THE LAW OF EQUILIBRIUM 125 



the phenomena ; second, that in spite of its known falsity, 

 they nevertheless universally teach and follow it as 

 true ; third, that in spite of its known falsity, all recent 

 cosmogonies are unconditionally grounded upon it, and 

 hence must stand or fall with it; fourth, that the con- 

 firmed practice of our astronomers is to seek the solution 

 of cosmic problems, not by uncompromising adherence 

 to strict natural laws, but by industriously searching for 

 loopholes of escape from it, not by the legitimate unfold- 

 ing of the established principles of terrestrial mechanics, 

 but by the invention of a sort of super-mechanics that 

 may serve to admit the introduction of teleological ex- 

 planations under the guise of being natural and normal ; 

 and, lastly, that the Law of Equilibrium to which Newton 

 sought to give quietus, and which his followers have all 

 along believed dead, still survives to rule and order the 

 universe of stars. 



KEPLER'S LAWS 



Newton demonstrated to the satisfaction of expert 

 mathematicians (who, by the way, alone can follow and 

 comprehend his treatise), that Kepler's laws and the law 

 of gravitation are in harmony. As the proponent of the 

 proposition that the law of equilibrium is just as deeply 

 rooted in this great law of gravitation as are Kepler's 

 laws, it would seem to devolve upon me to establish, 

 mathematically, the essential identity of all three. I shall 

 therefore make the attempt : 



The reader will remember that I recognize three 

 sorts of gravitational units, namely; (1) a simple body, 

 like the moon; (2) a compound body, like the binary 

 earth-moon system, and (3) a complex body, consisting of 

 a multitude of planets and satellites, all balancing them- 

 selves around their common center of gravity. More- 

 over, I define a gravitational unit as a single body, or a 

 congeries of cosmic bodies, seeking its lowest center of 

 gravity. The proposition I am now going to try to prove 

 is, that our solar system is a family of such bodies so in- 

 timately associated with each other, by virtue of their 



