8 T. A, Hirst on Ripples, 
ae, ee 
dy? v 
where 6 is thé inclination of the ripple to the direction of the 
current at any point M of the former. We are thus led to the 
following simple and interesting result :— 
At any point of a ripple, the sine of the angle between its direc- 
tion and that of the current ts inversely proportional to the velocity 
of the latter, and directly proportional to the velocity of propa- 
gation of the wave which touches the ripple im that point. 
10. This result may be arrived at in 
a simpler manner. When the velocity 
and direction of the current remain the 
same at all points, the waves produced 
at a point A retain their circular form 
as they float down the current. If the 
radi of the several circular waves in- 
crease with the same velocity A, then 
the ripple, their envelope, will clearly 
consist of two right lines diverging 
from A and touching all the circles. 
if from the centre B of any wave the 
radius B M be drawn to its point of 
contact with the ripple, then, since the 
wave has been propagated over the 
space BM in the same time that a 
point of the current has described the 
space A B, we have clearly 
eseeay GRE hf Sie Ge 
If, as Weber asserts (see art. 2), the 
velocity with which the wave is pro- 
pagated diminishes as its magnitude 
or radius BM increases, the ripple will 
no longer be rectilineal, but at the 
point M of the ripple the law of art. 9 
will still hold. To prove this, it is 
only necessary to consider two im- 
mediately succeeding circular waves 
around B and B/, and from these 
points to let fall the perpendiculars & 
BM, B'M’ upon their common tan- sige 
gent MM!, which will also be the 
tangent to the ripple at the point M ; 
