DETERMINATION OF ASTRONOMICAL REFRACTION. 81 



z n + z\ the sum of the zenith distances is simply the 

 difference of the circle readings, and is therefore inde- 

 pendent of the zenith point ; and finally the time necessary 

 to obtain sufficient data does not extend over a long interval; 

 also the simplicity of the reductions has much to commend 

 the method. 



The disadvantage in this method is that the declinations 

 of the stars must be known. Taking fundamental stars 

 and a large number reduces this difficulty, which will be 

 almost eliminated in the final results. 



Having obtained the refractions in the manner explained 

 in the preceding paragraphs, the correction to the constant 

 of the table can be deduced from the following equation 1 



dr = Ada + Bdfi 5 



A = r/a 



/l?d£ _ 1_\ 

 y (3 Kcip 2pJ 



Consulting an investigation by Professor Oomstock, 2 it will 

 be noted that the effect of the higher powers of Afi, for the 

 barometric pressures here used, and involved in the factor 



1 B ^ B ^ B 



need not be taken into account. The quantities neglected 

 will not be sensible at zenith distances less than 80 degrees. 

 In these reductions no modification of the factor of the 

 refraction depending on the barometer need be made. 



Therefore the coefficient P is asumed to be correct or that 



dp = o 

 Equation (5) reduces to the expression 

 dr = Ad^ = — da 



a 



1 Chauvenet. Vol. i., p. 672. 



3 Publications of the Lick Observatory, Vol. i. 



F— Sept. 6, 1905. 



