The Rev. Dr. Robinson on the Constant of Refraction. 181 



impossible to determine it to the tenth of a second. But it is practicable to go 

 about 10° lower, by a principle, first, I believe, remarked by Laplace ; namely, 

 that the refraction computed on the hypothesis of uniform temperature is greater 

 than the truth, and on the hypothesis of uniformly decreasing density less, and 

 that the mean of the two is nearly exact. For instance, Laplace gives for the 

 horizontal refraction, (t = 32° ; barometer, 29.92,) 



U. Temp. . . . 2394". 6 i 

 Observed . . . 2106 .o' 

 Uniform decrease of dens. 1 824 . 1 \ 



The arithmetical mean = 2109.3; the geometrical =: 2090. Ivory finds 

 (t = 50, bar. = 30.00,) 



French tables . . . 2031.5 < 



U. D. D.* ... 1722.7 \ ^^^-^ 



In this case the second deviates the most, arith. mean = 1988.6 ; geometri- 

 cal = 1970.7. 



At zen. dist. 85" 16'.70, t = 54.2, bar. 30.24, I find with Ivory's constant, 



U. T 624.3 > 3 Y 



Ivory's first tables . . 620.6 \ 

 U. D. D 615.8^4.8 



Henderson found the refraction (by 29 Cape observations of 7 Draconis) = 

 614.10, which, when increased for the difference between Ivory's constant, and 

 Bessel's reduced to the Cape, would become 617.86. 



The arithmetical mean =: 620*05, the geometrical = 620.03. 

 Ivory has given a table constructed on the hypothesis of u t for t = 70 

 and B = 28.85, from which I take, at zen. dist. 86°, 



U. T 653.1 > g 5 



Ivory .... 646.6^ 



U. D. D. . . . . 642.5S^-1 

 Arithmetical mean = 647.80, geometrical 647.77. 



* As corrected by Plana (Observations, Int. Ixxxvi.) The series for u T is slowly convergent, 

 and the computation would be very troublesome, were it not for the tables of the integral which 

 Bessel gives in the Fundamenta. 



