of the Principal Fixed Stars, 131 



In Dr. Brinkley's determination, « = 0",74. (vid. Trans. Roy. 

 Irish Academy, vol. xii.). It is not likely to have been greater 

 in JM. Bessel's investigation : which investigation, although it 

 may be very different in aj)pearance, must essentially be the 

 same. Therefore let us take Ik = j {p—p'). 



When we consider the irregularities of refraction at zenith 

 distances exceeding 60° or 70-", and consider the number of 

 circumstances relative to the corrections used in reducing the 

 observed zenith distances to the mean, it is not likely p' can be 

 depended on nearer than 0",3 ; and, although p is not equally 

 affected by the irregularities of refraction, yet the other cir- 

 cumstances may easily concur in making it uncertain to 0", 1 5 : 

 thus Zk may be uncertain to 0",6; v.-hich is required for our 

 supposition. In meridian circles 2^~P ansv.ers to the distance 

 of the Polar points determined by assuming the constant of 

 refraction = Jc : and here more causes of error interfere, be- 

 cause, instead of the plumb-line, the index error is used for 

 ascertaining the stability of the instrument. 



It appears that the eifects of irregular refraction have been 

 only lately duly appreciated. Formerly it was supposed that 

 p', on account of the greater number of stars used, was more 

 exact than j^. It is at present impossible to estimate the pro- 

 bable error arising from the effects of irregular refraction; 

 and therefore, in the probable error given by M. Bessel, he 

 seems to have cojnputed it generally with a reference only to 

 common observations. 



The conclusions that appear to follow from the whole 

 are, that it is quite uncertain whether the catalogue of Dr. 

 Brinkley or of M. Bessel be most exact ; and that probably 

 the mean between them will be nearest the truth. A circum- 

 stance favourable to M. Bessel's constant is, that the obh- 

 quity of the ecliptic, deduced from both solstices', comes out 

 nearly the same. In another way, this appears rather to ope- 

 rate differently, from the genei'al imwillingness of astronomers 

 to allow this great constant of refraction which so obviously 

 solved the difficulty. This showed they considered observation 

 to be against it. Another favourable circumstance of consider- 

 able weight, is, that Mr. Groombridge nearly agrees with M. 

 Bessel. But, by the recent comparison of North Polar distances 

 observed at Greenwich and Dublin, and wliich jnay be easily 

 made, it appears nearly certain that the same constant of re- 

 fraction is virtually employed in each observatr)ry. It is very 

 unlikely that the two constants should be inexact by the same 

 quantity. This, and tlie great agreement between tiic respective 

 North i\)lar distances, are much in ilivour of the exactness of 

 the North Polar distances of Mr. Pond and Dr. Brinkley. 



R 2 M. Bes- 



