relating to Forced Vibrations, 11 



the maximum value of which is 



2gh/r. 



The maximum value of the component due to the moon is |M; 

 and the quantities fa and fa in section 5 are proportional to 

 these maximum values. We have therefore 



l . ±j . . fa . fa-tfa . . — . — b. 2 alj 



T 2 : T?-T 2 : : ^ : #M, 



rM T 2 



97, — 3_ 



Z/i ~2 ^ T 2_ T 2 



10. By making T indefinitely great compared with T l} we 

 obtain the height of the equilibrium tide, which is therefore 

 (neglecting sign) 



irM/g. 



A positive value of 2h indicates low, and a negative value 

 high, water under the moon ; because we have taken as the 

 standard case that in which fa has the same sign as fa. 



Taking the moon's mass as one 80th of the earth's, the 

 moon's distance as 60 times the earth's radius, and this latter 

 as 4000 miles, the value of %rM/g comes out exactly 22 inches. 



11. The height of the equilibrium tide, and the distribution 

 of elevation and depression over the whole ocean on the equi- 

 librium theory, can be independently calculated by the follow- 

 ing simple method, which I have not been able to find in print, 

 though I am informed that it is not new. 



Imagine narrow tubes leading down from tw T o points (or 

 any number of points) on the surface to the centre of the 

 earth. The same distribution of water which gives equilibrium 

 when there is freedom for the water to traverse these tubes, 

 will still give equilibrium when they are blocked by dia- 

 phragms ; for the introduction of diaphragms cannot destroy 

 previously existing equilibrium. 



To determine the height of the tide, it suffices to consider 

 two points, one directly under the moon and the other 90° 

 distant. 



In the column of water which goes down from the first of 

 these points to the centre of the earth, the moon's disturbing 

 force is vertically upward, and varies as the distance from the 

 centre of the earth. At the top of the column the disturbing 

 force (with the notation of section 7) is 2M ; and its average 

 value for the whole column is therefore M. 



