438 Royal Irish Academy, 



His Grace the Archbishop of Dublin having taken the Chair, the 

 President continued the reading of Dr. Robinson's Paper " On the 

 Determination of the Constant of Refraction by Observations with 

 the Mural Circle of the Armagh Observatory." 



The author remarks, that the problem of astronomical refraction is 

 embarrassed by two causes of error. The differential of the refraction 

 is obtained by supposing the atmosphere to consist of spherical shells 

 concentric with the earth ; and the integral of this, by assuming 

 some mathematical relation between the height above the earth and 

 the corresponding density of the air. He shows that the first of 

 these cannot be rigorously true ; and that the relation between den- 

 sity and height, besides being unknown in general, may be expect- 

 ed to vary with the latitude. He therefore considers all existing re- 

 fraction tables as approximations which require correction for each 

 individual observatory. 



For about 74° from the zenith, the refraction is independent of the 

 law of density, and requires only an exact knowledge of the air's re- 

 fractive power ; this, however, has not been yet obtained with suffi- 

 cient accuracy by direct experiment, and therefore must be deduced 

 from astronomical observations. At greater zenith distances some 

 constitution of the atmosphere must be assumed, and if its expression 

 contain a sufficient number of arbitrary constants, the resulting re- 

 fraction can always be made to represent with sufficient exactness 

 what is actually observed. As, however, neither the formula of Bes- 

 sel, nor that of Ivory, very readUy admits such modifications. Dr. R. 

 used the method given by the late Bishop of Cloyne, in the twelfth 

 volume of the Royal Irish Academy's Transactions, which, however, 

 he has extended to 85° zenith distance. 



If the atmosphere be supposed of imiform temperature the refrac- 

 tion has been computed by Kramp ; it is found greater than the truth. 

 If the density be supposed to decrease uniformly as the height above 

 the surface increases, the refraction is given by Simson ; it is nearly 

 as much in defect as the other in excess, and it is found that their 

 mean is very near the truth. If, then, the differential equation of re- 

 fraction be developed in terms of the tangent of the apparent zenith 

 distance, it is found, on integrating, that the first term belongs to 

 an atmosphere bounded by parallel planes ; the second depends on 

 the equilibrium'of the strata, and the others alone are affected by the 

 assumed hypotheses. Their geometrical means are found to satisfy 

 the Armagh observations as far as 85° zenith distance, below which 

 the series ceases to converge, and the mean changes its relation to the 

 true refraction according to the temperature and pressure. The ex- 

 pression thus obtained for refraction admits of being tabulated with 

 the corrections for the thermometer and barometer in a couple of 

 pages ; and he thinks this form of tables more convenient than any 

 other with which he is acquainted. 



To compute them are required the expansion of air by heat ; the 

 ratio of the height of the homogeneous atmosphere to the radius of 

 curvature of the meridian at the place of observation, and the re- 

 fractive power of air at a given temperature and pressure. For the 



