THE SMITHSONIAN INSTITUTION. 365 



tity of copper wire is limited by the amount of money to be expended 

 in its construction. 



Suppose the resistance of a copper wire of a given length and thick- 

 ness, making n coils, to be equal to I, or the resistance of the electro- 

 motor ; tlien the force of the current is 



g_ E _ E 



and this acting in n coils on the magnetic needles in soft iron, we can 

 represent its effect by 



■M. = n~^ (1) 



If we make the wire m times as long, the mass remaining the same, 

 its section will be m times less, and then the resistance wr times 

 greater ; hence the force of the current is now 



Q/ E E 



but of this length of wire, m times as many coils can be made as be- 

 fore ; thus, the magnetic effect is now 



Wz=m.n. =« — (2) 



\ m/ 



But the value of M, as just proved, is always greater than the value 

 of M'. Hence loitli a given mass of ivire, a maximum of magnetic 

 effect is obtained by giving to the wire such a thickness and length that 

 the resistance in the coils is equal to that of the elements. 



For instance, if we have eight pounds of copper wire for construct- 

 ing an electro-magnet, to be excited by one of Daniell's elements, 

 described in section 9, how thick must the wire be made ? 



The resistance of this element is equal to the resistance of 11.1 

 metres of the normal wire. The normal wire has a section of 0.785 

 of a square millimetre, or 0.00785 of a square centimetre ; thus, a 

 length of 11.1 metres or 1,110 centimetres has a cubic contents of 8.71 

 cubic centimetres. The specific weight of the copper to be drawn to 

 wire is 8.88 ; hence the weight of the normal wire, which has the 

 same resistance to conduction as the element, is 8.71 X 8.88 = 77.34 

 grammes. 



But the mass of wire which we have at our disposal does not weigh 

 77.34 grammes, but eight pounds, or 4,000 grammes ; so that we have 

 ff ^-= 51.7 times as great a mass as that of the normal wire which 

 fulfils the condition. 



If, instead of a wire of given diameter and length, one of three 

 times the diameter be taken, its section is 3 X 3 = 9 times greater, and 

 a nine-fold length must be given to it, that it may retain its resistance 

 to conduction unchanged ; the volume of the wire is now 81 z=. 3* 

 times as great as it was before. A wire n times as thick must have a 

 lengtli /i^ as great, and consequently n* greater mass, if its resistance 

 is to remain unchanged. 



