10 
infinity as if it implied a definite state or time, rather than 
the limiting value of a process which must be defined 
precisely in each case; unless this is done the problem is 
really indeterminate. From this point of view, Maxwell’s 
statement seems inadequate, in that it accepts the forward 
displacement as definitely proved; on the other hand it 
points to a root of the matter, 
namely, the conditions at infinity. 
Leaving this till later, we discuss 
the previous solution as it stands, 
first stating the possibilities in 
general terms and then treating 
them analytically. 
In Fig. 5, O is the centre of the 
cylinder; the curved line represents 
the particles which were abreast of 
the cylinder when the centre was 
/ at O!. The flow of fluid backwards 
l is given by the difference between 
the areas behind and in front of the 
i Figure 5, line AO'B. As O!O increases, the 
| 
3 
points C move outwards along the 
line AO'B; the dotted curve, 
which is entirely in front of AO'B, 
shows the ultimate position of the same particles, according 
to the paths in Fig. 4, when O!0 becomes infinite. 
(A) Let 2, y be co-ordinates of any point P on the line 
AO'B referred to the centre O. If we fix any value of y, 
however large, we can make P be within the range O10 by 
making 2 large enough. This is the argument which leads 
to a permanent forward displacement. It clearly lays more 
stress on the infinity of extent of liquid fore and aft of the 
cylinder. 
(B) On the other hand, if we fix z, no matter how large, 
we can make the point P be beyond C on the line O!A by 
making y large enough. By giving more weight to the 
infinity of liquid abreast of the cylinder, this argument 
89 
