312 SECTION MECHANICS. 



But when we come to higher speeds we immediately see that the 

 other principal cause of resistance begins to operate ; the waves begin 

 to form themselves. The whole theory of an investigation of merit 

 in form is complicated by that condition, and you have to arrange your 

 form so as to produce the smallest amount of wave motion. I ought to 

 say that the problem to be solved in finding the best form for a ship 

 is one rather difficult even to state satisfactorily. When we say we 

 want to make a ship of a given length, breadth, and depth, which shall 

 go with the least resistance, or a ship of a given displacement, there 

 are, besides, a multitude of collateral conditions to be taken account of, 

 such as comparative first cost, comparative liabiliiy to wear and tear, 

 c. ; but these considerations can perhaps be more properly introduced 

 as make-weights when an approximate solution has been supplied on 

 broader grounds. Viewing the matter thus broadly, the clearest state- 

 ment of the proposition I can frame to myself is, that we wish to carry an 

 amount of useful displacement at a given speed with the least expendi- 

 ture of power. By useful displacement, I mean displacement available 

 for the purposes for which the ship is primarily intented, ^.,the carriage 

 whether of goods or passengers, and exclusive of that devoted to weight 

 of hull, of engines, coals, rigging, crew, and stores ; not that these things 

 are, as a matter of fact otherwise than useful, and indeed necessary, but 

 that any reduction in their amount, compatible with the primary 

 purpose of the ship, is a gain, not a loss. Now as any variation in the 

 ship's form must affect the outcome of each of these conditions 

 separately, it is plain that the solution is a very complex one, and in 

 point of fact we cannot arrive at anything like a general determination 

 of what is the best form for a ship. Another circumstance that makes 

 that difficult, is that the relative merits of different forms will vary 

 with the speeds at which they are compared. The form which is best 

 for a ship to go seven, eight, or nine knots, if it is a long ship, would 

 be very sensibly different from what it would be if she is to go sixteen 

 or eighteen knots, again you should adopt a much shorter ship for 

 moderate speeds, because at such speeds the surface friction is the 

 greatest element of resistance, and is relatively greater in the longer ship. 



What I have now to explain to you is how to frame the comparison 

 between a ship and her model. When we have got the curve of 

 resistance for the model, we draw on it a second curve, the ordinates of 



