VOL. I.] PHILOSOPHICAL TRANSACTIONS. Q5 



that common centre, as the moon describes her line of menstrual motion. Of 

 which I have in the scheme only drawn that of the earth, as being sufficient to 

 our present purpose ; parallel to which, if need be, we may suppose one de- 

 scribed by the moon, whose distance is also to be supposed much greater from 

 T than in the figure is expressed, or was necessary to express. And in like 

 manner E F G H I, from that new moon at E, to the next full moon at I. 



From A to E, from full moon to new moon, T moves, in its own epicycle, 

 upwards from the sun : and from E to I, from new moon to full moon, it moves 

 downwards toward the sun. Again from C to G, from last quarter to the fol- 

 lowing first quarter, it moves forwards according to the annual motion ; but 

 from G forward to C, from the first quarter to the ensuing last quarter, it moves 

 contrary to the annual motion. 



It is manifest therefore, according to this hypothesis, that from last quarter 

 to first quarter, from C to G, while T is above the line of the annual mo- 

 tion, its menstrual motion in its epicycle adds somewhat of acceleration 

 to the annual motion, and most of all at E, the new moon ; and from the 

 first to the last quarter, from G forw^ard to C, while T is below the line of the 

 annual motion, it abates of the annual motion, and most of all at I^ or A the 

 full moon. 



So that in pursuance of Galilaeo's notion, the menstrual adding to or detract- 

 ing from the annual motion, should either leave behind or cast forward the 

 loose waters incumbent on the earth, and thereby cause a tide or accumulation 

 of waters ; and most of all at the full moon and new moon, where those ac- 

 celerations or retardations are greatest. 



Now this menstrual motion, if nothing else were superadded to the annual, 

 would give us two tides in a month, and no more; the one upon the acceleration, 

 the other on the retardation, at new moon and full moon ; and two ebbs at the 

 two quarters ; and in the intervals rising and falling water. 



But the diurnal motion superadded, doth the same to this menstrual, as 

 Galilaeo supposes it to do to that annual ; that is, adds to, or subtracts from, 

 the menstrual acceleration or retardation ; and so gives us tide upon tide. 



For in whatsoever part of its epicycle we suppose T to be ; yet because, while 

 by its menstrual motion the centre moves in the circle L T N, fig. 4 ; each point 

 in its surface, by its diurnal motion, moves in the circle LMN: whatever 

 effect, accelerative or tardative, the menstrual would give, that effect by the 

 diurnal is increased in the parts LMN, or rather the semicircle 1 M n, and 

 most of all at M ; but diminished in the parts N O L, or rather n 1, and most 

 of all at O. So that at M and O, that is when the moon is in the meridian 

 below or above the horizon, we are to have the diurnal tide or high water, oc- 



