196 Wisconsiyi Academy of Sciences, Arts, and Letters. 



the first formula for mean velocity in terms of the slope and 

 dimension of cross-section. 



In 1782 was published a voluminous work of Belidor, Arch- 

 itecture Hydraulique, Paris. In 1874, M. I'Espinasse published 

 in the Memoirs of the Academy of Science, at Toulouse, two 

 papers on the expenditure of water through large orifices, and 

 on the junction and separation of rivers. 



In 1786 was published the celebrated work of M. Dubuat, 

 which is still a standard authority in the science. He pro- 

 duced a formula which is applicable to most problems respect- 

 ing the uniform motion of water. He fully illustrates its prac- 

 tical application and touches upon all the general questions of 

 interest to the hydraulic engineer. Valuable works on hy- 

 draulics were published by Bernard in 1787, by Briinings in 

 1790, by Woltmam between the years 1791 and 1799. Fabre 

 published a work on torrents in 1797. Venturi published a 

 memoir in 1798, giving the result of a series of experiments 

 upon the contraction of the fluid vein, in which he discusses, 

 among other things, the effect of eddies in rivers and shows 

 that they retard the current. 



In 1800 Coulomb published a paper in which he enunciated 

 the principle that the resistance arising from the friction be- 

 tween fluids and solids may be represented by a function 

 consisting only of two terms, being the first and second pow- 

 ers of the velocity. This is called Coulomb's law. In 180 1, 

 M. Eytelweine published a large work on hydraulics, following 

 the methods of Dubuat, which has been translated by Nichol- 

 son, and has received a very flattering notice from Dr. Young 

 in the Journal of the Royal Institute. In 1803, M. Girard 

 first applied the law of Coulomb to flowing water in open 

 channels, producing a much more simple and practical formula 

 than that of Dubuat. Some of his other articles, particularly 

 those on canals are of special importance. M. de Prony pub- 

 lished his first work on hydraulics between 1790 and 1796^ 

 his second work in 1802, and his third in 1804. These works 



