Mr maxwell, ON FARADAY'S LINES OF FORCE. 4& 



Finally, he has shewn that if there be two systems of circuits similar and similarly 

 situated, the quantity of electrical current in corresponding conductors being the same, 

 the resultant forces are equal, whatever be the absolute dimensions of the systems, which 

 proves that the forces are, ceeteris paribus, inversely as the square of the distance. 



From these results it follows that the mutual action of two closed currents whose areas are 

 very small is the same as that of two elementary magnetic bars magnetized perpendicularly 

 to the plane of the currents. 



The direction of magnetization of the equivalent magnet may be predicted by remembering 

 that a current travelling round the earth from east to west as the sun appears to do, would 

 be equivalent to that magnetization which the earth actually possesses, and therefore in the 

 reverse direction to that of a magnetic needle when pointing freely. 



If a number of closed unit currents in contact exist on a surface, then at all points 

 in which two currents are in contact there will be two equal and opposite currents which 

 will produce no effect, but all round the boundary of the surface occupied by the currents 

 there will be a residual current not neutralized by any other; and therefore the result will 

 be the same as that of a single unit current round the boundary of all the currents. 



From this it appears that the external attractions of a shell uniformly magnetized 

 perpendicular to its surface are the same as those due to a current round its edge, for 

 each of the elementary currents in the former case has the same effect as an element of 

 the magnetic shell. 



If we examine the lines of magnetic force produced by a closed current, we shall find 

 that they form closed curves passing round the current and embracing it, and that the total 

 intensity of the magnetizing force all along the closed line of force depends on the quan- 

 tity of the electric current only. The number of unit lines * of magnetic force due to a 

 closed current depends on the form as well as the quantity of the current, but the number 

 of unit cells f in each complete line of force is measured simply by the number of unit 

 currents which embrace it. The unit cells in this case are portions of space in which 

 unit of magnetic quantity is produced by unity of magnetizing force. The length of a 

 cell is therefore inversely as the intensity of the magnetizing force, and its section is inversely 

 as the quantity of magnetic induction at that point. 



The whole number of cells due to a given current is therefore proportional to the strength 

 of the current multiplied by the number of lines of force which pass through it. If by 

 any change of the form of the conductors the number of cells can be increased, there will 

 be a force tending to produce that change, so that there is always a force urging a conductor 

 transverse to the lines of magnetic force, so as to cause more lines of force to pass through 

 the closed circuit of which the conductor forms a part. 



The number of cells due to two given currents is got by multiplying the number of 

 lines of inductive magnetic action which pass through each by the quantity of the currents 

 respectively. Now by (9) the number of lines which pass through the first current is the 

 sum of its own lines and those of the second current which would pass through the first if the 



• Exp. Res. (3122). See Art. (6) of this paper. t Art. (13). 



Vol. X. Paet I. 



