1877.] 4:-jO [Mansfield. 



On Refraction Tables. 

 By a. K. Mansfield, Cordova, S. A. 



{Read before the American Philosophical Society, January 5, 1877.) 



The operation of computing the difference between the true and the ap- 

 parent zenith distances of stars, is usually performed by means of Bessel's 

 refraction tables, whicli are calculated from his formula, namely : 



R — dtan: [BTy^/* 



This operation is usually logarithmic, and the refraction tables are there- 

 fore tables of logarithms. The computation may, however, be very much 

 simplified, by the use of natural numbers in place of their logarithms, as 

 will appear from the following : 



In the above formula substitute R for d tanZ^ and p for (BT)^^. The 



formula then becomes 



R = B,p (1) 



in which R^ may be called the mean refraction, and ^ is a factor depending 

 almost entirely on the temperature and pressure of the atmosphere. For 

 general purposes two tables may be made, one of mean refractions (iJj), 

 being the natural numbers corresponding to the table "d tanl " of Bessel, 

 and the other of corrections to the mean refraction. But since these correc- 

 tions would be sometimes additive and sometimes subtractive, the latter 

 table would be reduced to a smaller compass, if each observatory or place 

 where the tables are adopted were to adapt them to the true mean refraction 

 of that place. This may be done as follows: 



Let p„ be tliat value of p, which substituted in equation (1), would give 

 true mean refraction for any particular place : and let R^ be that mean 

 refraction. Then 



i2o = ^i/>o (3) 



Ri is given by its log. in Bessel's first table " log. d tan'^," and a round 

 value for log p^ near the above mentioned mean, may be chosen. From 

 this formula a new table of mean refractions in natural numbers can easily 

 be made. 

 Let r be the correction to be applied to this mean refraction. Then 



r=R-B„ = R,{p-p,) (3) 



from which th6 table of corrections may be calculated. 



*See Peter's "Astronomische Tafeln und Formeln." 



