Fluviatile and Marine Oraveh. 499 



material and particularly the coarser stuff is carried landward, 

 thus defeating the object of wave attack. The highest effi- 

 ciency is reached when a profile of equilibrium adjusted to the 

 strength of the waves of a given shore is established ; for under 

 these conditions materials of all grades of coarseness may be 

 carried the maximum distance. 



The shape of the shore profile of maturity is directly related 

 to the force of waves. Fenneman has shown* that '* there is 

 a certain minimum slope for the bottom upon which the waves 

 may be propagated as a shallow water wave " and " a certain 

 maximum slope for the bottom upon which the wave may be 

 propagated without breaking." Wind acting on waves tends 

 to diminish both the minimum and maximum slope required 

 for normal swells. At and coastward of the line of breakers the 

 work of a normal wave of oscillation (waves of the second 

 order) may be modified or entirely counteracted by water 

 movements of various sorts, primarily waves of translation, 

 undertow, and long shore currents. Waves of translation, or 

 waves of the first order, move toward the shore line both at 

 bottom and surface and transport materials landward, not 

 backward and forward as in the case of waves of the second 

 order.f 



The effect of the undertow associated with w T aves is to carry 

 water and sediments seaward and thus offset the work of waves 

 of translation. In the contest between these two sets of forces 

 the waves under average conditions are more effective since 

 their activity is concentrated within a short time, whereas the 

 work of the undertow is more evenly distributed in time. The 

 result of these opposing agencies is to carry materials back and 

 forth over a narrow zone with a net tendency landward. Fen- 

 neman^; calls attention to an exceptional type of returning 

 bottom current, that developed in bays where water has been 

 heaped by wind-made or wave-made long shore currents. The 

 current developed under such conditions is regular and pow- 

 erful and may carry sediments or even erode below the point 

 of maximum wave agitation. Thus in Lake Michigan, where 

 waves disturb the bottom to depths of 60-70 feet, " a sand- 

 covered or gravel-covered bottom concave upward extends out- 

 ward to several times this depth with little or no evidence of 

 change of slope at wave base."§ A similar case is cited from 



*Jour. Geol., x, p. 17. 1902. 



f This view of the relation waves of the first order bear to those of the sec- 

 ond order as presented by Russell, Trans. British Assoc, 1837, is discussed 

 by Hunt (Sc. Proc. Eoy. Dublin Soc- vol. iv, pp. 251-254, 1883-85), who 

 reaches an opposite conclusion: that there is ''no evidence that a wave of 

 oscillation is transformed into a wave of translation on passing into shallow 

 water." 



% Journal of Geology, vol. x, pp. 31-32, 1902. 



§Loc. cit., p. 31. 



