ON HYDRAULICS AS A BRANCH OF ENGINEERING. 175 



form of veins ; and in his Traits des Machines, he states that 

 he had already given a description of veins issuing from circu- 

 lar, elliptical, triangular and square orifices, without having 

 entered into any detail respecting them, so that that part of 

 the subject was in a great measure involved in doubt. In 1829 

 a paper, entitled "Experiences sur la Forme et sur la Direction 

 des Veines et des Courans d'Eau, lances par diverses Ouvertures," 

 was read to the Academy of Sciences at Turin by M. Bidone, 

 giving an account of a series of experiments made in the years 

 1826 and 1827, in the Hydraulic Establishment of the Royal 

 University. The results of these experiments are divided into 

 five articles. The first gives a description of the apparatus 

 and mode of proceeding, and the figures obtained from veins 

 expended from rectilinear and curvilinear orifices, with salient 

 angles pierced in vertical plates, and whose perimeters are 

 formed by straight and curved lines, varying upwards of fifty 

 different ways, with variable and invariable changes, from zero 

 to twenty-two French feet: the area of water was equal to one 

 square inch. The sections of the veins were taken at different 

 distances from the aperture. The results are extremely curi- 

 ous, as illustrating the influence of pressure and divergence on 

 part of a fluid mass not in equilibrio, and may be assimilated to 

 the phsenomena presented by the undulation of streams of 

 light. The author contents himself with stating the results, 

 which are further illustrated by diagrams. 



In a second paper, read to the Accademia delle Scienze in 

 April following of the same year (1829), M. Bidone enters into 

 a theoretical consideration of his experiments, in which he re- 

 presents the greatest conti'action of the fluid vein to take place 

 at a distance not exceeding the greatest diameter of the orifice, 

 whatever be the shape ; from which it results that the expres- 

 sion for the expense of the orifice is equal to the sum of the 

 product of each superficial element multiplied by the velocity 

 of the fluid vein ; and as it was determined by experiment 

 that the area of the vena contracta was from 0"60 to 0*62 of 

 the area of the orifice, it follows that this coefficient of con- 

 traction, multiplied by the velocity due to the charge, repre- 

 sents the expenditure. 



M. Bidone considers the case of a fluid vein reduced to a 

 state of permanence, and expended from a very small orifice, 

 as compared with the sections of the containing vessel, accord- 

 ing to the theory of Euler ; and finds that the magnitude of the 

 section of the contracted vein does not depend upon the velocity 

 of the component filaments, but solely on their direction, a re- 

 sult conformable to experiment. 



