164

THE MOON’S CHANGES

nodical month, amounts to 27'212 days. It followsthat the mean interval between successive passagesof the lunar nodes is about 13 J days. Accordingly,the moon must always be twice at a node in everylunar month of 29| days, and may be three times ata node ; since, if she is at a node within the first 2'3days from new moon, she is again at a node within15'9 days from new moon, and yet again within29'5 days,—that is, before the next new moon.

The effects of the eccentricity of the lunar orbit aretoo obvious to need any special discussion. The moonmoves more quickly (in miles per hour) when inperigee than when in apogee, in the proportion ofabout 19 to 17 on the average; but as she is nearerin the same degree when in perigee, her apparentrate of motion along her orbit is yet farther increased,and in the same degree, so that her motion in herorbit is greater when she is in perigee than when sheis in apogee, in about the proportion of the squareof 19 to the square of 17, or about as 5 to 4.* (We

of days in a mean nodical month. This number is obviously thereciprocal of . This method is clearly the correct

method to pursue in all such cases. The rule may be thus ex-pressed :—Let P, P' be the periods in which two objects—whichmay be planets, nodes, perigee-points, and so on—make a circuitof the same celestial circle, P' being greater than P : then theinterval between successive conjunctions is the reciprocal of ~Jt~pif the objects move in the same direction, and the reciprocal of-jj + p if they move in different directions.

* When we wish to obtain a fair approach to the ratio of thesquares of two large numbers differing by two, we have a ready