THE TIDES 89 



the weight it would have were the globe at rest ; that is to 

 say, the centrifugal force there is equal to 1-289 of 

 gravity. Continuing, he reasoned that, inasmuch as this 

 force, being equal to 1-289 of gravity, sufficies to elevate 

 her equatorial regions by 85,472 feet, the attraction of 

 the sun, which is 1-12,868,220 the strength of gravity, 

 should be able to elevate those regions by 289 times 

 85,472 feet, or 24,701,408 feet divided by 12,868,200, or 

 very nearly 2 feet. But let me quote his own words 

 (Book III, Prop. 36, Principia) : 



Cor. Since the centrifugal force of the parts of the earth, 

 arising from the earth's diurnal motion, which is to the force of 

 gravity as I to 289, raises the waters under the equator to a height 

 exceeding that under the poles by 85,472 Paris feet, as above, in 

 prop. 19, the force of the sun, which we have now shewed to be 

 to the force of gravity as i to 12,868,200, and therefore is to that 

 centrifugal force as 289 to 12,868,200, or as I to 44,527, will be 

 able to raise the waters in the places directly under and directly 

 opposed to the sun to a height exceeding that in the places which 

 are 90 degrees removed from the sun only by one Paris foot and 

 11-1/30 inches, for this measure is to the measure of 85,472 feet 

 as i 1044,517. 



At this stage Newton appears to have rested his case, 

 but not so his successors, who have had the desperate 

 courage to pursue his fatal logic further, even to the 

 bitter extreme of swallowing the inescapable reductio ad 

 absurdum that neither the moon or the sun is the dynami- 

 cal cause of the tides, but that the centrifugal force of the 

 earth's axial rotation is! Nor, granting the premises 

 laid down by their leader, can one find any fault with their 

 logic, as such. Suppose, say they, that the earth did not 

 rotate on its axis at all, then there would be no centrifugal 

 force and, by the same token, there could be no equatorial 

 ring and, incidentally, no tide. Test the matter for your- 

 self: Substitute in the Corollary zero wherever the 

 quantity 85,472 feet appears and you will find that, 

 no matter how stupendous the tidal forces of the sun and 

 moon might nominally figure out, Newton's method of 

 computing would, did the planet not rotate, inevitably 

 reduce them all to nothing. Here is what no less a person- 

 age than the late lamented Sir Robert Stawell Ball, the 



