BOOK III.] OF NATURAL PHILOSOPHY. 419 decreases at the same rate as it had increased before, and ceases when the moon changes its declination, crossing over the equator to the south. Af ter which the flood is immediately changed into an ebb; and thenceforth the ebb happens at the setting and the flood at the rising of the moon : till the moon, again passing the equator, changes its declination. There are two inlets to this port and the neighboring channels, one from the seas of China, between the continent and the island of Lenconia ; the other from the Indian sea, between the continent and the island of Borneo. But whether there be really two tides propagated through the said channels, one from the Indian sea in the space of 12 hours, and one from the sea of Cliina in the space of 6 hours, which therefore happening at the 3d and 9th lunar hours, by being compounded together, produce those motions : or whether there be any other circumstances in the state of those seas. I leave to be determined by observations on the neighbouring shores. Thus I have explained the causes of the motions of the moon and of the sea. Now it is fit to subjoin something concerning the quantity of those motions. PROPOSITION XXV. PROBLEM VI. To find the forces with which the sun disturbs the 'motions of the moon. Let S represent the sun, T the earth, P the moon, CADB the moon's orbit. In SP take SK equal to ST; and let SL be to SK in the duplicate proportion of SK to SP: draw LM parallel to PT ; and if ST or SK is supposed to represent the accelerated force of gravity of the earth towards the sun, SL will represent the accelerative force of gravity of the moon towards the sun. But that force is compounded of the parts SM and LM, of which the force LM, and that part of SM which is represented by TM, disturb the motion of the moon, as we have shewn in Prop. LXVI, Book I, and its Corollaries. Forasmuch as the earth and moon are revolved about their common centre of gravity, the motion of the earth about that centre will be also disturbed by the like forces; but we may consider the sums both of the forces and of the motions as in the moon, and represent the sum of the forces by the lines TM and ML, which are analogous to them both. The force ML (in its mean quantity) is to the centripetal force by which the moon may be retained in its orbit revolving about the earth at rest, at the distance P'J , in the duplicate proportion of the periodic time of the moon about the earth to the periodic time of the earth about the sun (by Cor. 17, Prop. LXVI, Book I) ; that is, in the duplicate proportion of 27d. 7\ 43' to 365'1. 6". 9' ; or as 1000 to 178725 ; or as 1 to 178f J. But in the