PROTEOME SOBAOCHL OOS: SOK LERRA CE. 25 
would be simply the subaqueous earth slope. If it be in any 
arithmetical progression, the slope will be a plane whose steep- 
ness will vary with the rate of decrease, the slope being steeper 
when the rate is higher. If the loss of power be in some other 
manner than by arithmetical difference, the slope will show a 
curve which will be convex or concave according as the rate of 
decrease is augumented or diminished. In actual deposition by 
a current advancing into deep water, the decrease of power is at 
an increasing rate, as may be seen from the following. Ifa plane 
slope be assumed, so that depth increases in arithmetical ratio, 
then the velocity of the current will decrease in similar ratio, 
but transporting power varies as the square of the velocity, 
hence its rate of decrease is progressively augmented. This will 
require convexity of slope, a feature generally observed at the 
edge of embankments and subaqueous terraces. The general 
law of equilibrium, as given above for an eroding current still 
applies; current power is uniform over all parts of the bot- 
tom, if by the term current power is understood power with refer- 
vence to load and the current considered is the resultant of all con- 
jucting currents, In this case, while the current is acually losing 
power, the loss is balanced by the coincident loss of load, and 
the uniformity of power in comparison with load is maintained. 
Presence of a bank, equilibrium on a slope-—The presence of a 
bank fixes not only a horizontal limit to the bottom in question, 
but determines that at this limit the depth shall be zero. This 
involves a slope. If equilibrium is to exist on this slope in har- 
mony with the general law stated above, the advantage in power 
due to shallower water on one side must be balanced in one of 
four ways, @) the equality of transporting power in deep and 
shallow water may be partially maintained by the participation 
of more water where the depth is great than where it is small. 
In the case of undertow this has been shown to be true; (2) 
currents in both directions may be stronger, so that the result- 
ant motion in one direction may be more in shallow water than 
in deep water, it may even be zero or it may be in the opposite 
direction. The factors of translatory wave motion and on-shore 
