VOL. XVI.] PHILOSOPHICAL TRANSACTIONS. ^ 36l 



under what laws of decrease of density, the circle will become a proportional 

 spiral. Next, the density and compression of fluids is considered, and the 

 doctrine of hydrostatics demonstrated ; and here it is proposed to the contem- 

 plation of natural philosophers, whether the surprising phaenomena of the 

 elasticity of the air, and some other fluids, may not arise from their being com- 

 posed of particles which fly each other ; which being rather a physical than 

 mathematical inquiry, our author forbears to discuss. 



Next, the opposition of the medium, and its effects on the vibrations of the 

 pendulum are considered, which is followed by an inquiry into the rules of the 

 opposition to bodies, as their bulk, shape, or density may be varied : here with 

 great exactness is an account given of several experiments tried with pendula, 

 in order to verify the foregoing speculation, and to determine the quantity of 

 the air's opposition to bodies moving in it. 



From hence is proceeded to the undulation of fluids, the laws whereof are 

 here laid down, and by them the motion and propagation of light and sound 

 are explained. The last section of this book is concerning the circular motion 

 of fluids, wherein the nature of their vortical motions is considered ; and from 

 thence the Cartesian doctrine of the vortices of the celestial matter carrying 

 with them the planets about the sun, is proved to be altogether impossible. 



The third and last book is intitled de Systemate Mundi, wherein the demon- 

 strations of the two former books are applied to the explication of the principal 

 phaenomena of nature : here the verity of the hypothesis of Kepler is demon- 

 strated ; and a full resolution given to all the difliculties that occur in the astro- 

 nomical science ; they being nothing else but the necessary consequences of the 

 sun, earth, moon, and planets, having all of them a gravitation or tendency 

 towards their centres proportional to the quantity of matter in each of them, 

 and whose force abates in duplicate proportion of the distance reciprocally. 

 Here likewise are indisputably solved the appearances of the tides, or flux and 

 reflux of the sea ; and the spheroidical figure of the earth and Jupiter deter- 

 mined, from which, the precession of the equinoxes, or rotation of the earth's 

 axis is made out, together with the retrocession of the moon's nodes, the 

 quantity and inequalities of whose motion are here exactly stated a priore. 

 Lastly, the theory of the motion of comets is attempted with such success, 

 that in an example of the great comet which appeared in l68-f, its motion is 

 computed as exactly, as we can pretend to give the places of the primary 

 planets ; and a general method is here laid down to state and determine the 

 trajectoriae of comets, by an easy geometrical construction ; upon supposition 

 that those curves are parabolic, or so near it that the parabola may serve with- 

 out sensible error ; though it be more probable, says our author, that these 



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