THE MOON’S MOTIONS.

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concave towards S, even when, as at the points 0,1,2,3,&c., the convexity of the orbital path round the earthis turned directly towards the sun. In other words,as the moon travels in her orbit round the sun hercourse is continually being deflected inwards from thetangent line, or always towards the sun. It is to benoticed, however, that the earth’s perturbing influenceis an important element in determining the moon’s realorbit. For when the earth and sun are on the sameside of the moon, or at the time of full moon, the pullon the moon is the sum of the pulls of the earth andsun, or exceeds the sun’s pull alone in the ratio 22to 15; and on the other hand, when the earth and sunare on opposite sides of the moon, or at the time ofnew moon, the pull on the moon is the difference ofthe pulls of the sun and earth, or is less than the sun’spull alone in the proportion of 8 to 15. Thus at thetime of full moon the moon is acted on by a forcewhich exceeds that acting on her at the time of newmoon in the ratio'of 22 to 8'or 11 to 4. And thoughat the time of full moon the moon’s actual velocity(that is, her velocity in her orbit round the sun) is ata maximum, being then the sum of her mean orbitalvelocity round the sun and of her velocity round theearth; yet this by no means counterbalances theeffects of the greatly increased pull on the moon :* so

* The earth’s velocity in her orbit being about 65,000 miles perhour, and the moon’s about 2,000 miles per hour, the extremevariation of the moon’s motion in her orbit round the sun liesbetween the values 67,000 and 63,000 miles (roughly), or about four