| 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
|
