59 



fraction admits of being tabulated v^-ith 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 atmos- 

 phere to the radius of curvature of the meridian at the place 

 of observation, and the refractive power of air at a given 

 temperature and pressure. For the first he has used the 

 value given by Rudberg, namely, that 1 of air at 32° be- 

 comes 1'365 at 212°. This differs from Gay Lussac, but is 

 identical with that deduced by Bessel from astronomical ob- 

 servations. The second is derived from the researches of 

 Arago and Biot, corrected for the change of gravity from 

 Paris to Armagh. 



Of the refractive power of air there are different values 



of high authority. Denoting by the symbol fi the quantity 



sin T "^ sin r. 



-: r—rn') for 50° Fahrenheit and 29*60 inches pres- 



sm R X sin I" ^ 



sure, the experiments of Arago and Biot give it 57*82. The 

 observations of Delambre with a repeating circle give 57*72, 

 which is also adopted by Brinkley. But the barometer used 

 by this great astronomer is shewn by Dr. R. to require the 

 correction + 0-078, which would change the constant to 

 57'567 ; and as he also used the internal thermometer, per- 

 haps a further diminution might be necessary. That of 

 Bessel is 57'524', and that deduced by Dr. R. from his own 

 observations is 57*546 ; but they cannot be exactly compared 

 without a knowledge of the length of the pendulum at each 

 station, as the measure of density given by the barometer 

 depends on local gravity. 



It was determined as follows by circumpolar stars. The 

 refraction is obtained by subtracting from the subpolar dis- 

 tance 270° plus the declination observed above the pole. If 

 the constant of refraction require a correction, it affects this 



