1877.] 



427 



[Mansfield. 



plied to the log., and when 77° or more, another correction must be applied 

 on account of the exponent A. These corrections maybe found as follows : 

 Let log. pi z= log. (BT) -\- log. y, then the entire correction 



r, = log. p — log. p^ =^ log. y (/ — 1) + log. {BT ) (A — 1). . . . (5) 

 in which the two terms of the last member are th-e first and second correc- 

 tions respectively. The following will illustrate a method of tabulating 

 these corrections : 



The argument at the top is either log. (BT) or log. y, according to which 

 correction is sought for. The side arguments are zenith distances, which 

 may be replaced by declinations, &c. 



The first column is used when taking out the first correction, and the 

 last column, when taking out the second correction. To find the values of 

 the argument for the last column, enter Bessel's table "J." with the 

 value of X for any zenith distance of the first column, and against it will be 

 found the corresponding zenith distance for the last column. The units 

 place of the corrections, corresponds to the fifth place of log. p, and when 

 the logarithmic argument is negative, the correction is negative, and vice 

 versa. 



In place of the above table of corrections to mean refraction, a graphical 

 table may be constructed, which has some advantages. Let a right-angle 

 triangle A B C he drawn, containing lines parallel to the base, at equal 

 distances apart. 



c 



o.oSooo 



.02500 



. o2ooo 



■ olSoo 



o.olooo 



+.0. 00912 



+ -00450 



.00022 



. oo5o5 



. olooo 



These equal distances may represent seconds, or tenths of a second. The 

 distance i? C is made equal to the maximum correction nil, or the correc- 

 tion for the maximum zenith distance, and maximum value of log. p, whicli 



