ON WAVES. 



Table XXIK. 



379 



Comparisoti of Experiments on the Divergence dtie to given Velocities of 



Genesis. 



Column c is the constant measure in inches taken along the path of gene- 

 sis A B in the figure ; the adjacent column is the velocity of genesis along 

 A B in inches per second. 



Column b is the length A C, measured by observation in a direction at 

 right angles to A B. 



Column X is the length of x deduced from the measure b, and the adjacent 

 column shows the corresponding deduced velocity of the wave at right angles 

 to its ridge. 



Column B shows the angles of divergence given by these observations. 



Column b' and B' are numbers corresponding to b and B obtained from 

 the supposition that the velocity of the wave in a direction at right angles to 

 its own ridge is constant and precisely equal to the velocity of the free wave, 

 viz. 8,} inches per second. The deviations of b' and B' from b and B were 

 chiefly due to disturbance of the fluid produced by the apparatus employed 

 in genesis. 



Various considerations induced the acceptance of a constant velocity along 

 X of 8*5 inches per second. The deviations from it in the increasing veloci- 

 ties are due principally to the disturbance of the fluid by the peculiar method 

 of genesis in that instance employed as most convenient. On this assump- 

 tion the values of h were calculated by the following formula and placed in 

 the column V, and the values of the angle B found in this manner are written 

 under B'. 



In the triangle A B D, sin B= ^'"^^'^ ; 



whence in the triangle A C D, J= 



sinD xar 



sinC 



• From what has been said, it follows that there can be no difficulty in cal- 

 culating the velocity of a body or current from the divergence of the capillary 

 wave. 



Let b represent the amount of divergence per foot, the time in which a 

 foot will be described, and consequently the velocity per second, can be ob- 

 tained by the formulse which were first given ; thus, finding the length of x, 

 and its velocity being known, the absolute time occupied can at once be 

 found, which time is that in which the moving body traverses one foot. In 

 Table II., columns A, B, contain the divergence of the wave expressed in 

 inches per foot, and the corresponding velocity in inches per second. 



