208 Wisconsin Academy oj Sciences^ Arts^ and Letters. 



The attending currents are the motion of the water on the 

 slopes of the waves in obedience to gravitation. The excursions 

 cf these currents, at any particular point, are of short duration ; 

 the motion of the wave is so rapid compared with the current 

 that a point in moving down one side is elevated bv the advanc- 

 ing wave and left on the reverse slope to return and repeat the 

 journey. It is not uncommon during still weather, to observe 

 objects floating to and fro with the currents during several suc- 

 cessive tides. 



The figure of a normal or undistorted wave is nearly equal to 

 a curve of sines of a circle whose diameter extends from high to 

 low water with the 'center at mean level; if the semicircle and 

 the half wave are divided into an equal number of parts, the sines 

 and distances are the coordinates of the curve. As a rule the 

 advance slope of the wave is the steeper of the two, for the axis 

 is always inclined forward, owing to the resistance of friction. 

 By comparing a diagram of an observed tide with the theoretical 

 one, the distortion, if there is any, is at once recognized. 



In the deep water of the ocean the volume necessary to form 

 the wave in proportion to the force meets with little resistance, 

 whereas in shallow water the resistance of friction from the bot- 

 tom becomes considerable, and the wave which is thereby retarded 

 in its progress is modified and the horizontal force is transformed 

 into a vertical one ; the water in front of the wave is drawn down 

 to form the wave, thereby making the previous low water lower 

 while the momentum of the wave heaps the water upon the ob- 

 structed portion, making the high water higher ; and while the 

 range is thus increased the leogth is proportionally diminished. 



The tide is often much distorted by storms, so much in fact at 

 times, as to almost lose its identity. A remarkable case occurred 

 in New York Bay in the summer of 1869 ; it indicated that a 

 vere storm was raging somewhere ou the Atlantic ocean which 

 arrested for a time the progress of a portion of the wave"; the 

 entire volume arrived in due time, but in a distorted form. 



The force of the wind has also a great effect upon the tides in 

 bays .'md rivers where at times every feature is disturbed beyond 

 recognition. In the Delaware river in the winter of 1851 and 



