Royal Irish Academy. 439 



first he has used the value given by Rudberg, namely, that 1 of air 

 at 32° becomes 1-365 at 212°. This differs from Gay-Lussac, but is 

 identical with that deduced by Besselfrom astronomical observations. 

 The second is derived from the researches of Arago and Biot, cor- 

 rected for the change of gravity from Paris to Armagh. 



Of the refractive power of air there are different values of high 

 1 1 ii- 4.-U. sin I — sin R 



authority. Denotmg by the symbol /x the quantity _^_— _^— p 



for 50° Fahrenheit and 29-60 inches pressure, 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 shown 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, perhaps a 

 further diminution might be necessary. That of Besselis 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 distance 270° plus the 

 declination observed above the pole. If the constant of refraction 

 require a correction, it affects this declination both at the star and at 

 the polar point, and the latter also affects the subpolar observation ; 

 hence, calhng the tabular refraction ^ v, and the difference between 

 it and the observed d r, we have for each observation the equation 

 of condition. 



dvi = dix{v — v'— 2p} = rf /i X K ; 

 combining which by minimum squares, the value oi d y. for that star 

 is obtained. If the values of it at different zenith distances are equal, 

 or differ only by what may reasonably be considered error of obser- 

 vation, then it may be also inferred, that the formula correctly as- 

 signs the refraction tlirough the range of zenith distance included by 



the observations. •, . , , • i i. •, 



Dr. R. then gives details respecting the mural circle which he used, 

 the permanence of its microscopes as to run, and the mode of obtain- 

 ing its index correction, and the correction of its divisions. When 

 the stars are spectra, he bisects the yellow near the green, and remarks 

 that the fluctuations of irregular refraction are often of considerable 

 duration. The hygrometric state of the air does not seem to produce 

 any effect, and he shows that the external thermometer is to be used 

 at his observatory. The details of observation are then given for 

 seventeen stars, from 77° 10' to 84° 56' zen. dist., of which there 

 are 317 subpolar observations. 



If ii southern star be determined at a place when it passes near the 

 zenith, so that its place may be assumed as free from error of refrac- 

 tion, the value of rf ^ is multiplied by a much larger factor. This ad- 

 vanfeige, however, is more than balanced by the uncertainty caused 

 by the diftcrencc of instruments and local circumstaaces at the two 



