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pied (on the average). In this interval the line ofnodes has regreded through an angle equal to e 1 S e 9 ,which is an angle of about 18° 18-j'. The time oc-cupied by the line of nodes in making a completerevolution is 6793'391 days, or rather more than 18^years.
It is to be noticed that considerations resemblingthose dealt with in the case of the advance of theperigee apply to the regression of the nodes. Thus,when the nodes are regreding most rapidly they areshifting fastest from their position with respect to thesun; that is, the moon’s orbit continues for a shortertime than it otherwise would near the position mostfavourable for rapid nodal regression. However, thiscircumstance is not by any means so important as thecorresponding circumstance in the case of the advanceof the perigee, because the line of nodes regredes inevery lunation; there is not, as in the case of theadvance of the perigee, the important question whetherthe orbit lingers in or hastens from a position givingeither advance or regression as the balance on a com-plete revolution. The regression of the nodes isslightly reduced from what it would be if the line ofnodes did not, as it were, hasten away from the posi-tion most favourable for regression. But the change18 n °t so important as in the case of the advance ofthe perigee.
We have, then, as the main feature of the perturba-tions alfecting the position of the plane in which themoon travels, the circumstance that in every lunation