194 Wisco7isin Academy of Sciences, Arts, and Letters. 



od of estimating the discbarge of a river by the velocity of the 

 water. In 1643, Torricelli discovered the general theory of 

 hydraulics that neglecting resistances, the velocities of fluids 

 in motion are in the sub-duplicate ratio of the pressures. He 

 also argued that the acceleration of the currents of rivers was 

 due to the slope of their surfaces, basing his conclusions upon 

 the supposed analogy between spouting fluids and rivers. Pas- 

 cal made valuable contributions to the science in his works 

 published between 1646 and 1663. A dispute having arisen 

 in 1665, among the inhabitants of the Chiana valley as to the 

 disposition of the water of a certain stream, Eome and Florence 

 assembled a scientific congress to report upon the best plan of 

 accomplishing this task. Many theoretical essays upon river 

 improvements were submitted, but these added very little to 

 what was previously known upon the subject. 



Near the close of the seventeenth century appeared the 

 work of Mariotte and Guglielmini. These authors adopting 

 the parabolic theory of rivers, of the celebrated Torricelli, 

 perfected it. According to this theory the velocity of any 

 particle of water in a river will be the same as that of a body 

 falling from a state of rest through a distance equal to that of 

 the particle below the plane of the surface of its source pro- 

 duced. As this theory is contrary to observation and was 

 adopted by so many writers it shows how theoretical was the 

 science at this period of its history. The principal writers 

 upon it being philosophers whose lives were passed in invent- 

 ing theories and deducing therefrom practical laws instead of 

 making practical observations and building upon this founda- 

 tion their theories. 



Newton in his Principia, published in 1714, discusses the 

 friction of fluids on solids and the discharge through orifices, 

 and though some of his conclusions are erroneous his contribu- 

 tions to the science are valuable. 



The Marquis Poleni first discovered that by adapting a 

 .small cylindrical tube to an orifice in a thin plate the discharge 



