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When 0 is the radius of the disc, then the whole resistance 
front and back = zrpv"b". 
Ex. 2. To find the whole resistance experienced by a 
sphere of a radius b moving in a fluid with a relative velo- 
city v. 
We find the resistance =5 mpv'b’, which is half that found 
for a plane circular dise in the previous example considered as a 
great circle of the sphere. This resistance experienced by a 
sphere is, however, the double of that found in the treatises on 
hydrodynamics hitherto published. 
Ex. 3. To find the resistance experienced by a hemisphere 
of a radius 6 moving in a fluid in a direction perpendicular 
to its plane surface, but with either the plane or curved sur- 
face first. 
We find the resistance = = axpv'd® in each case, which is half 
as much again as that experienced by the whole sphere. 
Ex. 4. To find the resistance experienced by a spheroid 
moving in the direction of its axis of revolution im a fluid. 
Let a be the axis about which the revolution takes place in 
the formation of the surface, and 6 the other axis of the gene- 
rating ellipse. 
Then the resistance 
b* a” a” 
= =p op ap log. i = i} ; 
from which the results of Examples 1 and 2 as particular cases 
may be obtained by expansions for prolate and oblate spheroids. 
Ex. 5. To find the resistance experienced by a segment 
of a right cylinder on an elliptic base moving in a fluid in 
the direction of the major axis of the ellipse. 
If a be the axis of the ellipse in the direction of the motion, 
