12 THE TIDES. 



The following is a geometrical construction for the velocity 

 and height at any place: 



Round the radius OB describe a circle. Since the angle 

 at BcO is right, Be is equal to the perpendicular from CE, 

 i.e. to xl in fig. 1, and cp equal to Ik ; so that the tangential 

 disturbing force at a is proportional to the perpendicular cp. 



M: 



1'ig. 5. 



If aa f be the space passed over in the rotation of the earth in 

 one second, the force acting on the water may be supposed 

 unchanged while it passes from a to a' ; and its effect during 

 that interval (i.e. in this quadrant, the retardation) will 

 also be proportional to cp or its double cf y and to the 

 time : that is, to aa', or the angle at 0, aOa'. Calling H 

 the moon's greatest tide-producing force, r the earth's 



radius, and r the angular velocity = - : : 



seconds in lunar day 



2?r ,. , ,. Hcf aOd XT , , 



= rjTTYqs, t* 16 retardation = - x . Now the angle at 



oy4o/c v T 



= the angle at/, being in the same segment; and this 

 angle multiplied by cf= the small perpendicular cd, or pp' 9 



