714

to the amount of 1° 3b'. _ For this reason, then, as well as (<> !the one just stated, the Moon approaches the ecliptic. In suc-ceeding oppositions, the Moon , by the operation of both causeSi■would approach nearer and nearer to the ecliptic, till at lengthan opposition would occur, in which the Moon would be eitherexactly, or very nearly, in its node; and if in its node, then llwould be in the ecliptic, and in such case, an eclipse n' uS *happen.

S .

An eclipse may happen, if the Moon be near to the node of h etorbit; the least degrees of proximity are called the Lunar Eclip^Limits.

These limits are easily determined from the inclination of d> eMoon ’s orbit, the Moon ’s apparent diameter, and the appa rel,tdiameter of a section of the Earth ’s shadow at the Moon . Th etwo former conditions may be supposed to be known by previousmethods, (see pp. 661 , &c.) and it is the latter only that n°*requires to be investigated.

Apparent Diameter of a ■Section of the Earth’s Shadow st the Moon .

Let S represent the Sun’s centre, E the Earth ’s, and let th®circles described round the centres S, E represent sections 0those bodies. Draw A t C, at'C, tangents to the circular secti° nS

of the Sun and Earth , and the triangular space included with* 11tC, t'C, will represent the section of the conical shadow of t.Earth . Let mMnt be part of the Moon ’s orbit, then the seed 01 ’of the Earth ’s shadow at the Moon is mMm', and its app i,re ”