* Ramsey, , Hydromechanics, Part ii, p. 190;Google ScholarLamb, , Hydrodynamics, p. 156.Google Scholar In his recent book Theoretical hydrodynamics (London, 1938), p. 475,Google Scholar Milne-Thomson does not repeat the error.

* There is difficulty with the coefficients I ₁, J ₂, K ₃. I can prove them variable but not independently of one another, vide infra.

† Baltimore Lectures (Cambridge, 1904), p. 584.Google Scholar

* The factor D ² may suggest that the general solution of the differential equations will contain terms proportional to t. If it did then the motion would be unstable. Actually all the first minors of the determinant have a factor D and the determinant has two invariant factors equal to D, not one equal to D ². Consequently the general solution of (7) has constant terms involving two independent arbitrary constants, but no terms proportional to t.

* The transformation would be illegitimate if we were looking for factors D in the minors, but it is legitimate for our purpose.

* For general values of the constants there is no exception to this rule since two conditions have to be satisfied for a real quadric to become a quadric of revolution. These two conditions will not in general be satisfied for the same value of w. Cf. Lamb, H., Proc. London Math. Soc. 8 (1877), 273.Google Scholar

* Note also that is invariant.

* The three sheets of the manifold of screw motions give, for a real value of w, three mutually perpendicular directions. The three sheets cannot therefore wind into one another for any real value of w; hence w itself, not a root of w, is a suitable parameter on each sheet. The same applies near w = ∞, and hence infinitesimals of the first order are of order 1/w.

* This form holds in particular if a rotation through 180° about any one of the coordinate axes turns the solid into itself.

† This form holds in particular if the solid is symmetrical with respect to each of the coordinate planes.