142 
Proceedings of the Royal Society 
2. On the Steady Motion of an Incompressible Perfect 
Fluid in Two Dimensions. By Professor Tait. 
While discussing some of Mr Smith’s applications of Maxwell’s 
ingenious idea of representing galvanic currents by the motions of 
an imaginary fluid (ante, p. 79), I was led to the present investi- 
gation. I have since found that, as was only to he expected, I 
had been anticipated in a great many of the results I obtained — 
especially by Stokes, in the Trans, of the Cambridge Phil. Soc. 
1843. Still it appears to me that I have a few novel results to 
communicate. 
If if/ — const, be the equation of a current-line, Stokes has 
shown that — 
where /is an arbitrary function. 
By the integration of this equation various singular results are 
obtained, especially as to the nature of the families of curves which 
can be lines of flow. 
The equation of lines of equal pressure is then formed, and from 
it corresponding results are derived. A curious result is obtained 
when the motion is irrotational; in which case there is a velocity- 
potential <£, and we have — 
dx 2 dy 2 ~~ 
Here the elimination of gives us — 
d 2 log P d 2 log P 
cfa; 2 + dtf = • 
The method is also applied to certain cases of motion which, though 
not steady, can be treated as if they were steady — viz., cases in 
which a given state of motion is propagated in the fluid by transla- 
tion or rotation ; so that to a spectator moving in a given manner 
in a plane parallel to the fluid, the motion appears to be steady. 
Thus, for instance, we can treat as steady motion the case of two 
p = + c 
p 
d 2 (j> 
+ P, = 0 . 
