156 CONFOEMAL EEPRESENTATION FROM A MECHANICAL POINT OF VIE
i
where Fv Fz denote arbitrary functions. Another form of (9) is
For an individual particle jFa (£ + «?) is constant, say a+ib. The e of the stream-line followed by this particle is obtained by equating t imaginary part of F3 (x + iy),
As an example of (9), suppose that
x + iy ~ c sin {it + £ + irj], .......................
so that x = c sin f . cosh (17 + 1), y = c cos £ . sinh (?? 4- £), ........
whence on elimination of t we obtain (4) as the equation of the strean:
It is scarcely necessary to remark that the law of flow along the lines is entirely different from that with which we are familiar in the incompressible liquids. In the latter case the motion is rapid at an where neighbouring stream-lines approach one another closely. Hero, contrary, the motion is exceptionally slow at such a place.<?