permanent translation is made. The results are unsuited to reproduction here but I 

 mention one as a specimen. If r is the position vector of the centroid of the displaced 

 water relative to the centre of gravity of the body, permanent translation is impossible 

 if the body is immersed so that the plane containing the vector r and one of the 

 principal axes of the virtual mass ellipsoid is vertical but the vector r is not vertical. 



Hydrodynamics, as appears sufficiently from the little I have been able to say 

 presents many problems whose solution is to be desired. To keep in touch with the 

 literature which is published in so many parts of the world is an increasingly difficult 

 task. There is one obvious means by which knowledge could be diffused more quickly, 

 namely by a greater readiness of authors to distribute their off-prints to those who are 

 interested in the subject. Not every separatum will interest the recipient immediately, 

 but nevertheless it makes him aware of what is happening. Were it not for Mathe- 

 matical Reviews and Applied Mechanics Reviews much important work which is pub- 

 lished in various journals and in many languages from Russian to Roumanian would 

 be quite unknown. Moreover this work has often to endure a long delay before 

 appearing in print and so to that extent is old before it is born. 



I have quoted to you three pieces of work printed this year. Let me bring 

 you bang up to date by quoting a result [28] which has not yet been published. 



The equation of motion and equation of continuity of a viscous fluid, moving 

 in a conservative field of force when incompressible, and under no external force when 

 compressible, are satisfied identically by 



dx 

 p = V 2 x, pq = - V — (50) 



dt 



<f> = p(q;q) + [V - - - / + V A f A V (51) 



V qp I 



Here <£ is the stress-tensor, V = p Q, where Q is the potential of the field, ^ is an 

 arbitrary function and ■$■ is an arbitrary symmetric two-tensor. 



REFERENCES 



1. Milne-Thomson, L. M.. Theoretical Hydrodynamics, 3rd edition, Macmillan, New York 



(1956) 19.04. Cited below as M-T-H. 



2. Filon, L. N. G., "Forces on a cylinder," Proc. Royal Soc. (A) 113 (1926). 



3. M-T-H, 3.44. 



4. M-T-H, 2.60, 2.50. 



5. M-T-H, 5.01. 



6. Milne-Thomson, L. M., "Hydrodynamical Images'' Proc. Camb. Phil. Soc. 36 (1940). 



M-T-H, 6.22. 



7. M-T-H, 6.41. 



8. M-T-H, 5-43. 



9. M-T-H, 9.10. 



10. Rose, A. "On the use of a complex (quaternion) velocity potential" Comment. Mathemat. 



Helvetici 24 (1950) 135-147. 



11. Darwin, Sir Charles, Proc. Camb. Phil. Soc. 49 (1953) 342-354. 



12. M-T-H, 9.21. 



13. Bloh, E. L., Prik. Mat. Meh. 19 (1955) 353-358. 



14. Shiftman, M., Comm. Pure and Applied Math. 1 (1948) 89-99; 2 (1948) 1-11. 



15. Riabouchinsky, D., Proc. London Math. Soc. 19 (1921) 206-215. 



16. M-T-H, 12.23. 



17. Garabedian, P. R., "Mathematical theory of three-dimensional cavities and jets" Bull. 



Amer. Math. Soc. 62 (1956) 219-235. 



14 



