1851.] OF THE ROYAL INSTITUTION. 63 
distance is liable to small variations, and the moon’s distance to 
very considerable variations: when the moon is at the most distant 
part of her orbit, her apparent diameter is smaller than the sun's, 
and if she happens at that time to be between a spectator and the 
sun, she will be seen as a black disk covering the central part of 
the sun and leaving a ring.of light all round: when the moon is at 
the nearest part of her orbit, her apparent diameter is larger than 
the sun’s, and she will, to a spectator in the proper locality, com- 
pletely cover the sun, and produce a Total Eclipse. But neither of 
these things can happen unless the plane of the moon’s orbit be in 
such a position that the moon, when approaching the state of con- 
junction or new moon, is seen to pass not above the sun or below 
the sun but over the sun. 
The Lecturer then called attention to the circumstance that four 
successive total eclipses occur in the month of July at intervals of nine 
years, namely 1833, July 17; 1842, July 8; 1851, July 28; and 1860, 
July 18. For the explanation of this-curious circumstance it was ne- 
cessary to show, first, how it happened that at intervals of nine years the 
moon’s orbit was in such a position that, for a nearly definite apparent 
position of the sun, the moon’s path would cross the sun’s disk: se- 
condly, how it happened that at intervals of nine years the moon was 
at nearly her smallest distance from the earth, so that her apparent 
diameter was larger than the sun’s. In reference to the former, it 
was shown that the moon revolves in an orbit whose plane is in- 
clined to the plane of the ecliptic (the apparent orbit of the sun round 
the earth), and that the inclination is nearly invariable, but that the 
position of the line in which the plane of the moon’s orbit intersects 
that of the ecliptic is constantly changing, revolving steadily in the direc- 
tion opposite to the moon’s motion, and performing a complete revolu- 
tion in something more than nineteen years. Therefore if one node 
or extremity of this line of intersection were directed nearly to the 
July sun in 1833, the opposite node would be directed nearly to 
the July sun in 1842, and so on for four successive periods of nine 
years; and eclipses would be possible in July at the end of each 
period. But to show that they might be total eclipses, it was neces- 
sary to remark that the moon revolves in an ellipse of which the 
earth occupies one focus (a point much nearer to one end than to the 
other) and that the position of this ellipse is constantly varying, 
its long axis turning round in the same direction as the moon’s 
motion, and completing a revolution in nine years and a half. There- 
fore if in 1833 the shorter end of the ellipse were nearly turned to 
the July sun, in 1842 the axis of the ellipse would have completely 
revolved, so that the shorter end of the ellipse would again be nearly 
turned to the July sun: and thus the eclipse which occurred, if 
total in 1833, would, if central, be total (not annular) in 1842; and 
so on for four periods of nine years. 
The Lecturer then called attention to the great difference in the 
directions of the shadow-paths across Europe, for the eclipses of 1842 
