32 CoLOEADO College Studies. 



weight of the column of fluid having the area of the orifice 

 as a base. Therefore its weight, which is proportional to the 

 area of the orifice multiplied by the height of the fluid in the 

 vessel, must be proportional to the (piantity of motion engen- 

 dered in the particles which escape through the orifice each 

 instant. Continuing this analysis, he finally arrives at the 

 theorem already establislied by Torricelli by an entirely dif- 

 ferent method. 



The investigation of the flow of water in rivers attracted 

 considerable attention in Italy, probably on account of the 

 extensive landscape gardening. Besides Guglielmini, who was 

 inspector of rivers in Milanese, Marquis Polini deserves men- 

 tion in this connection. In 1(595 he wrote De Moiu Aquae 

 Mixto, and in 1718 another work concerning the flow of 

 water through orifices and short tubes. 



Newton (1642-1727) investigated the effects of friction 

 and viscosity in diminishing the velocity of running water. 

 In book 2, § 9. of the Principia, he otfers the following 

 hypothesis: The resistance which arises from the viscosity 

 of a fluid, other things being equal, is proportional to the 

 velocity with which the particles separate from each other. 

 This may be said to be the fundamental principle underlying 

 all that part of hydrodynamics which deals with viscous 

 fluids. The vena contracta as well as the oscillation of waves 

 seems to have been considered first by Newton. 



Daniel Bernoulli published his Hydrodynamica, Sive De 

 Viribiis et Moiihus Fluidorum Commentarii, in 1738, in 

 which he bases his theory upon the suppositions that the 

 surface of a fluid contained in a vessel which is being emptied 

 by an orifice remains always horizontal and that the hori- 

 zontal strata always remain contiguous to each other, and 

 that the particles descend vertically with a velocity inversely 

 proportional to the horizontal section of the reservoir. His 

 principle was not acceptable to his contemporaries, conse- 

 quently John Bernoulli and Maclaurin each attempted to 

 solve the problem by independent methods but did so with- 

 out marked success. 



Jean-le-Kond D'Alembert (1717-1783), aided by the dis- 

 coveries of Euler (1707-1783), took the first great step in 

 determining the general equations of motion of a perfect 



