Considerations on hyrodynamics

In the general theory of the motion of fluids, there are two doubly infinite systems of lines that have a fundamental importance for kinematic and dynamic studies of the motion itself. One of these systems is that of the lines of flux and the other system is the vortical lines. These two systems of lines are not, evidently, independent of each other, even if their mutual dependence is not explicit. They appear only in a very indirect way in the well-known hydrodynamic theorems. We will not speak about this question in general, but only about two cases that can be considered as extreme cases. The first is the case in which the lines of the two systems cross each other at right angles in each instant of time and in each point of the space occupied by the fluid. The second case takes place when these lines always meet at a 0 angle