 /^ — 20 f 4- 45 /^ -f- 8 jf — 12 ^ 

 "^ 1.2.3.4.5.6 ^ 



If we denote, for conciseness, the co-efficients of b, c, d, &c., in (1), 

 by X, X', X", &c. ; and those of c, d, e, &c., in (2), by T, T', T", &c., 

 we shall have : 



Value of function for argument t, = a4-5X4-cX'-|-dX"+cX% &c. 



Rate of variation for argument t, = b-\-cT-{-dT-{-dT"-{-eT"\^c. 



To apply these formulae to the reduction of moon-culminations, for 

 an assumed meridian t seconds in time 4- west of Greenwich, we must 

 make the argument the difference of meridians, the unit of interval 

 being 43200 seconds. Two sets of coefficients are required for each 



* The coefficient of g in (2), in Bessel's paper, is ihus stated, owing to a typographical 

 error. 



6 f5 _ 15 ^4 _ 40 t^^QOf'+lBt — 27 

 1.2.3.4.5.6 



