180 
PRESTON. 
The intersection of a horizontal line through b with the 
line B"o gives the line M N, by which we have 
M N = J? sin a sec $ = — 1.03. 
15 
The value of D on June 9 is — 20.07. 
This value is projected to a vertical line at a distance of 
10 units from the axis of ordinates, thus correcting for the 
factor 10 introduced in the value M N. 
A vertical line through N intersects the line N'o at a 
distance M' p f = 2.07 from the axis of abscissas, and we 
have finally 
M' P' — ~ sin « sec $ X D = -f 2.07. 
Attention may be called, in conclusion, to the striking 
manner in which the principal characteristics of the values 
A, B, C, and D are brought out in the graphic representa¬ 
tions. By reference to plate 7 it will be noticed that both 
A and B have two large maxima and minima during the 
year. In addition to this, each curve is marked by a number 
of smaller maxima and minima. C and D, being dependent 
on the cosine and sine of the sun’s longitude, present but one 
maximum and one minimum. 
The general increase of A is the result of the term depend¬ 
ing on the sine of the longitude of the moon’s ascending 
node, combined with the value of t, which increases much 
more rapidly than the sine term decreases. The term de¬ 
pending on twice this function being of the opposite sign 
would tend to diminish this effect, but as it is only about one 
per cent of the first term its influence is barely perceptible. 
The general decline of B, negatively, is caused by the cosine 
of the function mentioned, and is seen to be about three- 
fourths of one second, as the formula requires. As in the 
case of A, the function depending on the double angle modi¬ 
fies this to some extent. 
The two major maxima and minima in both A and B are 
produced by the terms depending on twice the sun’s true 
