Galvanism, from Gaivani to Ohm. 89 



ponderomotive forces are exerted on such currents by magnets. 

 To the science which deals with the mutual action of currents 

 he gave the name electro-dynamics ;* and he showed that the 

 action obeys the following laws : 



(1) The effect of a current is reversed when the direction of 

 the current is reversed. 



(2) The effect of a current flowing in a circuit twisted into 

 small sinuosities is the same as if the circuit were smoothed out. 



(3) The force exerted by a closed, circuit on an element of 

 another circuit is at right angles to the latter. 



(4) The force between two elements of circuits is unaffected 

 when all linear dimensions are increased proportionately, the 

 current-strengths remaining unaltered. 



From these data, together with his assumption that the force 

 between two elements of circuits acts along the line joining them, 

 Ampere obtained an expression of this force : the deduction may 

 be made in the following way : 



Let ds, ds' be the elements, r the line joining them, and i, i' 

 the current-strengths. From (2) we see that the effect of ds on 

 ds' is the vector sum of the effects of dx, dy, dz on ds', where 

 these are the three components of ds: so the required force 

 must be of the form 



r x a scalar quantity which is linear and homogeneous in ds ; 

 and it must similarly be linear and homogeneous in ds' ; so 

 using (1), we see that the force must be of the form 



F = ill | (ds . ds') 4> (r) + (ds . r) (ds'. r) i/, (r)} , 

 where < and i// denote undetermined functions of r. 



From (4) it follows that when ds, ds', r are all multiplied by 

 the same number, F is unaffected : this shows that 



4>(r) = - and f (r) = - , 



where A and B denote constants. Thus we have 



, M(ds.ds') (ds.r)(ds'. r)) 



F = n r \ + - - ; 



( r 3 r 6 ) 



*. Loc. cit., p. 298. 



