Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/329

 force in the lower apis is to the force in the upper apis in a greater than a duplicate ratio of the ditances. For the forces LM in the quadratures added to the forces of the body T compoe forces in a les ratio, and the forces KL in the yzygies ubducted from the forces of the body T leave the forces in a greater ratio. Therefore the ratio of the whole increae and decreae in the paage between the apides, is leat at the quadratures and greatet at the yzygies; and therefore in the paage of the apides from the quadratures to the yzygies it is continually augmented, and increaes the eccentricity of the ellipis; and in the paage from the yzygies to the quadratures it is perpetually decreaing, and diminihes the eccentricity.

That we may give an account of the errors as to latitude, let us uppoe the plane of the orbit EST to remain immovable; and from the caue of the errors above explained it is manifet, that of the two force NM, ML, which are the only and entire caue of them, the force ML acting always in the plane of the orbit PAB never diturbs the motions as to latitude; and that the force NM, when the nodes are in the yzigies, acting alo in the ame plane of the orbit, does not at that time affect thoe motions. But when the nodes are in the quadratures, it diturbs them very much, and attracting the body P perpetually out of the plane of its orbit, it diminihes the inclination of the plane in the paage of the body from the quadratures to the yzygies, and again increaes the ame in the paage from the yzygies to the quadratures. Hence it comes to pas that when the body is in the yzygies the inclination is