M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 117 



For this observatory, whose altitude is 4,209 feet and 

 where the mean annual pressure is less than 26 inches, 

 an investigation into the effect of the higher powers of 



A /3 involved in the factor fi== i -) - = i -| 



r> B B 



(in Bessel's notation for r) was necessary. In his memoir, 

 " Untersuchungen iiber die Constitution der Atmosphare 

 und die Strahlenbrechung in Derselben," St. Petersburg, 

 1866, (jylden has neglected the squares and higher powers 



of %-, since for places at low altitudes An is a very small 



D ' . D 



quantity. This investigation was made by Professor Corn- 

 stock (Vol. I, " Publications of the Lick Observatory"). 

 From his investigation the conclusion is drawn that " the 

 Pulkowa Refraction Tables may be used for atmospheric 

 pressures as low as 25 inches without taking into account 

 the squares and higher powers of ^b, and the quantities so 

 neglected will not be sensible at zenith distances less than 

 80. " The minimum reading of the barometer during these 

 observations was 25.72 inches, so that in these reductions 

 no modification of the factor of the refraction depending 

 upon the barometer need be made. 



This question having been disposed of, the assumption is 

 here made that all of the error in the refractions is due to 

 an error in the constant of refraction. This amounts to 

 assuming the constant j3 to be correct or that d/3=o. The 

 equation above then reduces to the very simple expression 



dr Ada = da ; 



hence 



da dr 



a r 



or dloga = dlogr. 



Having dlogr from the reductions, we thus have dloga, and 

 hence da. 



This assumption would perhaps seem somewhat risky f6r 

 stars whose zenith distances are greater than 80. But at 

 the conclusion of the reductions, the value of dloga deduced 



