courſe into the orbit PAB, and the force of the body S, which cauſes the body P to deviate from that orbit) would act always in the ſame manner, and in the ſame proportion; it follows that all the effects will be ſimilar and proportional, and the times of thoſe effects proportional alſo; that is, that all the linear errors will be as the diameters of the orbits, the angular errors the ſame as before; and the times of ſimilar linear errors, or equal angular errors as the periodical times of the orbits.
Cor. 16. Therefore if the figures of the orbits and their inclination to each other be given, and the magnitudes, forces, and diſtances of the bodies be any how changed; we may, from the errors and times of thoſe errors in one caſe, collect very nearly the errors and times of the errors in any other caſe. But this may be done more expeditiouſly by the following method. The forces NM, ML, other things remaining unaltered, are as the radius TP; and their periodical effects (by cor. 2. lem. 10.) are as the forces, and the ſquare of the periodical time of the body P conjunctly. Theſe are the linear errors of the body P; and hence the angular errors as they appear from the centre T (that is the motion of the apſfides and of the nodes, and all the apparent errors as to longitude and latitude) are in each revolution of the body P, as the ſquare of the time of the revolution very nearly. Let theſe ratio's be compounded with the ratio's in cor. 14. and in any ſyſtem of bodies T, P, S, where P revolves about T very near to it, and T revolves about S at a great diſtance, the angular errors of the body P, obſerved from the centre T, will be in each revolution of the
