I^nii Motion of a perfect liquid. 117 



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

 loug" time before it was realized 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 of rivers or pipes, or the resistance of ships, have largely 

 consisted in the determination of the amount of deviation from the 

 foregoing simple law. 



About one hundred years ago it was discovered that the resistance 

 of friction varies nearly in accordance with the simple law of Torri- 

 celli, and also, althoughfor a totally different reason, the resistances 

 due to a sudden contraction or enlargement of cross section of channel or 

 to an}' sudden obstructions appear to follow nearly the same law. Now 

 it is extremely convenient for reasons which will be understood by stu- 

 dents 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 labor has consequently been expended in finding 

 for all conceivable conditions in actual work tables of coefficients or 

 empirical expressions which are required for calculations 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 ques 

 tion. 



On the other hand, eminent mathematicians, since the days of New- 

 ton and the discovery of the method of the calculus, have been pursuing 

 the investigation of the behavior of a perfect liquid. The mathemat- 

 ical methods, which I have already alluded to as being so wonderful, 

 have, however, scarcely been brought to bear with any apparent result 

 upon the behavior 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 those of actual ships, or 

 of liquid moving through ordinary channels of varying section, even 

 for the case of a perfect liquid, but he has had to take those cases, and 

 they are very few indeed, that he has been able to discover which fit in 

 with his mathematical powers of treatment. 



This brief summary may possibly serve to indicate the nature of the 

 diflicuities which I have pointed out, and will show you the vast field 

 there yet lies open for research in connection with the subject of hydro- 

 mechanics, and the great reception which awaits the discovery of a 

 theoretical method of completelv dealing with viscous liquids, instead 

 of having recourse as at present principally to empirical formulas based 

 on the simple law already alluded to. 



We may, however, console ourselves with the thought that in the 

 application of the laws of motion themselves to any terrestrial matters 

 the friction of bodies must always be taken into account, and renders 



