90 Prof. Magnus's Hydraulic Researches. 



investigation on this subject. In his memoir entitled " Expe- 

 riments upon the forms and directions of Jets and Currents of 

 Water*/' the forms of fifty jets issuing from different openings 

 are described. The same author gives an explanation of the 

 production of their peculiar forms, which, however, has already 

 been pronounced, and I think justly so, insufficient by Poncelet 

 and Lesbrosf. Bidone asserts that one of the most interesting 

 of these phsenomena depends upon an illusion. Some observers 

 have asserted that peculiar spiral-shaped intersecting lines are 

 visible on the surfaces of jets. With respect to these lines, 

 Bidone says that the nodes and ventral segments which may be 

 observed on the jets J continually approach one another when 

 the pressure is diminished. Since the eye only momentarily 

 perceives the continual changes thus produced in the positions 

 of the glittering points, it was thought that the parts on the sur- 

 face of the jet described spirals, and that the several threads of 

 water crossed one another and passed from one side of the jet to 

 the other. It is remarkable that Bidone has overlooked the 

 conditions under which spiral-shaped lines are produced ; never- 

 theless, without kno^ving these conditions, it is impossible to 

 comprehend the complicated phsenomena which jets of liquid 

 present. Consequently, although Bidone's knowledge of the 

 forms of jets is worthy of great praise, his explanations have not 

 been accepted. My object is not to furnish a history of the 

 published researches on the forms of jets. I will only further 

 remark, that Poncelet and Lesbros have very accurately measured 

 and described the form of a jet issuing from a vertical square 

 orifice. As far as I know, this is the only exact measurement 

 of a jet. But the authors of this celebi'ated research, after reject- 

 ing the explanati«n given by Bidone, did not furnish another 

 calculated to explain the production of the remarkable forms 

 which their measurements revealed. With respect to the before- 

 mentioned spiral-shaped lines they gave no explanation, but 

 merely asserted that they cannot be illusory. 



3. In order to study the form of a water-jet, it will, I believe, 

 be found most convenient to examine first the action of two jets 

 upon one another. It may appear strange to commence with the 

 more complicated case ; nevertheless, the nature of a water-jet, 

 even when it issues from the simplest circular orifice, can easily 

 become so complicated that the phgenomena produced by the 

 action of two jets upon one another are, if not simpler, at least 

 more certain to observe. 



* Memorie delV Academie di Torino, vol. xxxiv. p. 229. 

 t Exp6-iences hydrauliques sur les lois de Vecoulement de I'eau, par MM. 

 Poncelet et Lesbros, p. 149. 

 X Memorie dell' Academie di Torino, vol. xxxiv. p. 346. 



