The first of these relates to what is called the “_corresponding speeds_.” Suppose we have a real ship 250 feet long, and we make an exact model of this ship 10 feet long, then the ship is twenty-five times longer than the model. Mr. Froude’s law of corresponding speeds is as follows:— If the above model and the ship are both made to move over still water, the ship going five times as fast as the model, the system of waves made by the model will exactly reproduce on a smaller scale the system of waves made by the ship. In other words, if we were to take a couple of photographs, one of the ship going at 20 miles an hour, and one of the model one twenty-fifth of its size going at 4 miles an hour, and reduce the two photographs to the same size, they would be exactly alike in every detail. Expressed in more precise language, the first law of Froude is as follows: When a ship and a model of it move through smooth water at such speeds that the speed of the ship is to the speed of the model as the square root of the length of the ship is to the square root of the length of the model, then these speeds are called “_corresponding speeds_.” At corresponding speeds the wave-making power of the model resembles that of the ship on a reduced scale. If we call _L_ and _l_ the lengths of the ship and the model, and _S_ and _s_ the speeds of the ship and the model, then we have— _S_/_s_ = √(_L_/_l_) where _S_ and _s_ are called corresponding speeds. Mr. Froude then established a second law of equal importance, relating to that part of the whole resistance due to wave-making experienced by a ship and a model, or by two models when moving at corresponding speeds. Mr. Froude’s second law is as follows: If a ship and a model are moving at “corresponding speeds,” then the resistances to motion due to wave-making are proportional to the cube of their lengths. To employ the example given above, let the ship be 250 feet long and the model 10 feet long, then, as we have seen, the corresponding speeds are as 5 to 1, since the lengths are as 25 to 1. If, therefore, the ship is made to move at 20 miles an hour, and the model at 4 miles an hour, the resistance experienced by the ship due to wave-making is to that experienced by the model as the cube of 25 is to the cube of 1, or in ratio of 15,625 to 1. In symbols the second law may be expressed thus: Let _R_ be the resistance due to wave-making experienced by the ship, and _r_ that of the model when moving at corresponding speeds, and let _L_ and _l_ be their lengths as before; then— _R_/_r_ = _L_^3/_l_^3 Before these laws could be applied in the design of real ships, it was necessary to make experiments to ascertain the skin friction of different kinds of surfaces when moving through water at various speeds.