ON ELECTRICAL THEORIES. 101 
finds expression for the forces along and perpendicular to a’, due to an 
infinite rectilinear current starting from a definite point. The force of 
such a current along a’ does not depend on the angle the current makes 
with the line from its end to a’, so that the effects of two such currents 
starting from the same point and flowing in opposite directions, 7.e. of a 
‘ Winkelstrom,’ will be to produce no force along a’; thus the effect of a 
‘ Winkelstrom ’ on an element of current in its own plane will be a force 
at right angles to the element. The force at right angles to a’ due toa 
rectilinear current will consist of two parts, one independent of the angle 
made by the current with the line joining its end to the element, the 
other depending upon this angle. The first part will vanish when we 
consider a ‘ Winkelstrom’; the second part only will produce any effect. 
t 
Now Grassmann says that it will much simplify the analysis, and obviously 
(since any closed circuit may be built up of ‘Winkelstréme’) lead, for 
closed circuits, to the same result as Ampére’s formula, if we suppose that 
the law of force between elements of currents is such that the only effects 
produced by a rectilinear current are those which do not vanish for a 
*Winkelstrom,’ and hence that a straight current exerts on an element of 
eurrent a force at right angles to the projection of the element on the 
plane containing the centre of the element and the rectilinear current, 
and that the magnitude of this force is 
aj ds’ 
r 
Tag 
co 5 
where 7 is the strength of the rectilinear current, j the strength of the 
