Mansfield.] 



42G 



[Jan. 5. 



In making the table, comparatively few values need be computed, for, 

 having these few values, the others may be supplied by interpolation. The 

 following is a small portion of a table of these corrections, in what appears 

 to be its most convenient form. It was computed from Bessel's tables, as 

 given by Peter's. 



Apparent zenith distance is here used as argument at the side. It may 

 be replaced, however, b}' the corresponding declination, or the circle read- 

 ing. Log. p is used as argument at the top, and — 0.01000 is the assumed 

 value of log. p^. When log. p = log. p„ the correction is zero, therefore we 

 have written the table of mean refractions in that column, thus combining 

 both tables in one. This may be done when the arguments at the side are 

 not chosen so far apart as to make the second differences of the mean re- 

 fraction too great. In computing the tables from the above formula?, the 

 arithnuficnl comjdeinent of log. p must be used, when that log. as found 

 from Bessel's tables, is negative. When log. p occurs in the line at the 

 top of the table, the correction is negative, when in the line at the bottom, 

 it is positive. To find the values of log. p for the lower line, corresponding 

 to those of the upper line, call the natural number corresponding to anj' 

 particular value in the upper line p^, and its corresponding value for the 

 lower line p.^ Then from formula (3), since r is minus in one case and 

 plus in the other, 



— /'I + /»« = /'■.' — /■',, 

 or ^2 = 2/>„ — /,, (4) 



Before entering the table of corrections, Ion. B, log. T, and log. y are taken 

 as usual from Hessel's tables, are then added, and tiieir sum is the argument 

 log. i„ when the zenith distance is less than 4")°. When the zenith dis- 

 tance is 450 or more, a correction on account of the exponent ), is to l)e ap- 



