momentum transfer tensor. As an application the equation of steady motion under no 

 body forces can be written [1] 



V • [* - P (q;q)] = 0, (1) 



where 



$ = - pi - % M (V • q)I + fx(V;q + g;V) (2) 



is the stress tensor, I being the idemfactor or unit 2-tensor. 



From this form of the equation of motion, by integration over a sphere of large 

 radius, an expression for the force on a moving solid is readily obtained. By applying 

 Oseen's approximation at a distance we next analyse this force into a lift and a resist- 

 ance or drag. The resistance is of particular interest since its expression is VF where 

 V is the velocity of the body and F is an inflow of liquid into the sphere, predominantly 

 an inflow into the wake behind the body. Moreover the result is of an asymptotic 

 character improving in accuracy as the radius of the sphere is increased. The two- 

 dimensional form of this result was obtained by Filon [2] 30 years ago. 



Tensor expression also pinpoints the Lagrangian form of the equation of 

 motion [3] 



d;r / dh- \ 1 dp 



__. F + = o, (3) 



dr \dV ) p dr 



where r is the position vector at time t of the particle originally at r . The equation 

 of continuity is 



P ( — ) = Po, (4) 



where the notation indicates the third scalar invariant of the tensor derivative. 

 Integration from to / leads directly to Weber's transformation 



d;r d x 



— • q - q<> = , (5) 



where 



C l i fdv ) 



F = - VG. (6) 



The Lagrangian form of the equation of motion has been applied to the one- 

 dimensional motion of a gas and more recently to free surface problems which I shall 

 mention later. 



The point that I want to make here is that the Lagrangian form is not quite so 

 repulsive as the three equations which result from its expression in coordinates would 

 seem to indicate. In the hydrodynamic case we have p zz p and a consequent simpli- 

 fication. The equation, in my opinion, should repay further study. 



The two great weapons of general fluid mechanics are the theorems of Gauss 

 and Stokes [4] and their vector forms are suggestive : 



JdS o X = /V ° Xdr, jdC ° X = J(dS A V) o A', (7) 



-St C S 



where, in the first the closed surface S encloses the region t, and in the second the 

 diaphragm S spans the closed curve C. Here the small circle indicates scalar, vector 

 or dyadic multiplication and X is a general function of position, scalar, vector or tensor. 



