•VOL. LXXVir.] PHILOSOPHICAL TBANSACTIONS. 231 



made of his instrument by parts for every 7±° (see Memoires of the Royal Aca- 

 demy of Sciences for 1751, p. 405), could not determine the error of the whole 

 arc, as the difference from the truth might be insensible on such small arcs, and 

 the examination seems to have been intended to find the differences of these small 

 arcs from each other, rather than from the true arc which they represent. We 

 may therefore be allowed to doubt of the truth of this circumstance. This doubt 

 will be further strengthened by several particulars which I shall adduce. 



1. The apparent altitude of the pole at the Royal Observatory 48° 51' 12^'', re- 

 sulting from the Abbe de la Caille's observations, exceeds 48° 5l' 4" the mean of 

 the observations of Mess. Maraldi, le Monnier, and Cassini de Thury, by 8''', and 

 at the same time his refractions for that altitude exceed what they adopt by the 

 same quantity. 2. His refractions are greater than all other tables give, Dominico 

 Cassini's, Flamsteed's, Newton's, Bradley's, Mayer's, Simpson's, and Lord Mac- 

 clesfield's. The latter I have by me in a manuscript of Dr. Bradley, being what 

 he used to correct his observations by, before he had been enabled to determine 

 the refractions with the new mural arc. They were deduced from a brass qua- 

 drant of 5-feet radius made by Mr. Sisson, still remaining in the Observatory at 

 Sherburn- Castle, and are the more to be esteemed because the divisions of the 

 instrument had been submitted to the strictest re-examination, by which, in the 

 opinion of Dr. Bradley, it was probably rendered as perfect in its kind as any ex- 

 tant, or as human skill could at that time produce. See Dr. Bradley's Letter to 

 Lord Macclesfield, Phil. Trans, vol. 45, p. 5. The refractions in this table are 

 less than Dr. Bradley's by 2'''.4 at the altitude of 45°, and 4" at the altitude of 20°. 

 Mayer's refractions agree almost exactly with Dr. Bradley's, and are entitled to 

 much weight, having been determined by a 6-feet mural arc constructed by Mr. 

 Bird. 3. The refractions were found by the French Academicians at the polar 

 circle, according to M. Maupertuis's Book on the Figure of the Earth, to agree 

 nearly with Dominico Cassini's table. Hence it may be inferred, that the re- 

 fractions in a warmer climate, as France, should be less than according to the 

 same table, and therefore much less than according to M. de la Caille's, and ap- 

 proaching to Dr. Bradley's, which are a little less than M. Cassini's. 4. M. le 

 Monnier, after his return from the polar circle, with a quadrant examined at the 

 zenith and horizon, and after making allowance for the error thence inferred in 

 the total arc, observed a great many refractions of stars under the pole, with the 

 state of the thermometer, and sometimes of the barometer also, as recorded in his 

 Histoire Celeste. These I calculated formerly, and found the refractions observed 

 in very hot and very cold weather, compared together, to follow the same rate of 

 increase and decrease, according to the changes of temperature, as Dr. Bradley 

 has assigned ; and, reducing the observed refractions to the mean temperature, I 

 found them agree nearly with Dr. Bradley's. 5. The refractive power of the air 



