] The Transactions of the South African Philosophical Society 
The lunar inequality of the earth. 
The lunar parallax. 
The parallactic inequality of the moon. 
The constant of precession. 
The constant of nutation. 
The constant of aberration. 
The light equation and the velocity of light. 
If the form and dimensions of the earth are known with sufficient 
accuracy from the combination of the geodetic surveys made in different 
parts of the world, the determination of the mean distance of the sun 
resolves itself into the measurement of the angle which the earth’s 
equatorial radius subtends when viewed from the sun at its mean 
distance from the earth—in other words, the determination of the solar 
parallax. The earth’s radius in any direction is known with tolerable 
certainty—probably within 1,000 feet, or, in round numbers, to sgGo0 
part of its whole, whilst the utmost accuracy we can hope to attain in 
the determination of the solar parallax for many years to come is barely 
zoo part. 
Geodetic processes have therefore given us a measure of the earth’s 
radius which we may assume for our purposes to be sufficiently exact ; 
for our further purposes we have, then, no longer to deal with the 
distance of the earth trom the sun, but with the solar parallax, or the 
angle which the earth’s equatorial radius subtends at the sun at mean 
distance. But when we proceed somewhat further in our inquiry, it 
will be seen that geodesy has not yet furnished us with all the data 
requisite for the rigorous correlation of all astronomical constants. The 
effect of the sun’s action on the spheroidal form of the earth has the 
effect of changing the direction of the earth’s axis in space, so that the 
plane of the earth’s equator intersects the plane of the ecliptic at 
different points in different years, and this point of intersection moves 
slowly in the opposite direction to that in which the earth revolves. 
The moon has a still larger effect in changing the position of the earth’s 
axis by its attraction on the spheroidal form of the earth. ‘The result 
of these two attractions is to create movements of the pole of the earth 
in space. One of these movements goes through a complete revolution 
in about 26,000 years, the other in a period of nineteen years, besides 
shifting the place of the pole in a more irregular way. 
These movements are respectively the well-known phenomena of 
precession and nutation. The constants of these quantities can, on one 
hand, be determined with more or less precision by direct observation ; 
on the other hand, they can be computed as a dynamical problem from 
‘purely mathematical considerations, provided that we know all the re- 
quisite data. The data involve chiefly the masses of the sun and moon 
