W. HarJcness — Magnitude of the Solar System. 239 



in terms of the solar parallax. Conversely, the solar parallax 

 can be deduced from the observed value of the parallactic 

 inequality, but unfortunately there are great practical difficulties 

 in making the requisite observations with a sufficient degree of 

 accuracy. Notwithstanding the ever recurring talk about the 

 advantages to be obtained by observing a small well defined 

 crater instead of the moon's limb, astronomers have hitherto 

 found it impracticable to use anything but the limb, and the 

 disadvantage of doing so as compared with observing a star is 

 still further increased by the circumstance that in general only 

 one limb can be seen at a time, the other being shrouded in 

 darkness. If both limbs could always be observed we should 

 then have a uniform system of data for determining the place of 

 the center, but under existing circumstances we are compelled 

 to make our observations half upon one limb and half upon the 

 other, and thus they involve all the systematic errors which 

 may arise from the conditions under which these limbs are 

 observed, and all the uncertainty which attaches to irradiation, 

 personal equation, and our defective knowledge of the moon's 

 semi-diameter. 



Our fifth gravitational relation is that which exists between 

 the solar parallax, the lunar parallax, the moon's mass and 

 the earth's lunar inequality. Strictly speaking the moon does 

 not revolve around the earth's center, but both bodies revolve 

 around the common center of gravity of the two. In conse- 

 quence of that an irregularity arises in the earth's orbital velo- 

 city around the sun, the common center of gravity moving in 

 accordance with the laws of elliptic motion, while the earth, on 

 account of its revolution around that center, undergoes an alter- 

 nate acceleration and retardation which has for its period a 

 lunar month, and is called the lunar inequality of the earth's 

 motion. We perceive this inequality as an oscillation super- 

 posed on the elliptic motion of the sun, and its semi-amplitude 

 is a measure of the angle subtended at the sun by the interval 

 between the center of the earth and the common center of 

 gravity of the earth and moon. Just as an astronomer on the 

 moon might use the radius of her orbit around the earth as a 

 base for measuring her distance from the sun, so we may use 

 this interval for the same purpose. We find its length in miles 

 from the equatorial semi-diameter of the earth, the moon's 

 parallax and the moon's mass, and thus we have all the data 

 for determining the solar parallax from the inequality in ques- 

 tion. In view of the great difficulty which has been expe- 

 rienced in measuring the solar parallax itself, it may be asked 

 why we should attempt to deal with the parallactic inequality 

 which is about twenty-six per cent smaller? The answer is, 

 because the latter is derived from differences of the sun's Tierht 



