118 THE ORBIT OF URANUS. 



In 1831 — 1".42; 

 1834 — 2.10. 



Then comparing Airy's reducetl decimations of Uranus with Pond's, we find the 

 following mean ditferences: 



In 1831, Airy — Pond = — 3". 18 

 1834, — 3 .50. 



To reduce Airy to Anwcrs we must there apply to the declinations 



In 1831 + 1".76 

 1834 + 1 .40. 



I have regarded the correction -)- 1".60 as applicable throughout the period in 

 question. 



1836-72. 



During this interval the corrections in right ascension have been derived by the 

 following two sets of comparisons: (1) A comparison of the several collected six 

 and seven year catalogues with Gould's standard, from which it appears that they 

 require the following general corrections in right ascension : 



Six year catalogue of 1840 + 0\047 



Six year catalogue of 1845 +0 .002 



Seven year catalogue of 1860 -|- .003 



Seven year catalogue of 1864 -\- .022 



(2) A comparison of the corrections.applied to the right ascensions of the indi- 

 vidual years to reduce them to the standard of the catalogue, as given in the 

 introduction to each catalogue. The sum of these two number's gives the correc- 

 tions for each year. 



A slightly different method is to regard the above correction for each catalogue 

 as applicable to all right ascensions which depend fundamentally upon that cata- 

 logue. I have sometimes combined both methods so as to derive what seemed to 

 be the most probable result, and sometimes used but one. 



The corrections to the declinations during the interval in question have been 

 derived from Auwers' " Tafeln zur Reduction der Declinationen verschiedener 

 iStcDivcrzeiclinisse anf ein Fundamentidsysiem" Astronomische Nachn'chfen, No. 

 1536. These tables include the Greenwich seven year catalogue for 1860, when 

 the correction corresponding to the declination of Uranus is about -|-0".45. The 

 corrections for the previous catalogues vary between 0".35 and 0".68. The cor- 

 rection corresponding to the interval 1861-67 has been derived by a direct com- 

 parison with Auwers' declinations, and the result is -\- 0".44, agreeing with the 

 two preceding catalogues. But, on making a similar comparison with the annual 

 catalogue for 1869, a considerable change was found, the correction being — 0".17, 

 a cliange of more than half a second. I shall use this correction for and after the 

 beginning of 1868, as the change is probably due to the introduction of a new 

 constant of refraction in the reduction of the observations for 1868 and subse- 

 quent years. 



