294 NEWTON S PRINCIPIA. 



in its perigee to the height of ] 2J feet, and more, especially 

 if the wind sets the same way as the tide. 



Newton makes some remarks on the observed nature of 

 the tides in different parts of the world. His explanations 

 are not always perfectly correct. To have a full tide 

 raised, an extent of sea from east to west is required of 

 no less than 90 degrees. Hence, he infers, the tides 

 in the Pacific are greater than those in the Atlantic, 

 and those in the North Atlantic than those within the 

 tropics. In some ports, where the water must be forced 

 in and out through narrow channels, the flood and ebb 

 must be greater than ordinary, and this force of efflux, 

 being once given to the water, may, he argues, con 

 tinue until it raises the tide as much as fifty feet. But 

 on such shores as lie towards the sea with a steep ascent, 

 where the waters may freely rise and fall without that 

 precipitation of influx or efflux, the proportion of the 

 tides agrees with the forces of the sun and moon. 



The force of the moon being - only ^^th part of 

 gravity at the surface of the earth, will not be sensible 

 in any statical or hydrostatical experiment, or even in 

 those of pendulums. It is in the tides only that this 

 force shows itself. 



I have already mentioned that the mass of the moon was 

 unknown in Newton s time. He makes use of the obser 

 vations on the tides to determine her mass and density. 

 Her force is ^th part of the sun s force to raise the 



4 4815 * 



tides. And, by lunar theory, these forces vary as the 

 masses of the attracting bodies directly and the cubes of 

 their distances directly; that is, as their densities and 

 the cubes of their apparent diameters. These diameters 

 being 31 , 16J,&quot; and 32 , 12&quot;, the ratio of the densities is 

 4 8 91 to 1. But the density of the sun was known to be 

 one-fourth that of the earth. Hence the moon is denser 



