Equations of Motion of a Viscous Liquid. 31 



that of the water in the reservoir, concluded that the velocity 

 of discharcfe is equal to the velocity which the water would 

 acquire by fallint^ freely through a distance the same as the 

 heif?ht of the water above the orifice. As a result of this 

 observation he obtained the 'correct relation between the 

 velocity of discharge and the head of water (1643). 



Mariotte (1620?-1684), the author of a posthumous work, 

 enti tied Trait (^ du Mou vemont des Enux et des A uires Fluides 

 (1686), made extensive use of the theorem of Torricelli. He 

 seems to have been the first to attempt to reconcile theory 

 and experiment by attributing the retardation to friction. 

 The filaments slidiiig along the surface of the pipe were sup- 

 posed to be retarded and other filaments having a greater 

 velocity than those near the surface were retarded by rub- 

 bing against the slower ones. The retardation was supposed 

 to be proportional to the distance from the axis of the pipe. 



Guglielmini, a contemporary of Mariotte, devoted himself 

 to the study of the motion of the water in rivers and canals. 

 He assumed that every particle in a vertical section moves 

 witli a velocity equal to the velocity of discharge from an 

 orifice at an equal depth belov/ the surface of the water, and 

 explained the discrepancy between theory and fact as due to 

 transverse currents caused by the irregularities in the bed of 

 the stream. Later, however, when Mariotte showed that the 

 same retardation takes place in a glass tube, where it cannot 

 be explained by cross-currents, Guglielmini accepted the ex- 

 planation of the French philosopher, but also maintained that 

 viscosity had considerable to do in retarding the motion. 



In the latter part of the seventeenth century Varignon 

 ( 1654-1722 ) gave to the Acad^mie des Sciences de Paris a very 

 natural and plausible explanation of the relation existing 

 between the velocity of discharge and the head of water. 

 Having remarked that when water fiows from a cylindrical 

 vase (vessel) through a small orifice in the bottom the water in 

 the vase moves with a very slow and sensibly uniform motion 

 for all the particles, he concluded that there is no accelera- 

 tion and that the portion of the fluid escaping each instant 

 receives all its movement from the pressure produced by the 



