THE TIDES AND TIDAL ROTATION 79 



do not cause the tides, but rather that they do not cause 

 them in the mariner generally supposed. The orthodox 

 explanation is that the sun (or moon) attracts the water 

 on the side of the earth nearest it more than it does the 

 solid part or kernel, and the kernel in turn more than 

 the water on the rearward side, thus heaping up her 

 oceans fore and aft. 



Now, the simple law of gravitation, formulated by 

 Newton and known by heart to every freshman, reads 

 as follows : 



"All bodies attract each other directly as their 

 masses, and inversely as the squares of their distances 

 apart/' 



Through one of those fatal lapses to which astron- 

 omy of all the sciences has been most prone, she has 

 applied to tides the second half only of this law, there- 

 by giving rise to an error which has vitiated two cen- 

 turies of thought and calculation on this and other 

 cosmic problems. When the full rule is given effect, it 

 will be found that instead of the water being heaped up 

 under the attracting body, it is depressed, and by a 

 force indefinitely greater! 



In the diagram (Fig. 1) let E represent a planet in 

 space, and endowed naturally with the property of grav- 

 itation. It consists, let us say, of a solid kernel 10,000 

 miles in diameter, entirely homogeneous throughout, 

 and surrounded by an envelope of water five miles in 

 depth. Let us suppose this water frozen to a depth of 

 one mile (merely in order to aid the imagination). We 

 now bring in touch with E a second body M, which, 

 let us suppose, has no water envelope, and, for the 

 moment, lacks altogether the gravitational power pos- 

 sessed by E. It is evident that under these conditions 

 E will not be affected by this juxtaposition in the least. 



