378 S. Newcomb on Hansen’s Theory, ete, 
rately with precision, because their coéfficients have the same 
sign in that part of the moon’s orbit where nearly all the me — 
ridian observations are made. From this cause Airy’s value of — 
the parallactical inequality from all the Greenwich observations _ 
from 1750 to 1830 was 3” in error, And when, in his last in- — 
vestigation,* Airy rejected the observations previous to 181], 
owing to some uncertainty as to what semi-diameter should be 
employed, the result was still a second too small. It is there 
fore interesting to find what value of the variation will result 
if we substitute the known value of the parallactic inequality — 
in Airy’s equations for the determination of that element 
Neglecting those unknowns which have small coéfiicients, these 
equations are, from 1806 to 1851, 
1806—15  10-66W+ 28-14V = + 172 
16—24 9°45 + 30°92 249 i 
25—33 943 + 29°26 + 421 : 
3449 929 + 2728 + 108 “ 
43—51 905 + 23°36 + 19 
Sum, 47-88W +138°96V = +1029 t 
125”50—122'"10 _ 
hE e- pemae <: 
The sum of the preceding equations gives 
W = 2:15—2:90V = —0-46, is 
The resulting correction to the provision variation 2370") : 
046x073 = —0'-34, making t 69°96, 
therefore — g the bee 4g 
fived from observation. ...... _.. s._-.-s- asenmaew 9369 4a 
while Hansen’s theoretical value is-------- “ro ae 2 ) 
EA, i a sn ie sone 
The differences are too minute to found any theory UP tis ae q 
aving the evection and variation, the other snes ee | 
so minute that their product by Hansen’s coéflicient * © | 
gether insensible, me that 
oe up the results of our inquiry, it appear tweet = | 
the case of the evection the supposed disco Hansen's 
theory and observation would not follow from be attribatel = | 
pothesis, and therefore, even if it exists, cannot be en 6 | 
; é f the vane” ther 
age of ne Se 
inequalities the discordance would be insensible, jation. : 
* Memoirs Royal Astronomical Society, vol. x= 
