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Proceedings of the Royal Society 
uniformly in a circle or spiral so as to keep at a constant distance 
from the 11 axis of the impulse,” and that the components of 
angular velocity round the three fixed rectangular axes are con¬ 
stant. 
An isotropic helicoid may he made by attaching projecting 
vanes to the surface of a globe, in proper positions; for instance, 
cutting at 45° each at the middles of the twelve quadrants of 
any three great circles, dividing the globe into eight quadrantal 
triangles. By making the globe and the vanes of light paper, a 
body is obtained rigid enough and light enough to illustrate by 
its motions through air the motions of an isotropic helipoid 
through an incompressible liquid. But curious phenomena, not 
deducible from the present investigation, will no doubt, on account 
of viscosity, be observed. 
Part II. 
Still considering only one movable rigid body, infinitely remote 
from disturbance of other rigid bodies, fixed or movable; let there 
be an aperture or apertures through it, and let there be irrotational 
circulation or circulations (§ 60 “ Vortex Motion ”) through them. 
Let £, 77 , £, be the components of the “ impulse ” at time t, parallel 
to three fixed axes, and A, p,, v its moments round these axes, 
as above, with all notation the same, we still have ( 26 “Vortex 
Motion ”) 
dP 
— = X. Ac. 
dt 
— = L + Zy - Yz, &c. 
dt * 
( 6 ) (repeated). 
But, instead of for T a quadratic function of the components of 
velocity as before, we now have 
T = E + ^{[w, u\ u 2 + . . . + 2 \u, v\uv + . . .} . . . (13). 
where E is the kinetic energy of the fluid motion when the solid 
is at rest, and A{[h, u\id + . . .} is the same quadratic as before. 
The coefficients \u ) u\, [u, v], Ac., are determinable by a transcen¬ 
dental analysis, of which the character is not at all influenced by 
the circumstance of there being apertures in the solid. And 
dT 
instead of £ = — , Ac., as above, we now have 
du 
