METHOD PURSUED. 



about the mean, or follow one another at equal intervals, which is sufficiently near the truth 

 for our purposes. 



Let # be the interval of time (in hours) between each pair of successive comparisons, and our 

 factor will become 



or since _ t (1l) t 



Since the correction sought is only sensible for the more extended series of comparisons, we 



may almost uniformly substitute unity for and consequently 



n 1 



n) 



This very simple expression shows that for the longest series of comparisons (which extends 

 over about five hours) the factor is very nearly=l ; but that in other cases it is a real fraction. 



By simple inspection of the ephemerides, we shall find the maximum values of the second dif 

 ferences to be 



Mars I. Mars II. Venus I. Venus 11. 



f&quot;($) 9&quot;. 6 14&quot;. 9 49&quot;.9 29&quot;. 3 



5-W&quot;( ) -02 .03 .09 .05 



f&quot;(r] .01 .01 .04 .04 



The change in the apparent semi-diameter is thus seen to be certainly insensible, and it is also 

 evident that in declination the influence of these second differences can be possibly perceived 

 only in a few particular cases, occurring in the first Venus-series. 



Therefore Jd oT Jo om 24 ( t t 



The only quantity remaining for consideration is/&quot;(p), which may be directly obtained by 

 differencing the formulas which represent the parallax in declination, as computed for successive 

 hours, and will easily be found to be 



f&quot;(p) = 1 p costf 1 sino cos(d a) 4 sin 2 i 15 



A 



R&quot; ^7&quot;! 1 A 

 ^i - [8.83346] p cos^ 1 sino cos(0 a) 



Substituting this value in the expression above, we obtain finally, 



which gives the correction applicable to the mean of the observed differences for the mean time 

 T; the declination, hour-angle and distance from the earth being denoted by 3, 6 , and A; 

 the distance from the center of the terrestrial spheroid and the corrected latitude by p and ^ ; 

 and the times of the first and last comparisons by t and t w respectively. 



If we represent that part of the expression which is constant for the same place by 7, we may write 



AZ AX I /.*(&quot;) j/\ 2 COS(# - a) . 2, 



JO O T _ Jo o m -f f lt (&amp;gt; f \ - L_ - 1 sin o 



Adopting Bessel s value of the eccentricity of the terrestrial spheroid, so that 



log. e = 8.9122052, 

 we have, by the ordinary formulas, (Berl. Astr. Jahrb. 1852, p. 325,) 



p sn &amp;lt;p = iZZ 



VI e 2 sin 2 (f&amp;gt; 



( &amp;gt; cos &amp;lt;p _ acos ^ . 

 v 7 1 e 9 sin 2 



