NOTES. 247 



Of course there is not, practically, in any of these cases absolute 

 discontinuity of motion. It was shewn in Art. 132 that a surface of 

 discontinuity may be regarded as made up of a system of vortices 

 distributed in a certain way. Owing to fluid friction the vortex-motion 

 does not remain concentrated in this surface, but is diffused through the 

 fluid on each side. Thus the boundary of the dead water is marked by 

 a band of eddies. 



C. The effect of a rigid boundary to the fluid may be estimated 

 from Art. 125 (a). It appears that if the dimensions of the solid be 

 small compared with its distance from the boundary, the influence of 

 the latter may be neglected. 



A free surface at a great distance from it also has little effect on 

 a solid. The case is otherwise however when the solid is only partially 

 submerged, e. g. a ship. One effect of the motion is to make the pressure 

 deviate from its statical value ; to increase it, for instance, at the bows 

 and at the stern, and to diminish it amidships*. Hence the level of the 

 fluid is disturbed, there is an elevation of the water at each of the 

 former points, and a depression between. A wave like this, accom 

 panying the ship, would of course cause no loss of energy beyond what 

 is necessary to maintain it against viscosity. But we have also waves 

 produced which travel over the surface, and carry off energy to the 

 distant parts of the fluid. The energy thus dispersed must of course 

 come directly or indirectly from the ship ; and the loss from this cause 

 constitutes a special form of resistance, called wave-resistancet. 



A body moving through air will in like manner experience a resist 

 ance due to the dispersion of energy by air-waves. It appears, however, 

 that if the motion be steady, and the velocity of the body small compared 

 with that of sound, the resistance due to this cause is inappreciable. 

 For we have, with the same notation as in Art. 169, 



1 &amp;lt;/&amp;lt; ds 



* This is easily seen by impressing on everything a velocity equal and opposite 

 to that of the ship, and so reducing the case to one of steady motion. 



f For a discussion of the various kinds of waves produced by a ship, and of the 

 probable laws of wave-resistance, we must refer to a paper by Eankine, in the 

 Phil. Trans, for 1871. The student may also consult, on the general question, 

 Eankine &quot;On Stream-Lines in connection with Naval Architecture,&quot; Nature 

 vol. n, and Froude &quot;On Stream-Lines in Relation to the Resistance of Ships,&quot; 

 Xature, vol. in. 



