of long period in the mean motion of the Moon. 185 
he omitted the sun’s perigee from this argument by the author- 
ity of La Place; himself, who now attributed the inequality to 
a difference of compression between the two retin of the 
earth. The function was also changed from sin to cos and the 
coefficient altered. The adopted term thus ioe he 
df= —12''5 cos [291° 57'+(2° 0'45)(t— 1800) 
= 125 sin por? 57'+(2° 0/-45)(t—1800) 
Succeeding investigators have regarded the theoretical coeffi- 
cients of both of these terms as insensible. It does not seem 
likely that there is any such difference between de two terres- 
trial hemispheres as could produce the second, but I am not 
aware that the coefficient of the first has ever been shown to be 
insensible by any published computation. This coefficient is 
of the ninth order and the argument is, 
In aoae s notation, oe 2i— 1+30; 
In Hanse —3w 
The period is 184 years, and the ice. cals, of the ratio of 
this period to that of the moon itself might render the coefficient 
sensible. Both Hansen and De aunay pronounce it insensible, 
but neither publish their computations of its magnitude. 
These terms have ceased to figure in the theory of the moon 
since Hansen ‘saad that the action of Venus was capable 
se eosin ag inequalities of the kind in question. So far as I 
ware, Hansen’s first publication on this subject is eet found 
in sg 597 of the Astronomische Nachrichten (B. 25, S. 325.) 
Here, in a letter dated March 12, he alludes to La Place’s coeffi- 
cients, and says he has not been ‘able to find any sensible coeffi- 
cient for La Place’s argument of long period. But on examin- 
ing the action of Venus on the moon he found, considering only 
the first power of casa: force, the following term 1n the 
moon’s mean longi 
ee a 01 sin (—g—16g'+189"+35° ee 
g and g” being the mean anomilies of the moon, the earth 
Ae Venus respectively. As this expression still ‘failed to ac- 
inne Ss ae observed variations of the moon’s longitude he 
my roximation to the fourth power of the dis- 
Sabine & Big found that the terms of the third and fourth 
order increased the coefficient to 27-4, the angle remaining un- 
changed, so that the term became 
27-4 sin (—g—16g'+189"-435° 20’), 
But this increase made the Sieosy rather worse, and the term 
depending on the argument of Airy’s equation between the 
earth and Venus was then tried with the result— 
31 = 23-2 sin (8g” —13g’4+315° 30’). 
The introduction of this term seemed to reconcile the theory 
with observation. 
Am. Jour. Sci.—Srconp Srrizs, Vor. L, No. 149.—Sept., 1870, 
: 12 
