Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/471

 venture to depart from it too far, in eſtabliſhing equations entirely new; ſince I am well affured, upon the beſt au- thority, that it is never found to err more than feven or eight minutes. And therefore, hoping that the rea- der, who confiders the ſudden occafion and neceffity of my publiſhing theſe Pro- pofitions at this time, will make due allowance for the want of order and me- thod, and look upon them only as fo many diftinct Rules and Propofitions not con- nected: I ſhall begin, without any other preface, with fhewing the origine of that inequality, which is called the Va riation or Reflection of the Moon.

THE variation or refle- ction is that monthly in- equality in the Moon's mo- tion, wherein it more manifeftly differs from the laws of the motion of a pla- net in an elliptic orbit. Tycho Brabe makes this inequality to arife from a kind of libratory motion backwards and forwards, whereby the Moon is accelerat- ed and retarded by turns, moving fwifter in the firſt and third quarter, and flower in the fecond and fourth, which inequali-. ty is principally obſerved in the octants.

Sir Isaac Newton accounts for the