501 



accordingly, in his computation of a formula for that purpose, i? Ursa 

 Majoris, at 70 10' zenith distance, was the lowest star included in 

 his estimate. By applying that formula to stars below 80 zenith 

 distance, Mr. Groombridge has since found some correction to be 

 necessary ; for the refraction at the low altitudes is not really so 

 great as might be presumed from that of stars less distant from the 

 zenith. He has consequently been induced to make a course of ob- 

 servations on other circumpolar stars, beyond the former limits, and 

 as near to his north horizon as the situation of his observatory would 

 permit. Since the formula of Dr. Bradley appears most conveniently 

 applicable to the purposes of the practical astronomer, but not quite 

 correct in the numbers assumed for refraction at 45, and for the co- 

 efficient of x, the author has endeavoured to find out such numbers 

 as would correspond more accurately with observation, and has found 

 that the same formula may be made to serve as low down as to 87 

 of zenith distance, by increasing the amount of the numbers before 

 mentioned still a little more than he had formerly done. 



But for stars of less altitude than this, or within three degrees of 

 the horizon, he found that the same formula could not be made to 

 serve throughout, but that it became necessary to vary the amount 

 of the coefficient y nearly in proportion to the excess above 87 ze- 

 nith distance. 



The table of observations on which these estimates are founded is 

 divided into two parts ; the former of which is the result of more 

 than 240 observations made upon sixteen stars between 80 and 87 

 zenith distance ; and the latter is founded upon six other stars be- 

 tween 87 and 88 42' zenith distance. 



The difference of the obliquities of the ecliptic, as deduced from 

 the summer and winter solstices, or disagreement between the eleva- 

 tion of the equator, thence deduced, and the zenith distance of the 

 pole, as inferred from the zenith distance of circumpolar stars, is 

 ascribed by the author to error in the quantities of refraction, which 

 was assumed too small by Dr. Bradley. And he remarks, that, on 

 the contrary, his observations of the solstices, when reduced accord- 

 ing to his own improved formula for refraction, agree in giving re- 

 sults that correspond with his observations of circumpolar stars. 



With respect to thermometrical corrections, Mr. Groombridge ob- 

 serves, that his results appear to be most correct when reduced by 

 the state of the thermometer without-doors instead of that which is 

 within ; and that the difference is very considerable where the zenith 

 distances are so great as those included in the present remarks. 



