L. On the variation of the semi-axis major of the moon's orbit

John William Lubbock
1840 The London Edinburgh and Dublin Philosophical Magazine and Journal of Science  
la Terre, has considered the following theorem, that the expression for the variation of the semi-axis major contains no argument of long period, accompanied by a multiple of m less than m ~. In this paper he has take-n into account the terms which arise from the second approximation, or that in which the squares and products of the quantities ~', Sa, Be, b~0, $7 and ~a may be neglected. It is evident that terms may arise in the next, and indeed in every succeeding approximation of the order m
more » ... ion of the order m s, which must be taken into account in order to prove the proposition with sufficient generality. Thus the variation of thv eccentricity contains terms multiplied by m, as of the argument 9, (2 r-~ ~); these, muhiplied by others of the order m ~, give in ~ e ~ terms of the d sR give in dR order m a, and these multiplied by d e ~ d e ~ d t terms
doi:10.1080/14786444008650189 fatcat:ptv7xrfkcrehlmm72awuvxtu3u