CHAP, vi.] ELECTRICITY AND MAGNETISM. 315 



separate conductivities. And if we call the joint resist- 

 ance R, it follows that 



i _ i . i_ _ r' + r 

 "R r "*" r' . rr' ? 



whence R = , rr , or, in words, the joint 



resistance of a divided conductor is equal to the product 

 of the two separate resistances divided by their sum. 



Kirchhoff has given the following important laws, both of 

 them deducible from Ohm's law. 



(i. ) In any branching network of wires the algebraic sum of 

 the currents in all the wires that meet in any point is 

 zero. 



(ii.) When there are several electromotive -forces acting at 

 different points of a circuit ', the total electromotive -force 

 round the circuit is equal to the sum of the resistances 

 of its separate parts multiplied each into the strength of 

 the current that flows through it. 



354. Current Sheets. When a current enters a 

 solid conductor it no longer flows in one line but spreads 

 out and flows through the mass of the conductor. When 

 a current is led into a thin plate of conducting matter it 

 spreads out into a " current sheet " and flows through 

 the plate in directions that depend upon the form of the 

 plate and the position of the pole by which it returns to 

 the battery. Thus, if wires from the two poles of a 

 battery are brought into contact with two neighbouring 

 points A and B in the middle of a very large flat sheet 

 of tinfoil, the current flows through the foil not in one 

 straight line from A to B, but in curving " lines of flow," 

 which start out in all directions from A, and curl round to 

 meet in B, in curves very like those of the " lines offeree " 

 that run from the N.-pole to the S.-pole of a magnet 

 (Fig. 50). When the earth is used as a return wire to 

 conduct the telegraph currents (Fig. 160), a similar 

 spreading of the currents into current sheets occurs. 



