Ihe Tides. 227 



of Tjcho Brahe^ and published in 1609, the planets revolve 

 around the sun in elliptical orbits and their radii vectores describe 

 equal areas in equal times. The moon is supposed to revolve 

 about the earth in this manner, the orbit being elliptical with the 

 earth occupying one of the foci. Now, Keppler's laws are strictly 

 true when only one planet and the sun are considered, but in a 

 system, they are subject to complicated pertutbations. I^ewtpn's^' 

 Principle, based upon Keppler's laws half a century later, is con- 

 sequently subject to equally complicated modifications. 



According to the laws of gravitation, all bodies attract each 

 other in proportion to their mass and inversely as the squares of 

 the distance, also, bodies which mutually attract each other re- 

 volve around their common centers of gravity. These apply to 

 our whole system, and we may say, to the whole universes 

 Between the earth and moon there will be a point which will de-: 

 scribe an orbit around the sun while the earth's center will 

 describe a circle around this common center of revolution^ 

 There will appear some complication, for while the two bodies 

 revolve about a'common center, the moon is describing an ellip- 

 tical orbit whose excentricity varies between 1-18 and 1-15 and 

 whose major axis makes a complete revolution in about nine 

 years in direct motion, and although both conditions cannot be 

 entirely true at the same time, yet this will not alter the law 

 while it modifies the results. When the moon is in quadratures 

 both bodies are affected alike by the sun, as the common center 

 lies in their mutual orbit. At this instant either law will apply 

 as the respective orbits of the moon due to either law coincide at 

 this point, and although it may be said that the earth has actual 

 control, its force being at right angles to that of the sun at this 

 point, the moon is actually performing a planetary orbit about 

 the sun. 



As soon however as the moon moves out of quadratures in the 

 ellipse, the earth yields to the law of mutual attraction, on account 

 of the dominant force of the sun, its center describes an undu- 



^ Tycho Brahe, a Dane. Bora 1546, died 1601. Rejected Corernicus. 

 •^ Newton, born 1643, died 1737. Principia, 1637. 



