ON NAVAL ARCHITECTURE. 313 



which are lines representing the surface friction of the model. The 

 differences between the ordinates of the two curves are the forces 

 solely due to the formation of the models waves. Now it is a property 

 of waves that similar waves move with speeds proportionate to the 

 square roots of their dimensions, and from that, if it is fairly looked 

 into, it follows that comparing a ship and a model of given lengths, 

 the waves made by the ship, and the waves made by the model will 

 be exactly similar if the speeds at which the ship and the model 

 respectively move, are proportional to the square roots of their 

 respective dimensions. Bear in mind that the resistance consists in 

 effect of two elements, one surface friction and eddy-making, the other 

 wave-making ; I deal now with the latter in its comparative effect with 

 ship and model : If the ship of which we make the model is sixteen 

 times as long as the model, the waves that the ship makes at a speed 

 of ten knots, will be similar to those which the model makes at 

 two and-a-half knots, since four is the square root of sixteen, and 

 two and-a-half is a quarter of ten ; and on that basis we calculate 

 the resistance that the ship will experience in wave-making, compared 

 with that which the model experiences in wave-making. It comes out 

 that if the speeds are what I call the "corresponding speeds," that is are 

 proportionate to the square roots of the dimensions, at such speeds 

 the resistances due to wave-making are proportioned to the cubes of the 

 dimensions, that is to say, in the instance just given, the ship going 

 ten knots will have a wave-making resistance 4096 times that which 

 the model has at two and a-half knots, 4096 being the cube of sixteen, 

 and, as before, two and a-half being ten divided by the square root of 

 sixteen. In that way we can calculate the ship's resistance due to 

 wave-making from the model's resistance due to the same cause. 

 Then again in calculating the ship's surface friction, knowing her 

 surface, and the speed at which she is moving, and the quality of the 

 surface, we can calculate what will be the resistance due to it at each 

 speed, and by adding this to the resistance due to wave-making we 

 can construct a complete curve of resistance for the ship from the 

 resistance of a model similar to the ship. If the resistance due to 

 surface friction were simply as the area, and as the square of the speed, 

 irrespective of the question whether the given area were a long one or a 

 short one, it would follow that in comparing ship and model the 



