Q4 PHILOSOPHICAL TRANSACTIOXS. [aNNO 1666. 



motion about its axis the earth should be carried by a contemporary period, 

 whereby the same face of the moon should be ever towards us ; but that by the 

 earth's revolution about its axis in 24 hours, the moon should be carried about 

 it in about 29 days, without any motion on its own axis : and accordingly, that 

 the secondary planets about Jupiter and Saturn are not, like their principals, 

 turned about their own axes. And therefore I am not at all inclined to be- 

 lieve that the menstrual period of the tides with us is to be solved by such an 

 hypothesis. 



Instead of this, that surmise of mine, for I dare not yet with confidence 

 give it any better name, is to this purpose. 



The earth and moon being known to be bodies of so great connexion 

 (whether by any magnetic, or what other tie I will not determine) as that the 

 motion of the one follows that of the other, may well enough be looked upon 

 as one body, or rather one aggregate of bodies which have one common centre 

 of gravity ; which centre, according to the known laws of statics, is in a 

 straight line connecting their respective centres, so divided as that its parts be 

 in reciprocal proportion to the gravities of the two bodies. As for example, 

 suppose the magnitude, and therefore probably the gravity of the moon to be 

 about the one and fortieth part of that of the earth ; and the distance of the 

 moon's centre from the centre of the earth to be about 56 semidiameters of 

 the earth, the distance of the common centre of gravity of the two bodies 

 will be from that of the earth, about the 42d part of 56 semidiameters ; that 

 is, about 44 or 4- of a semidiameter, that is about 4- of a semidiameter of the 

 earth above its surface in the air, directly between the earth and moon. 



Now supposing the earth and moon jointly as one body, carried about by 

 the sun in the great orb of the annual motion ; this motion is to be estimated 

 according to the laws of statics, as in other cases, by the motion of the com- 

 mon centre of gravity of both bodies. For we are accustomed in statics to esti- 

 mate a body or aggregate of bodies to be moved upwards, downwards, or other- 

 wise, so much as its common centre of gravity is so moved, howsoever the parts 

 may change places amongst themselves. 



And accordingly the line of the annual motion will be described, not by the 

 centre of the earth, nor by the centre of the moon, but by the common centre 

 of gravity of the bodies, the earth and moon, as one aggregate. 



Now supposing A B C D E, (fig. 2 and 3, pi. 3) to be a part of the great orb of 

 the annual motion described by the common centre of gravity, in so long time 

 as from a full moon at A to the next new moon at E ; the centre of the earth at 

 T, and that of the moon at L, must each of them, supposing their common 

 centre of gravity to keep the line A E, be supposed to describe a periphery about 



