169 



meters and mean of the Thermometers, and thus obtain the value 

 of k S corresponding to the zenith distance of that Star, and hence 



in. 



its mean value for Barom. 29,60 and Therm. 50. 



By selecting 3 or 4 stars between 88° and 90° zenith distance, 

 and 3 or 4 between 80° and 88° zenith distance, the mean values of 

 k S may be determined, (if a sufficient number of observations be 

 used to make the effects of the irregular refractions disappear.) Then 

 a Table of the mean values of k S between 80° and 90° zenith dis- 

 tance, may be interpolated. From the mean value for any zenith 

 distance obtained by this Table, the actual value of k S may be 

 computed from the heights of the Barometer and Thermometer, 

 and then the refraction is easily had. 



By this method a Table may be much more readily constracted, 

 and, if I mistake not, with greater exactness, than by help of any 

 hypothesis of the actual variation of density. 



Or this method may be applied to the verification of any Table 

 of refractions. From such a Table, we can readily find, by compu- 

 tation, '^^' (-- ^^^^^ ) for each zenith distance. 



' sin. 1 V a 2 ' 



The parts of this quantity have a given ratio to each other, what- 

 ever be the zenith distance ; therefore each can be readily de- 

 duced from the whole, and the first may be put into a convenient 

 Table. From this Table we may readily find for any height of the 

 Barometer and Thermometer, 



kta.nd' ( —, \ and k tan ff ( '^^^P^\ 



\ a sin. 1 7 \,'2 sm. 1 / 



by substituting foir I and m their values above given. 



Their difference =k S and the refraction = !^^?tan (6 — k S) be- 



ing compared with the observed, will easily show the correction tliat 

 k S requires; and thence the correction required by the mean 



VOL. XIII. A A ^ 



