4G0 FOURTH RKPORT — 1834. 



in the first part of this paper. As we before stated, M. Proiiy 

 confined himself in his great work on Hydraulic Architecture to 

 the consideration of the dynamics of fluids ; but in the year 

 1801, having been called upon by the Ecole des Pouts et Chaus- 

 sees to report on the produce of the streams which were re- 

 quired to supply the summit level of the canal that joins the 

 rivers Somme and Scheldt, M. Prony investigated the subject 

 with his usual sagacity, and the result was the publication of his 

 work, in the year 1802, on the measurement of streams*. His 

 method was to inclose a certain portion of the channel of the 

 stream by means of dams thrown across it at certain distances 

 from each other; and, by noting the time required to fill or empty 

 the space so inclosed, the volume of water which passed through 

 a given section in a given time was easily ascertained. M. Prony, 

 however, does not deny the superiority of the system (where 

 practicable) of ascertaining the expenditure of streams by means 

 of recipients of any given capacity ; but it is in his Physico- 

 Mathematical researches f that he developes his general prin- 

 ciples of fluids. 



The principal results are : 



1st, That a fluid, such as water, which runs through a pipe 

 or canal of a sufficient length to establish an equilibrium, ex- 

 periences resistances which are equal to the force of gravity, 

 and produce uniformity in the motion of the stream ; 



2ndly, That although the experiments of Amontons and 

 Coulomb on the friction of solids give the results in the direct 

 ratio of the pressure, the experiments of Dubuat, Dobenheim 

 and Benezeck on the friction of fluids show that pressure has 

 little or no efffect ; 



3rdly, That in every transverse section the different molecules 

 taken perpendicularly to the section move with different velo- 

 cities ; but that there is a point where the velocity is a maximum, 

 as in the centre of a pipe or at the surface of an open canal, 

 and that from these centres there is a progressive diminution of 

 velocity towards the periphery ; 



4thly, That besides the maximum velocity, there exists a 

 minimum and meau velocity, by which the motion of the general 

 mass is regulated; 



5thly, That when the fluid runs through a pipe or channel 

 capable of being wetted, a film or bed of fluid adheres to the 

 interior of the pipe or channel, which is the true bed of the fluid 

 mass in motion ; 



• Jaugeage des Eaux Courantes : par M. Prony. Paris 1802. 

 t Recherches Physico-Mathematiques sur la Theorie des Eaux Courantes : 

 par M. Prony. Paris 1801. 



