34 Colorado College Studies. 



flows infinitely smooth, its motion would be continually ac- 

 celerated, like that of bodies descending on inclined planes. 

 But since the motion of rivers is not accelerated, and soon 

 arrives at a state of uniformity, it is evident that the viscosity 

 of the water and the friction of the channel in which it de- 

 scends must equal the accelerating force. Dubuat, therefore, 

 assumes it as a proposition of fundamental importance, when 

 water flows in any channel or bed, that the accelerating force 

 which obliges it to move is equal to all the resistances which 

 it meets with, whether they arise from the viscosity or from 

 the friction of the bed." 



In 1779 Abb6 Bossut conducted very extensive investiga- 

 tions to determine the amount of retardation in pipes due to 

 adhesion and friction. He reached the conclusion that with 

 pipes of the same length the discharge is proportional to the 

 diameter, and when the diameters are equal the discharge 

 is inversely proportional to the square root of the length. 



The general equations of motion are so complex that little 

 could be done with them. This resulted in the numerous 

 efforts which were made by one class of investigators, such 

 as Dubuat, Bossut and Prony, to develop by experiment sim- 

 pler formulas for the velocity of running water. However, 

 the more theoretical mathematicians, among whom were 

 Lagrange, Laplace, and Poisson, endeavored to obtain solu- 

 tions for the equations of D 'Alembert, and thus solve the 

 various problems of hydrodynamics. These men, together with 

 other eminent mathematicians of both France and Great 

 Britain, devoted much time to the investigation of waves and 

 tides. 



Navier (1785-1886) was j)robably the first to offer equa- 

 tions of motion for a viscous fluid (1822). He bases his in- 

 vestigation upon the following suppositions: The fluid is com- 

 posed of ultimate molecules, acting upon each other with forces 

 which, when the fluid is at rest, are functions simply of the 

 distance, but when the molecules recede from or approach 

 each other are modified by this circumstance so that two 

 molecules repel each other less strongly when they are reced- 

 ing and more strongly when they are approaching each other 

 than when they are at rest; and the alteration in the attrac- 



