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



U. T 802.5 > j2 4 



Again, zen. dist. 87°, 



U. T. 



Ivory .... 790.1 J 



U. D. D. . . . . 776.1 \ ^^-^ 



Arithmetical = 789.30 ; geometrical = 789-19. 



Lastly, Brinkley gives the comparison of 42 observations of a Lyrae s p 

 with these hypotheses, zenith distance = 87°.42', t = 35°, B. 29-50, 



U. T. . . . . 1067". 0> 20.5 



Observed . . . 1046 .bl 



U. D. D. . . . 1011 .OS^^-^ 



Arithmetical = 1039" ; geometrical = 1038-6. But it must be remarked, 

 that the temperature is by the internal thermometer, the external being 31.3 ; 

 the barometer also is 0'.078 too little ; in respect of the first of which the observed 

 refraction should be lessened 9"-2, and for the second 2".90. 



It is evident that these means are not in error one-twentieth of the difference 

 between the two hypotheses ; and, therefore, as far as 85° from the zenith may 

 be depended on as certainly as any table extant. 



Laplace used this principle not only in constructing the French tables, but 

 also to show that the refractions above 74° are independent of the law of density. 

 Brinkley, however, showed that the same method could assign them as far as 

 80°.45 ; the most important of the terms omitted by Laplace in the development 

 of R in tang. 6 has at that zen. distance in the two hypotheses the values 2".60 

 and 1".73 ; the arithmetical mean of these cannot be 0".43 wrong, and its error 

 is probably less than 0".04. The opinion expressed by this great astronomer in 

 his second memoir on refraction. Transactions Royal Irish Academy, vol. xiii. 

 p. 169, that, by the method given there, a table of refractions could be more 

 certainly derived from observation " than from any hypothesis respecting the 

 actual variation of density," probably hindered him from pursuing the pre- 

 sent method to its full extent, which, however, may be done with extreme facility. 

 In his notation. Transactions Royal Irish Academy, vol. xii. p. 83, the 

 equation of refraction is, 



_ — rfp X oft sin / 1 + V 



CLd. — 



2r(l + 6p)y l + V-^(l+¥)sin^e 



