92 C. J. MERFIELD. 



stars are taken between limits of time, separated by some 

 hours, greater accuracy in the reductions, to obtain the 

 correct positions, can be attained, by taking fully into con- 

 sideration the fluctuations of the height of the barometer, 

 and especially the variations of the temperature indicated 

 by the readings of the thermometer, when computing the 

 refractions for a series of observations that extend over 

 some hours of time. Adopting the state of the atmosphere 

 for a mean of the times of observations does not seem 

 sufficient. The refraction tables in use at this Observatory 

 would represent the observed refractions better, if a cor- 

 rection 1 be applied to them for the difference in the force 

 of gravity at Greenwich 2 and Sydney represented by the 

 equation 



A log a =0*00225 Sin (<£'-<£) Sin (>' + <£) 



And further the refraction corrections computed from the 

 Pulkowa tables, with a similar correction applied, would 

 no doubt represent the observed refractions of the Sydney 

 Observatory, much better than those of Bessel. 



1 The theory of this correction, which is neglected in text books, 

 is as follows: — The corresponding heights of the barometric column 

 will be inversely proportional to the force of gravity, assuming 

 equal density of the atmosphere at two places, the latitudes of 

 which are cf> and <£', that is 



p : p' : : y' : g : : 1 - a cos 2 <f>' : 1 — a cos 2 <f> 

 from which 



Log p = Log p + 2 aM Sin (ft - </>) Sin (<£' + </>). 



M = 0-4343 and a = 0-0026. 



Now the quantity p in the above expressions is contained as a 



factor in the coefficient B of the refraction tables, so we may 



therefore write, in units of the fifth decimal place, 



Log B = Log E + 225 Sin (<£' - <£) Sin (<£' + </>). 

 Tables that give a correct value of log B, for a latitude <£, when 

 used at another latitude, denoted by <f>', will furnish a value of 

 log B', that should be corrected by the last term of the preceding 

 equation. For most purposes this term may be united with the 

 value of a of the tables, thus 



A log a = 225 Sin (<}>' -<p) Sin (<f>' + <£). 



2 Bessels' table of refractions, given intheTabulce RegiomontancB, 

 are prepared with a value of a derived from Bradley's observations 

 made at Greenwich during the years 1750 and 1762. 



