97 
1914-15.] Resistance to Motion of a Body in a Fluid. 
can then be constructed by choosing as the fixed boundary that one 
at a point on which the modulus of is zero, that is to say, where 
ctz 
the velocity is zero, so that the stream divides at this point. 
Against the kind of motion we have here supposed to exist, and to 
remain steady, may be levelled some very serious criticisms. A free surface 
is equivalent to a vortex sheet, and is therefore essentially unstable. As 
a result of any slight disturbance, it tends to roll itself up at points and 
finally to break up into a series of isolated vortices (fig. 2). 
There is another objection. Behind the moving body an infinite mass 
of dead water is dragged, a state of affairs with no counterpart whatsoever 
in actual fact. The pressure in this dead-water region being constant, we 
have also lacking the suction effect which is so noticeable behind a body 
in motion. As a result, the expression for the resistance, calculated on the 
foregoing assumptions, does not agree at all closely with measurements 
obtained. 
In a paper ^ by Lord Kelvin on the formation of coreless vortices by 
the motion of a solid through an inviscid incompressible fluid, a suggestion 
was thrown out which Von Karman f has made the basis of a theory of 
the motion of a body through a fluid in the case of vanishingly small 
viscosity. Suppose the body, a cylinder, has been in steady motion from 
* Proc. Roy. Soc., Feb. 3, 1887 ; Phil. Mag., xxiii, 1887, p. 255 ; Math, and Phys. Papers, 
vol. iv, p. 149. 
t “ Fliissigkeits und Luftwiderstand,” Phys. Zeitschrift, xiii, 1912. 
VOL. XXXV. 
7 
