﻿34 Mr. S. Neweonib on the Physical Constitution of the Moon. 



That Hansen overlooked this point is to be attributed to his 

 method of determining the lunar perturbations by numerical 

 computation from the various elements of the moon's motion, so 

 that the manner in which the inequality depends on the elements 

 does not appear. It is only when we determine the perturba- 

 tions in algebraic form that this dependence appears. 



Passing now from the evection, the next great perturbation of 

 the moon's motion is the variation. Bat the value of this per- 

 turbation has not been accurately determined from observation, 

 because, attaining its maxima and minima in the moon's octants, 

 it is complicated with the moon's semidiameter and parallactic 

 inequality. Even if the semidiameter is known, the two inequa- 

 lities in question cannot be determined separately with precision, 

 because their coefficients have the same sign in that part of the 

 moon's orbit where nearly all the meridian observations are 

 made. From this cause Airy's value of the parallactical inequa- 

 lity from all the Greenwich observations from 1750 to 1830 was 

 3" in error. And when, in his last investigation*, Airy rejected 

 the observations previous to 1811, owing to some uncertainty as 

 to what semidiameter should be employed, the result was still a 

 second too small. It is therefore 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 determina- 

 tion of that element. Neglecting those unknowns which have 

 small coefficients, these equations are, from 1808 to 1851, 



1806-15 . 



. 10-66 W + 



28-14V= 



= 4- 



17-2 



1816-24 . 



. 9-45 + 



30-92 



4- 



24-9 



1825-33 . 



. 9-43 + 



29-26 



4 



421 



1834-42 . 



. 9-29 4 



27-28 



4 



10-8 



1843-51 . 



. 9-05 + 



23-36 



4 



7-9 



Sum 



47*88 W + 138-96 V= +102-9 



In these equations W x 0"*73 represents the correction to the 

 coefficient of variation, and Vx3"*77 that to the coefficient of 

 parallactic inequality. We now know from recent special investi- 

 gations that the latter coefficient is very near 125"- 50. Airy's 

 provisional one was 122"- 10, whence 



125"-50-122''-10 



3"-77 

 The sum of the preceding equations gives 



W=2-15-2-90V=-0-46. 

 The resulting correction to the provisional variation (2370 "-3) 



■* Memoirs of the Royal Astronomical Society, vol. xxix. 



