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closely with Newton’s, having fallen into the samemistake. For some time it seemed as though thetheory of gravitation were endangered, Clairaut himselfsuggesting that a force acting according to someother law than that of the inverse squares of thedistances, seemed to be in operation. This opinion ofa mathematician on a strictly mathematical questionwas energetically opposed by the non-mathematicianBuffon, who argued in favour of the simple Newtonianlaw. Clairaut was thus led to re-examine the sub-ject, taking into account considerations which hehad hitherto neglected, and which he did not expectto find importantly influencing the result. To his sur-prise he found in the hitherto neglected indirect effectsof the tangential action, the explanation of the diffi-culty which had so long perplexed mathematicians.[See, however, note on p. 137.] i
The actual motion of the perigee from conjunctionto conjunction with the sun is indicated in fig. 42, PlateXI., except that no account is taken of the oscillationswhich occur within the periods of successive lunations.The circle e 1 e 2 e 3 , &c., is the orbit of the earth, whilethe lines p l e y a l , p 2 e 2 a. 2 , p 3 e 3 a 3 , indicate successivepositions of the major axis of the moon’s orbit, p v p 2 ,P 3 >&c., being the perigee. When the earth is at e v theperigee is at p u or in conjunction with the sun. Herethe position corresponds to that illustrated in fig. 34,the advance is rapid; and accordingly we see that atthe next station the perigee p 2 is no longer parallel tothe line e 2 S, but has shifted in a direction agreeing