'158 FOURTH REPORT — 1834. 



The section on Hydrodynamics is confined to the exposition of 

 tlie ordinary motion of fluids, and the resolution of the problem 

 of the efflux of a fluid from an orifice made in the side of a pris- 

 matic vessel on the principle of the parallelism of sections. 



The discovery of the law of the i*esistances of a fluid in rela- 

 tion to the velocity, by Coulomb, paved the way to its success- 

 ful application to the case of a fluid moving in natural or artificial 

 channels by Girard ; that distinguished mathematician and en- 

 gineer was then charged with the works of the Canal de L'Ourcq. 

 The researches made by him on that subject led to the publica- 

 tion of several memoirs on the theory of running water, in one 

 of which he proposed the adoption for the value of the resist- 

 ance, of the product of a constant quantity (determined from 

 twelve experiments of Chezy and Dubuat,) by the sum of the 

 first and second powers of the velocity, from which he obtained 

 a formula applicable to every case ; that is, supposing the mass 

 of water to glide over a film of the same fluid adhering to the 

 periphery of the channel, the mass is at first retarded by the 

 viscosity of the rubbing surfaces in the proportion of the 

 velocit)'^, a second resistance arising from the asperities of the 

 channel compounded of the number and force of the impulsions 

 in a given time, and hence proportional to the square of the 

 velocity. 



The analogy supposed by M. Girard to exist between the 

 motion of water in an inclined chaiuiel, and a perfectly flexible 

 chain placed on a fixed or flexible surface, and his examination 

 of the best form for the transverse section of a channel, which 

 he finds to be the arc of a circle, are ingenious conceptions. His 

 theory of the resistances which influence the motions of water 

 was first published in the year 1804, and is remarkable for ex- 

 pressing them by a very simple function, compounded of the 

 two first powers of the mean velocity, and with more accuracy, 

 than the formula of Dubuat. Mons. Girard is also the author 

 of several interesting memoirs on the river and canal of Ourcq*, 

 the latter of which was laid out upon the funicular principle. 



On the subject of locks for navigable canals, M. Girard devotes 

 three memoirs, for the purpose of developing the advantages 

 obtahied in point of economy, by reducing the height of locks. 

 The system is explained with that simplicity and elegance which 

 characterize the writings of this author. The conclusions, how- 



• Memoires sur le Canal de L'Ourcq el la Distribution de ses Eaux, IcDeseche- 

 ment et V Assainissement de Paris et les divers Canaux navigables qui ont ete mis 

 en Execution oti projetes dans le Basin de la Seine pour I' extension du Commerce 

 de la Capitale. Tome 1 . Paris 1 830. 



