INTRODUCTION 21 



has committed a grave blunder in concluding too careless- 

 ly that by falling in vacuo bodies circumvent the law. 



5. By basing my theory of tides on the strict law of 

 equilibrium instead of on the spurious exception, I have 

 succeeded in demonstrating ; (1) that the heights of the 

 tides are commensurate with the dynamical causes I as- 

 sign to them, (2) that the times of high and low tides are 

 synchronous with those causes, and not eight hours or 

 more apart, (3) that the sun, and not the moon, is the 

 chief cause of the tides, notwithstanding the seeming 

 paradox, and (4) that, far from retarding the earth's 

 axial rotation, the tides actually cause it ! 



6. The principle of gravitation is not restricted to 

 the limits of our system, as Newton construed it, but ex- 

 tends throughout and across the whole length and breadth 

 of the universe, organizing the latter into a single coordi- 

 nate unit. 



7. The true pole of the ecliptic is a mathematical 

 point situated about a half light year from us, in the line 

 of the earth's axis extended, and marks the direction in 

 which our solar system is falling in response to the joint, 

 or resultant, attraction of the stars. 



8. However, we are not falling in a direct line, but 

 in a huge conical spiral path, like that of a circling falcon 

 approaching the earth. The length of a single coil of 

 this spiral is approximately five million, million miles, 

 its describing period about 26,000 years, and its mean 

 plane very nearly that of the ecliptic. The apex and an- 

 tapex of the sun 's way are respectively the fore and aft 

 celestial ends of the double tangent to this curve passing 

 through the sun's center. 



9. This movement of the solar system is due to the 

 gyroscopic reaction resulting from the whirling of the 

 system in the opposite direction about its own axis. 



10. The revolution of the planets around the sun is 

 a vortical, or whirlpool, effect produced and maintained 



