282 
MR. Gr. T. WALKER ON REPULSION AND ROTATION 
there will be no couple acting on the cylinder : as a particular case, if the external 
field have the same phase throughout there will be no couple. 
The next case considered is that of two long cylindrical shells in the presence of an 
alternating current in a long parallel wire. 
If the current in the wire be I cos pt, and cr, <x' be the resistances (across unit length 
of the surface) and a, a' the radii of the shells, while p, p are their distances from 
the wire, d from one another, and c of the wire from the plane containing the two 
axes, then the couple on the a shell is in the direction represented in fig. 3, of amount 
where 
Fig. 3. 
v 87r 2 pWaV 3 c I" 1 4 ft (p' 2 - ft) 
p 2 p'*d L d iT>i D,p 2 ft + 
D,, EE 47 ftcdpr + crbr, 
D' n = 47ra'Y + 
In this case the couples on the two shells are, considering only the most important 
term, of equal magnitudes and of opposite signs. 
If a second wire conveying a current of strength — I cos 'pt be laid close to that 
already present, we obtain in effect a filament periodically magnetised in a direction 
Fig. 4. 
perpendicular to its length. Let this direction make a with the plane containing the 
axes. Then, if QQ' (the line of length d ) subtend (f> at the magnet M, the couple on 
the a shell is 
