308 ON THE GENEKAL VALUES OF THE OBLIQUITY OF THE ECLIPTIC. [41 



where the quantities g { are expressed in seconds and have reference to a 

 Julian year as the unit of time, and the quantities y t are expressed in 

 circular measure. 



Now in the figure before given the point N' is the descending node 

 of the invariable plane on the ecliptic of 1850, so that the longitude of 



N' is 286 14' 18". 



Also the longitude of the point E, which is the autumnal equinox, 

 is 180. Hence N'E = 253 45' 42". 



Whence we may find for 1850: 



6= 23 3' 43" 

 <f)-<f)' = 257 20 31 

 or <=183 34 49 



Also, according to Stockwell, the obliquity of the ecliptic in 1850 

 was 



w = 23 27' 31"-0. 



Hence by repeated approximation we may find : 



h= 23 18' 54" nearly 

 a=177 25 52 

 also Z'=-50"-4607 



whence by substitution all the terms in 0, <j), and u> may be found 

 numerically. 



ADDITION. If we wish to take into account the variability of the 

 eccentricity of the Earth's orbit, the value of k should be taken 



= 50"'4548 + 24"'034 (e' J - e/), 

 and the quantity kt in the above formulae should be replaced by 



50"'4548i!+ 



Where e is the eccentricity of the Earth's orbit at time t, and e 2 the 

 mean value of the square of the eccentricity, which, according to Stockwell's 

 determination, is 



= 0009864. 



