1899.] on the Motion nf a Perfect Liquid. 63 



present, since it is due to viscosity that the rain is distributed, instead 

 of falling upon the earth in a solid mass when condensed. In a word, 

 it may be said that the absence of viscosity in water would result in 

 changes which it is impossible to realise. 



We may now briefly try to consider the difference between 

 practical hydraulics and the mathematical treatment of a perfect 

 liquid. The earliest attempts to investigate in a scientific way the 

 flow of water appears to have been made by a Roman engineer about 

 1800 years ago, an effort being made to find the law for the flow of 

 water from an orifice. For more than 1500 years, however, even the 

 simple principle of flow according to which the velocity of efflux varies 

 as the square of the head, or what is the same thing, the height of 

 surface above the orifice varies as the square of the velocity, remained 

 unknown. Torricelli, who discovered this, did so as the result of 

 observing that a jet of water rose nearly to the height of the surface 

 of the body of water from which it issued, and concluded therefore 

 that it obeyed the then recently discovered law of all falling bodies. 



Though it was obvious that this law did not exactly hold, it was a 

 long time before it was realised that it was the friction or viscosity of 

 liquids that caused so marked a deviation from the simple theory. 

 Since then problems in practical hydraulics, whether in connection 

 with the flow in rivers or pipes, or the resistance of ships, have largely 

 consisted in the determination of the amount of deviation from tho 

 foregoing simple law. 



About 100 years ago it was discovered that the res : stance of 

 friction varies nearly in accordance with the simple law of Torricelli 

 and also — although for a totally different reason — the resistances due 

 to a sudden contraction or enlargment of cross section of channel or 

 to any sudden obstructions appear to follow nearly the same law. 

 Now it is extremely convenient for reasons which will be understood 

 by students of hydraulics, to treat all kinds of resistance as following 

 the same law, viz. square of velocity which the variation of head or 

 height of surface has shown to do. But this is far from being exact; 

 and an enormous amount of labour has conrequently been expended 

 in finding for all conceivable conditions in actual work tables of 

 co-efficients or empirical expressions which are required for calcula- 

 tions of various practical questions. Such data are continually being 

 accumulated in connection with the flow of water in rivers and pipes, 

 for hydraulic motors and naval architecture. This is the practical 

 side of the question. 



On the other hand, eminent mathematicians since the days of 

 Newton and the discovery of the method of the calculus, have been 

 pursuing the investigation of the behaviour of a perfect liquid. The 

 mathematical methods which I have already alluded t > as being so 

 wonderful, have however scircely been brought to bear with any 

 apparent result upon the behaviour of a viscous fluid. Indeed, the 

 mathematician has not been really able to adopt the method of the 

 practical investigator, and deal with useful forms of bodies such as 



