88 FROM NEBULA TO NEBULA 



inverse cubes of the distances, hence he now felt driven, 

 in the interest of consistency, to go on and alter the first 

 clause to match its changed companion. Accordingly, he 

 made that to read, that gravitational attraction, when 

 operating as a tidal force, disregards differentiations of 

 density ! In support of this new absurdity, he introduced 

 what is known as the vacuum-tube experiment (to be dis- 

 cussed later), from which he drew the fallacious inference 

 that, inasmuch as all objects, regardless of density, fall 

 in vacuo with the same rapidity, the law of equilibrium 

 does not apply to them or, by analogy, to cosmic bodies in 

 general. 



Newton's next step was to invent some method, 

 favorable to his theory, for computing the tidal heights. 

 Making use of his rule of inverse cubes, he ascertained 

 the tidal force of the moon to be 1-2,871,400 of the 

 earth's gravity and that of the sun, 1-12,868,200. (Young 

 gives 1-8,640,000 and 1-19,600,000 respectively) The ques- 

 tion with him. was: How are these quantities to be trans- 

 lated into terms of tidal height so as to obtain plausible 

 results 1 



It was well-known to the generation before Newton 

 that the figure of the earth is not that of a sphere, but of 

 an oblate spheroid, and her equatorial ring seems always 

 to have been assumed, as a plain matter of course, to be 

 the running effect of the centrifugal force of her axial 

 rotation. This view was blindly adopted by Newton him- 

 self, and is the one universally acquiesced in to-day by all 

 recognized scientists. Some skeptical lay readers may in- 

 fer that the ring, to some extent at least, may be the cum- 

 ulative effect of the long past, but let me assure him 

 solemnly that this is not the orthodox interpretation. In 

 the time of Newton the thickness of this ring at the equa- 

 tor was supposed to be 85,472 Paris feet (a Paris foot be- 

 ing about 1-15 longer than the American standard), but 

 the modern estimate is only 13-^ miles (71,280 feet). 



By a combined process of pendulum experimenting 

 and computation, Newton arrived at the conclusion that 

 the centrifugal force of the earth's rotation at the equator 

 serves to lighten any given body at that place by 1-289 of 



