148. TABLE OF ENERGIES AND INERTIA COEFFICIENTS 



a, b, c Radius of a circle or semiaxis of an ellipse or ellipsoid, 



or half-width or width of a lamina 



e Ellipticity 



k Coefficient of inertia, a dimensionless constant 



apparent increase in mass 



In translation, k = 



mass of displaced fluid 



yfc = 



2 T 



2T, 



M'U^ M[V'^ 



apparent increase in moment of inertia 



In rotation, k = -— ; — 



moment of inertia of displaced fluid 



k = 



2T 



2T, 



Moment of inertia of displaced fluid rotating as a rigid body 

 about the assumed axis of rotation 



J{ 



See under T ^ 



M' 



Mass of fluid displaced by body 



M[ 



See under T^ 



T 



Kinetic energy of fluid 



T,, I{, Mi: 



Values o( T, r, M' for fluid betv 



the motion and unit distance apart, in cases of two- 

 dimentional motion 



U Velocity of translation of body 



6 An angle in radians 



p Density of the fluid, in dynamical units 



• <u Angular velocity of rotation of a body, in radians per 



second. 



The fluid is assumed to surround the body and to be of infinite extent and at rest at 

 infinity, except where other conditions are indicated. In regard to units, see Sections 18, 147o 



384 



