140 Royal Astronomical Society, 



total refractions for the planet or comet, and thence deduce the dif- 

 ferences of refraction corresponding to the measured differences of 

 11. A. and N.P.D. It may be questioned whether any approximate 

 formulae, requiring only the calculation of differences of refraction, 

 would lead to a less amount of calculation in this kind of observation. 

 If P be the pole of the heavens, Z the zenith of the observer, S the 

 place of the object, and ZQ be dravvn a perpendicular on PS, the 

 formula used for the total corrections for refraction in R.A. and 

 N.P.D. are the following : — 

 Correction for refraction in N.P.D. = A. tan (PS— PQ) 



Correction for refraction in R.A. = A. — tf^* cosec PS. sec (PS — PQ). 



15 



The factor A is given by the tables in Bessel's Astronomische Unter- 

 suchungen, vol, i. pp. 198, 199, the argument in. the case of the star 

 being the true zenith distance, which is obtained by the formula 

 sec ZS = sec Q,Z sec (PS— PQ). The argument in the case of the 

 compared object is the apparent zenith distance, which is deduced 

 from the same formula, the apparent N.P.D. and hour-angle being 

 first obtained by applying the corrections for refraction in N.P.D. 

 and R.A. of the star (with signs changed) to its true N.P.D. and R.A., 

 together with the measured differences of N.P.D. and R.A. affected 

 only by refraction. 



" The above calculations will be much facilitated by two tables, 



one containing the values of PQ, log sec QZ, and log — — — (to 



five figures) for every minute of hour-angle from 0^ to 6^, which will 

 be found to require interpolations only to first differences, and which 

 is, in fact, merely an expansion of the table mentioned in the Monthly 

 Notices, vol. viii. No. 9, p. 210. The other is a table for obtaining 

 the factor A. It will save much trouble, and be sufficiently accurate 

 to take account of the barometer and thermometer by the empirical 

 formula given in the Monthly Notice above cited, viz. 

 logA = log/c+0-015B4-0-001(100°-T), 

 in which log k is log a or log aJ of Bessel, according as the argu- 

 ment is the true or the apparent zenith distance, diminished by the 

 constant 0-49572. Any error which the use of this formula induces, 

 will very nearly disappear in the differences of the refractions. Thus 

 the second table need merely consist of values of log a— 0*49572, 

 and log a'— 0*49572 ; and the most convenient argument is log sec 

 ZS, the consecutive logs differing by 0"01. This table would, there- 

 fore, very well range with the table of values of log a" — 0*4957, re- 

 quired in the computation of differential refractions." 



The Astronomer Royal gave a description of the gigantic tele- 

 scope erected by the Earl of Rosse, at Birr Castle, which he visited 

 and carefully examined this autumn. The mode of grinding and 

 polishing the speculum, the mounting, &c. were fully described and 

 illustrated by models, and the residual difficulties stated. He also 

 exhibited models of Mr. Lassell's grinding and polishing machine, 

 and of the mounted instrument, dome, &c. It was clearly shown 



