OF ARTS AND SCIENCES. 



201 



values of 8r and 8r' given in the table will not be in error more tliau 

 0".01, for any zenith distance less than SO'*. For temperatures, pres- 

 sures, or zenith distances, beyond these limits, if great accuracy is 

 desired, the values of a", 8r, and dr', must be multiplied by the factor 

 ^^// yA//^ in ^yhich ^ = BT, and the values of A", I", B, T, and 7, are 

 to be taken from Bessel's table, cited above. To prevent misappre- 

 hension, it may be well to note that the values of A" and X" given by 

 Bessel apply rigorously only to the first derivative of the refraction ; 

 but their use with the second derivative gives rise to so little error that 

 it does not seem worth while to recompute them especially for it. 



Washington, May 30, 1877. 



