| Art. |
Page |
| 503. His method of experimenting | 146 |
| 504. Ampère's balance | 147 |
| 505. Ampère's first experiment. Equal and opposite currents neutralize each other | 147 |
| 506. Second experiment. A crooked conductor is equivalent to a straight one carrying the same current | 148 |
| 507. Third experiment. The action of a closed current as an element of another current is perpendicular to that element | 148 |
| 508. Fourth experiment. Equal currents in systems geometrically similar produce equal forces | 149 |
| 509. In all of these experiments the acting current is a closed one | 151 |
| 510. Both circuits may, however, for mathematical purposes be conceived as consisting of elementary portions, and the action of the circuits as the resultant of the action of these elements | 151 |
| 511. Necessary form of the relations between two elementary portions of lines | 151 |
| 512. The geometrical quantities which determine their relative position | 152 |
| 513. Form of the components of their mutual action | 153 |
| 514. Resolution of these in three directions, parallel, respectively, to the line joining them and to the elements themselves | 154 |
| 515. General expression for the action of a finite current on the element of another | 154 |
| 516. Condition furnished by Ampère's third case of equilibrium | 155 |
| 517. Theory of the directrix and the determinants of electrodynamic action | 156 |
| 518. Expression of the determinants in terms of the components of the vector-potential of the current | 157 |
| 519. The part of the force which is indeterminate can be expressed as the space-variation of a potential | 157 |
| 520. Complete expression for the action between two finite currents | 158 |
| 521. Mutual potential of two closed currents | 158 |
| 522. Appropriateness of quaternions in this investigation | 158 |
| 523. Determination of the form of the functions by Ampère's fourth case of equilibrium | 159 |
| 524. The electrodynamic and electromagnetic units of currents | 159 |
| 525. Final expressions for electromagnetic force between two elements | 160 |
| 526. Four different admissible forms of the theory | 160 |
| 527. Of these Ampère's is to be preferred | 161 |
