NO- 15.] APPLICATION OF SMALL SCALE EXPFRIMENTS. 53 



It may be pointed out that the two rules above, hold approximately even 

 if the whole resistance be considered. For the frictional resistance varies 

 approximately as the wetted area of the vessel and as the square of the 

 velocity, so that it is obvious it will vary approximately according to the two 

 rules given. The eddy-making resistance is of smaller importance; the same 

 rules hold true for it, provided the motions are really "similar", because it 

 is a resultant of pressure. It could not, however, be taken into account when 

 deducing the rules, because it should not exist at all in a frictionless fluid. 



Besides the viscosity, we must also take account of the capillary forces, 

 which influence the small scale experiments more strongly than those on a full 

 scale, and thus disturb the similarity. On the one hand, these forces prevent 

 the creation of ordinary surface waves in the experiments; on account of 

 capillarity these waves cannot move with a velocity slower than 20 or 23 cm. 

 per second, and the boat-models were towed at still smaller velocities. This 

 effect of capillarity is, however, of no importance, because, at the slow speeds 

 at which dead-water occurs, even full-sized ships do not produce any appreci- 

 able surface-waves. The secondary waves in the surface which are produced 

 by the boundary-waves, are — on account of their greater length — not ap- 

 preciably influenced by the capillarity. 



On the other hand the surface-tension directly impels the vessel. If it 

 were the same on all sides of the vessel it should have no effect; if, however, 

 the water is even very little contaminated with grease, its surface-tension is 

 reduced, but in a smaller degree in the wake of the vessel, where the cont- 

 aminated surface film becomes ruptured by the eddies. A superficial resi- 

 stance then arises, which although quite insignificant in the case of full-sized 

 ships, might be of considerable importance in experiments on a small scale. 

 It will be shown later, that even this effect of capillarity is of no essential 

 influence on the experimental results. 



