THE SMITHSONIAN INSTITUTION. 331 



of its simplicity. But the knowledge of the force which the appa- 

 ratus yields in a special case, with a definite quantity of contingent 

 resistance, is not sufficient for determining the effect of the apparatus 

 in all cases ; for this purpose the actual resistance of the hattery and 

 its electro-motive power must be known. We now pass to the deter- 

 mination of the actual resistance. 



The resistance, as well as the force of the current, must he reduced 

 to a definitive unit, to admit of the comparison of different experi- 

 menters. For this, also, different units have been proposed and used. 

 Many physicists assume as a unit of resistance, the resistance of a 

 copper ivire one metre long and one millimetre in diameter. This unit 

 I shall adopt. 



To determine the resistance of a battery, the force of its current^ of 

 course, must be measured, if different resistances are inserted succes- 

 sively in the circuit. 



The resistance of the inserted piece of wire must be first brought to 

 the adopted unit. The simplest way of doing this would be to use 

 only copper wire of one millimetre in diameter and of different lengths ; 

 for a piece 10, 15, 20, &c., metres long, of this normal wire^ the resist- 

 ance would be 10, 15, 20, &c. But, since it is difficult to obtain 

 wires having exactly this diameter, it must be measured accurately, 

 and the computation made how long a copper wire one millimetre in di- 

 ameter should be, which makes the same resistance. In computing the 

 actual resistance of the battery, this reduced length of wire is used. 



This section of our normal wire has a surface of 0.185 square milli- 

 metre. Since, with equal resistance the length of the wire increases 

 in proportion to its section, it is evident that a copper wire I metres 

 long, with a radius r, and section rcr-, excites the same resistance as 

 a normal wire of the length, 



-^_ Z 0.785 



in which L is the reduced length of the wire. A wire, for instance, 

 having a diameter of 0,74 millimetre, a section of 0.43 square milli- 

 metre, and a length of 6 metres, will exert the same resistance as a 



copper wire — ^ = 10.95 metres long and 1 millimetre in 



^^ 0.43 



diameter ; thus 10.95 is the reduced length of the wire used in the 

 experiment. 



From this inserted copper wire many pieces of different lengths 

 may be obtained, 5, 10, 20, &c., metres long, for similar experiments, 

 and ready at all times. Instead of longer copper wires, short pieces 

 of wire of badly conducting metals, as platinum, iron, or German sil- 

 ver, are best ; their resistance reduced to the normal wire must be de- 

 termined by experiment. Wires to about 10 metres long can be 

 ■wound suitably into coils and fixed in wooden cylinders from 2 to 3 

 inches in diameter, and corresponding lengths. Longer wires are 

 covered with silk and wound on Avooden rollers and used thus. On 

 these cylinders or rollers, the length of the wire reduced to the normal 

 ■ wire can be written so that there will be no further necessity for a re- 

 duction of the inserted wire. 



