232 PHILOSOPHICAL TRANSXtlTIONS. [anNO 1787. 



about its mean temperature was carefully observed by Mr. Hawksbee, as related 

 in his Physico-Mechanical Experiments, and the ratio of the sine of' incidence 

 to that of refraction, out of air into a vacuum, found to be as 999736 to 

 1000000. Hence the astronomical refraction at the altitude of 45** should be 

 54^'.6, only '2" A less than Dr. Bradley's, and 2" less than the same when his 

 higher refractions are new calculated with the true parallax of the sun, and I", 2 

 less than I have before shown to result from my observations of the apparent 

 zenith distance of the equator compared . with Dr. Bradley's of the apparent 

 zenith distance of the pole, both taken with the same brass mural quadrant, 

 but 1 2" less than the Abbe de la Caille's. 



From all these facts, I think I may be allowed to conclude, that the Abbe de 

 la Caille's refractions are not just, but considerably too large ; and consequently, 

 as there can be no doubt of the care or diligence used by this astronomer in his 

 observations and calculations, that the total arc of his instrument is too large 

 for the radius, and, as I shall show presently, gives the measures of the zenith 

 distances too small. 



But it may be asked, are then all the observations of this great astronomer, 

 with their results, the fruit of so much labour and pains, to be considered as 

 uncertain, or lowered in their value, in proportion to the error of his instru- 

 ment ? I am happy to answer, that the very ingenious method which he used of 

 getting his refractions, from the comparison of the sum of the apparent altitudes 

 of the poles at Paris and the Cape, with the sum of the apparent zenith dis- 

 tances of stars passing the meridian between the two places, has fortunately, 

 without his being aware of it, given him the refractions affected with the error 

 of the arc of the instrument, and consequently proper for correcting his obser- 

 vations ; for if the instrument be supposed ill divided, any error in the divisions 

 will naturally be thrown on the refractions ; and if the total arc is too large for 

 the radius, the stars will appear to approach the zenith by the error of the divi- 

 sions as well as the refractions, and the refractions in the table will come out too 

 large, but still suitable to the instrument because a correction is necessary to be 

 added to the observed zenith distance, on account of the error of the instru- 

 ment, as well as of the true refractions, and the table deduced from the instru- 

 ment gives the sum of the two corrections together, without determining them 

 separately. 



Hence his table of refractions, though well adapted to his instrument, may 

 be very unfit to be applied to any other. His latitude of his observatories and 

 his declinations of the stars will not lose any of their certainty, at least within 

 the limits of the zenith distances measured by his sector, viz. 6o°. And this 

 accounts for a circumstance, at first sight rather extraordinary, that his declina- 

 tions of stars should agree so nearly (generally within 5" of Dr. Bradley's, as 



