96 Prof. Magnus's Hydraulic Researches, 



has the greatest velocity on account of the pressure which the 

 particles exert upon each other, consequently the surface is there 

 thinnest. The velocity of the water in the direction cd decreases 

 with the distance from the place of contact, and hence, owing to 

 cohesion, the surface is thickest at such places. This effect is 

 most apparent at the edges of the surface. 



i9. The cause of this contraction at the edges is easily ex- 

 plained. If we suppose that all the particles in the same surface 

 move forward parallel to each other, and consider the effect of 

 the mutual attraction of the particles which lie in a line perpendi- 

 cular to the direction of motion ; if we further suppose that the 

 particles are separated from each other at equal distances, for 

 example, if abed . . . dppfi^ represent these particles of which a 

 and «y move at the extreme edges of the surface, then in conse- 

 quence of the attraction between a and h they will approach each 

 other, and for a similar reason h will approach c. But h cannot 

 approach c without a simultaneously approaching c, for otherwise 

 the distance between a and h would be greater than it originally 

 was. The attraction between h and c necessitates the motion of 

 the particles a and h, consequently h and c cannot approach one 

 another as much as a and h can. In a similar manner, c and d 

 cannot approach each other as much as h and c, or as a and h. 



This consideration applies equally to all the particles of a sec- 

 tion of the water surface perpendicular to the direction of trans- 

 lation, and it also holds good when the particles in such a section 

 are in immediate contact with each other, only in this case they 

 do not merely approach, but displace one another, so that the 

 section in question is thicker at the edges than in the middle. 

 This thickening of the surface often produces a sharply defined 

 cylinder. 



20. Not only the edges, but the whole water surface also is 

 made thicker and thereby smaller ; the edges approach one an- 

 other, and thus the peculiar pointed form of the surface dcf, 

 figs. 4 and 5, ensues. 



As the edges, however, possess a certain quantity of motion, 

 they either strike against one another with a corresponding force, 

 or, if owing to any circumstance they have not both remained 

 in the same plane, they pass one another and continue on their 

 separate journeys. But if the edges encounter one another cen- 

 trally, a new sui-face perpendicular to the last ensues. This 

 process may be repeated several times, as shown in fig 9. 



21. When the axes of both jets are not in the same plane, and 

 when they encounter one another partially, the surface which is 

 produced between them remains, in consequence of cohesion, 

 connected with both jets. The latter would pursue their paths, 

 and continue to recede further from each other if they were not 



