45(3 Messrs. Watson and Burbury on the Law 



tial can have no other form than 



V^Hp^efocfe' 



and, further, that there can be no potential at all unless the 

 relation between the constants a and b be 2« + & = 0, which 

 was the relation obtained by Ampere from different reasoning. 

 It thus appears again that Ampere's law leads to the correct 

 expression for the potential. 



Stefan has, further, considered the consequences of assu- 

 ming mutual action in the nature of attraction or repulsion 

 between the radial component of one, and the transverse com- 

 ponent of the other element. The radial component of ds is 

 i cos 6 ds ; the transverse component of ds' in plane of r and 

 ds is i f sin 6 cos (j> ds' . If we suppose i cos 6 ds to exert on 

 i sin 6 cos <p ds f a force tending to move it in the direction of r, 



c 

 ii f -$ cos 6' sin 6' cos <f> ds ds', 



and, in like manner, the transverse component of ds, namely 

 i sin ds, to exert on i' cos 6' ds f , the radial component of ds' , a 

 force in direction of r, 



ii' -5 sin 6 cos & ds ds' 



where c and <i;are two new constants, then Stefan shows that 

 the potential, if there be a potential, must have the same form 

 as before, and that there can be no potential unless 

 2a + b + c-2d=0, 



which, by making c=0 and d=0, includes Ampere's law as a 

 particular case. 



8. Carl Neumann, in a very elaborate memoir*, has deduced 

 the following as the attractive force between the two elemen- 

 tary currents ids, i' ds' ', viz. 



—ii' \ ~2 cos e — j cos 6 cos 6' > ds ds', 



and this without assuming that the closed circuit exerts a 

 normal force on each element of another current. 



C. Neumann, however, excludes from his consideration 

 " couple-action," whereby one element may tend to turn an- 

 other round an axis without altering its position in space. 



9. We may here add that Clausius considers that the x 



* Ueber die den Kraften electrodynamischen Ursprungs zuzuschreibenden 

 Elementargesetze : Leipzig, 1873. 



