II. 



PRELIMINARIES. 



A. THE RESISTANCE TO VESSELS UNDER ORDINARY 



CIRCUMSTANCES 1 . 



Imagine a vessel towed on a hawser. When her speed has become uni- 

 form, the resistance is evidently equal to the stress in the tow-rope; its im- 

 mediate cause is the sternward resultant of the water pressure, against the 

 vessel. In this pressure is then included, the "tangential pressure" or friction 

 of the water against the sides of the vessel. Further, the resistance is equal 

 to the work done in towing or propelling the vessel a unit of distance; this 

 work is heaped up as energy (heat and vis viva), communicated by the vessel 

 to the surrounding water. The resistance may consequently be regarded from 

 two points of view : either, as the resultant of pressure (and friction) of the 

 mater against the vessel or, as equal to the energy communicated to the 

 water per unit of distance covered by the vessel. One must, of course, be 

 careful, not to use these two views simultaneously, so that the resistance, or 

 part of it, be not taken into account twice. 



If the water were frictionless, and if its surface could be held plane 

 as under a sheet of ice, vessels would, according to a well known hydro- 

 dynamical theorem of Kirchhoff 2 , experience no resistance, when moving 



1 Part of the substance of this section is drawn from Chapter XI of Sir W. H. White's 

 very interesting "Manual of Naval Architecture", London 1900, and from Chapter IX 

 of the excellent "Hydrodynamics" of Prof. Horace Lamb, Cambridge 1895- To these 

 books reference may also be made for further information on the subject. 



- Vorlesungen ilber Mathematische Physik, von G. Kirchhoff. Mechanik. Neunzehnte 

 Vorlesung § 2. 



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