THE PROGRESS IN STEAM NAVIGATION. 685 



The earlier theories of resistance assumed that the resistance experi- 

 eficed by ships varied as the square of the spe^d. We now know that 

 the frictional resistances of clean- painted surfaces of considerable 

 length vary as the 1.83 power of the speed. This seems a small dif- 

 ference, but it is sensible in its effects, causing- a reduction of 82 per 

 cent at 10 knots, nearly 40 per cent at 20 knots, and 42 per ccpt at 25 

 knots. On the other hand, it is now known that the laws of \ai-iatiou 

 of the residual or wave-making resistance may depart very widch- f i-oin 

 the law of the square of the speed, and it may be interesting to ti-ace 

 for the typical destroyers how the resistance actually varies. Take, 

 first, the total resistance. Up to 11 knots it varies nearly as thc^ scjuare 

 of the speed; at 16 knots it has reached the cube; f i-om bs to 20 knots it 

 varies as the 3.3 power. Then the index begins to diminish: at 22 knots 

 it is 2.7; at 25 knots it has fallen to the square; and from there to 30 

 knots it varies practically as does the frictional resistance. Th<> resid- 

 ual resistance varies as the square of the speed up to 11 knots; as the 

 cube, at 12^ to 13 knots; as the fourth power, about 14^ knots; and at 

 a higher rate than the fifth power at 18 knots. Then the indox l)egins 

 to fall, reaching the square at 24 knots, and falling still lower at higher 

 speeds. It will be seen, therefore, that when this smalhessel has l)een 

 driven up to 24 or 25 knots by a large relative expenditure of power 

 further increments of speed are obtained with less ])i-oporti()iiate 

 additions to the power. 



Passing from the destroyer to the cruiser of similar foi-m but <>f 

 14,100 tons, and once more applying the scale of comparison, it will be 

 seen that to 25 knots in the destroyer corresponds a speed of 474 knots 

 in the large vessel. In other words, the cruiser would not reach the 

 condition where further increments of speed are obtained with com 

 paratively moderate additions of power until she exceeded 47 knots, 

 which is an impossible speed for such a vessel under existing condi- 

 tions. The highest speeds that could ])e reached by the cruiser with 

 propelling apparatus of the lightest type yet fitted in larg(^ seagoing 

 ships would correspond to speeds in the destroyer, foi- which the 

 resistance is varying as the highest power of the speed. 



These are suggestive facts. Frictional resistance, as is well known, 

 is a most important matter in all classes of ships and at all speeds. 

 Even in the typical destroyer this is so. At 12 knots the friction, with 

 clean-painted" bottom, represents 80 pei- cent of the total resistance; at 

 16 knots, 70 per cent; at 20 knots, a little less than 50 per cent: and 

 at 30 knots, 45 per cent. If the coefficicmt of friction wre doubled, 

 and the maximum power developed with ciiual eliicieiu'V, a loss of 

 speed of fullv 4 knots would result. In the cruiser of sinular form 

 the friction represents 90 per cent at 12 knots, S5 p<«r «vnt at IH knots, 

 nearlv 80 per cent at 20 knots, and over 70 per <-ent at 2:^ knot>. if 

 the coeflicientof friction were doubled at 23 knots,and the <orresp..nd- 



