- THE AUTHOR'S THEORIES OUTLINED 41 



we are acquainted is, that they accelerate, and this they 

 do according to a well-settled law, to wit, their advance 

 varies with the square of the time elapsed. From our 

 premises, then, it follows that not only are the planets 

 gyrating around the sun for the reasons given, but that 

 they are travelling faster and faster from year to year 

 and century to century. But how can we hope to prove 

 this fact, seeing that all the movements are simultane- 

 ously accelerating? There is only one way that offer? 

 any prospect of success. This is, to pick out those cir- 

 culating bodies whose times of revolution are most rapid 

 and whose orbits vary most widely from the circle (the 

 ideal curve for evenness of balance) in the hope of dis- 

 covering some slight excess of speed. Our choice is soon 

 made, and falls upon the moon our satellite, and Mercury 

 a planet. Nor, fortunately, are we doomed to disap- 

 pointment. For have we not found Young telling us 

 about the secular acceleration of the moon's mean motion 

 advancing with the square of the time, and have we not 

 also learned from Poor that Mercury 's perihelion pro- 

 gression is explicable on the supposition that the sun's 

 gravity decreases in a slightly faster ratio than the 

 square of the distance (of which there is no proof), the 

 converse being (as I now show) that the centrifugal force 

 correspondingly increases? 



Again. The earth's line of apsides, which joins her 

 perihelion and aphelion, has been proved not to point 

 steadily, but to revolve, exceedingly slowly, in the same 

 direction as the planet. Newton, himself, showed mathe- 

 matically that just such an effect as this would follow an 

 augmentation of the centrifugal force relatively to the 

 centripetal. Now, this is exactly what the Prime Resul- 

 tant supplies, for in every succeeding year the planet 

 descends a matter of a score or so of miles farther than 

 in the year immediately preceding. 



THE TIDES 



It cannot fail of the reader's perception that in thus 

 invoking the principle of equilibrium as applying to 



