LET. XXII. SUN AND MOON. z8z

through the earth’s shadow: so that in this cafethe fun would be eclipsed at every change, andthe moon at every full. But as the moon movesin the circle V W X Y, which is inclined to theformer in an angle of about five degrees and athird, there can be no eclipse but when she is inor near one of the nodes V or X, at the time offull or change: for in all other positions, stiewill be too much out of the plane of the eclipticfor her shadow to fall upon the earth, or for theearth’s shadow to fall upon her.

When the moon is in conjunction with thefun at z, her shadow N must fall upon the earthat a, because soe is then very near one of hernodes; and at her opposition n she must gothrough the earth’s soadow I, because she is thennear the other node. But in the time she goesonce round the earth, according to the order ofthe letters' X Y V W, the earth will have ad-vanced forwards from E to e ; and as the line ofthe nodes VEX, is always carried nearly parallelto itself, the moon at her next change will be atthe point f, which is too high above the eclipticfor any part of her shadow to fall upon the earth.And, for the same reason, as the earth is stillmoving forward in its orbit, the moon, at hernext opposition, will be at g ; which is too farbelow the ecliptic for her to go through anypart of the earth’s soadow.

Again,