CASE OF GLOBE COVERED WITH WATER. 15 



The effect of the vertical component may be estimated 

 as follows : 



As shown above the whole attraction of the moon 



= SlFx-60 5 = 29M60 nearly " 3 is re P resented in the 

 figure by ME. The vertical component of the disturbing 

 force is represented on the same scale by xh which is greatest 

 when x coincides with (7, and is then 



ME g g 



"60" = 293650 T~30 = 8800000' nearly> 



This is the proportion in which the weight of a particle 

 directly under the moon is diminished. It is less than two 



grains in a ton, or equivalent to less than T^th of an inch 



in a depth of three miles with the water at a temperature 

 of 50 F. ; an increase in temperature of one-tenth of a 

 degree would produce more than a hundred times this 

 effect. 



In the preceding demonstrations we have supposed the 

 water to be limited to an equatorial canal, the moon also 

 being in the equator. It is desirable to consider what 

 modifications will be introduced, first, by supposing the 

 earth to be uniformly covered with water ; and secondly, 

 by taking into account the moon's declination. 



It will save repetition if we state once for all certain 

 general principles which we shall have to employ : 



1. First, suppose an accelerating force acts alternately 

 in opposite directions; the effect (measured by velocity) 

 increases as long as the force acts in either Direction ; and 

 therefore the velocity in that direction is greatest at the 



