ELEMENTARY LAWS OF CONTINUOUS CURRENTS 7 



long and one square inch in cross-section would have 

 one-tenth as much resistance as a piece of the same cross- 

 section and ten feet long; the resistance of a piece one foot 

 long and one-thousandth of a square inch in cross-section 

 would be one thousand times as great as that of the first 

 piece. 



Formula for Resistance. The variation of resistance of 

 a body with its cross-section and length is expressed by the 

 equation, 



B = (, (2) 



where Z = length of the conductor. 

 a = area of cross-section, 

 p = a constant, depending upon the material and upon 



the units in which I and a are measured. 

 R resistance in ohms. 



Generally electrical engineers measure I in feet and a 

 in circular mils, a circular mil being the area of a circle 

 one-thousandth of an inch in diameter. 



Then p is the resistance in ohms per mil-foot of the sub- 

 stance of which the conductor is made. The constant p 

 varies greatly with different metals, being lowest for silver 

 and copper; for some special alloys p may be very large. 

 A few metals have the following values for p at C. 



Copper 9.6 ohms 



Aluminum 17.5 ' ' 



Iron 58.3 " 



German silver 125.7 " 



Special alloys 450.0 " 



Wire table. It is convenient to have the resistance of 

 copper wires put in the form of a table. Such a table is 

 given here, the number of the wire being that given by the 

 Brown & Sharpe gauge. 



