116 THE MOTION OF A PERFECT LIQUID. 



be admitted that the matter is a difficult one. Probabl}^ one of the 

 most perplexing things in engineering science is the absence of all 

 apparent connection between higher treatises on hydrodynamics and 

 the vast array of works on practical h3'draiilics. The natural connec- 

 tion between the treatises of mathematicians and experinjcntal 

 researches of engineers would appear to be obvious, but ver}' little, if 

 an}% such connection exists in reality, and while at every step electrical 

 applications owe nuich to the theories which arc common to electricity 

 and Indromechanics, we look in vain for such applications in connection 

 with the actual flow of water. 



Now the reason for this appears to l)e the immense difl^'erence between 

 the flow of an actual liquid and that of a perfect one owing to the 

 property of viscosity. A comparison of the various experiments which 

 you have seen to some extent indicates this. 



In the flrst place, let us consider for a moment some of the things 

 which would happen if water were a j)erfect li(|uid. In such a case, 

 a shii) v.ould cx])eri(Mice a very ditt'erent amount of resistance, because, 

 althouuh wa\'es would ))e raised, owing to the reasons which we have 

 already seen, the chief causes of resistance, viz, skin friction und <'ddy- 

 ing motion, would 1h' entli'ely absent, and of course a su))inai"in(> boat 

 at a certain depth would experience no resistance at all, since the pres- 

 sures fore and aft would be equal. On the other hand, there would 

 be no waves raised by the action of the wind, and there would ])e no 

 tidal flow, but to make up for this rivers Avould flow with incredible 

 velocit}^, since there would be no retarding forces owing to the fric- 

 tion of the banks. But the rivers themselves would soon cease to flow 

 because there would be no rainfall such as exists at 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 ))e said that 

 the absence of viscosity in water would result in changes which it is 

 impossible to realize. 



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 eighteen hun- 

 dred 3'ears ago, an effort being made to find the law for the flow of 

 water from an orifice. For more than fifteen hundred 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 velocity, 

 remained unknown. Torricelli, who discovered this, did so as the 

 result of observing that a jet of water rose nearlv to the height of the 

 surface of the body of water from which it issued, and concluded there- 

 fore that it obeyed the then recently discovered law of all falling 

 bodies. 



