The study of aerodynamics is still largely empirical, and there seems little hope at present that the gap between theory and practice will be sensibly diminished by any means at present known to the applied mathematician. Yet the light that would, in all likelihood, be thrown on a number of practical problems by the complete solution of even a single case of turbulent motion would be very great. Of the problems that can be attempted, that of the flow of a fluid past a circular cylinder is likely to prove the least intractable.