W. Harkness—The Solar Parallax. 383 
in which p’ and P’ are the actual values of the solar and lunar 
parallaxes at the instant for which dy is required. For any 
given lunation, dy will evidently attain its maximum value 
when sin (»’—y)=1, that is, when the ptt of the sun 
and moon differ by ninety degrees. If now we have an.ex- 
possible values, the mean of which will be the constant of the 
lunar inequality ; p’ will have assumed all possible values, ne 
mean of which will be the constant of solar parallax ; and th 
moon will have had all possible latitudes, a mean of aries 
will be zero. With P’ the case will be somewhat different. It 
is equal to the constant of lunar parallax, pia a series of terms 
multiplied by factors made up of the mean anomaly of the 
sun, the mean anomaly of the moon, the mean distance of the 
moon from its ascending node, and the difference of the mean 
longitudes of the sun and moon. All these terms, except 
those involving the difference of the mean longitudes, will as- 
sume all possible values and vanish from the mean. e 
mean of all the values of P’ will therefore be, P + terms de- 
pending upon the difference of mean longitudes of the sun 
and moon.* Turning now to the second volume of Delaunay’s 
theory of the moon, we find that the only term of this kind in 
the lunar parallax is the one numbered (27), upon page 917, 
and its value is 281788 cos 2D. As we have supposed all 
our observations of dy to be made when D was 90°, the value of 
this term will be —28/’-18, and the mean value ‘of P’ will be 
P—28/"18 = 8894/52. Substituting the mean ie thus 
found in (18), and rearranging the terms, we obta 
+M 
p = 00164564 L (5 Tv) ee (1S) 
In connection with be aie (14) the reader may compare, 
Le Verrier, OPM, iv, 100; Newcomb, WOb, 1855, App. IL 
p. 28; E. J. Stone, MNt, 1868, vol. hecie p. 24. 
The Moon’s Mass. 
Before the solar parallax can be obtained from equations (12) 
and (14), it is necessary to know the moon’s mass. Let us con- 
sider the different ways of determining i it. 
The first determination of the moon’s mass was made 
the tides, by Newton, in 1687. Since then other sieestiedoss 
ave em mployed the same method, but owing to the side sa 
and practical difficulties inherent i in it, their results have 
So discordant as to command very little confidence. Pais 
* In strictness it should be the difference of the ¢rue longitudes of the sun and 
moon. 
