NO. IB.] EFFECT OF A SURFACE-LAYER. 47 



the vessel being narrow, its velocity there becomes increased, and consequently 

 the friction against the bottom of the vessel becomes increased, by the effect 

 of the surface-layer. Further, because the fresh-water is hinderd in its aft- 

 ward motion, the surface rises a little — and the boundary is lowered — 

 ahead of the vessel. Thus the vessel becomes influenced by a sternward- 

 pressure, which may be calculated approximately by formula (7). When the 

 vessel is moving at some greater speed, and the inertia of the water conse- 

 quently becomes of greater importance, the difference of density of the two 

 water-layers is insufficient to hold their common boundary nearly plane. 

 The fresh-water displaced by the vessel, presses down the salt-water below, 

 and the resulting disturbance of boundary level, persists as waves giving 

 rise to wave-making resistance. Finally, when the vessel moves at velo- 

 cities higher than the maximum velocity of the boundary-waves, she cannot 

 be followed by any train of boundary-waves, and the corresponding part 

 of the resistance accordingly disappears. The vessel when moving at such 

 high velocities, may leave only a very small disturbance, in the boundary 

 behind. For the water-particles, on account of their inertia, then move in 

 nearly the same paths as if the water were homogenous; the gravity has not 

 time to appreciably alter the motion of a particle, before it has already passed 

 by and is at rest behind, in the same level as it had ahead of the vessel. 

 As the water-particles move past the vessel in nearly the same paths as if 

 the water were homogenous, the increase of frictional resistance will, of course, 

 also vanish at these high velocities. 



If the vessel does not move in a narrow channel but in open water, the 

 influence of the surface-layer may be discussed in a similar manner. Whether 

 the vessel reaches the salt-water or not, the fresh water has free passage past 

 her. If the vessel is moving slowly, the boundary between the two water- 

 layers will therefore remain nearly horizontal, and the frictional resistance will 

 be increased just as if the vessel moved in shallow homogenous water of the 

 same depth as the actual surface-layer. Really, it may be increased even more 

 than in shallow water, for the depth of the latter, down to the bottom, must 

 be greater than the draught of the vessel, which on the other hand, can proceed 

 in an even shallower water-layer resting on the top of heavier water. At greater 

 velocities the inertia of the water becomes of more importance, and waves will 

 consequently be created in the boundary between the fresh-water and the salt- 



