52 , KESEAKCHES ON . II. 



is connected with the length of central resistance. It is now to be found how this 

 may have any influence on the results, and the following considerations are the 

 best which occurred to me on this subject, which I give only as conjectures, being 

 ready to abandon them when better shall be presented. 



As the origin of differences is connected with the length of resistances, so we are 

 led to inquire into the law of Ohm, which is connected with them, rather than to 

 suppose for the present any inexactitude in our formula or in Ampere's principles. 

 Ohm's law, as we have said, is this simple one, that the forces are in inverse ratio 

 of resistances ; against this simple enunciation no objection can be raised, but it is 

 not so when we consider the manner of estimating resistances. This is supposed 

 to be for wires of the same metal, in inverse ratio of their section and direct of 

 their length, and the experiments which I have made myself with short lengths 

 proved it to be accurate, but I did not try wires longer than a few yards. I am 

 not the first to suspect that the law of Ohm may not be accurate for great lengths 

 of wire. Marie, Davy, and several others thought so ; but I have not been able as 

 yet to see his original papers. However this may be, it is certain that, in estab- 

 lishing the law of Ohm, no consideration is made of the heat which is produced by 

 the electric current passing through wires, and which increases their resistance 

 very much. 



Since the year 1846, I made the following experiment : I rolled a platina wire 

 about 15 inches long in a spiral, and tried by the rheostat its resistance at the 

 common temperature of 16°, and I found it equivalent to 3 turns of the rheostat. 

 After this, I ignited it with a spirit-lamp in the middle, to avoid difference of tem- 

 perature at the parts of junction with the rest of the circuit, and so avoid also 

 thermo-electric currents ; the needle of the galvanometer fell immediately several 

 degrees, and 10 turns more of the rheostat were to be uncoiled from the wooden 

 cylinder to reduce it to the former position. This shows an increase of resistance 

 by heat, so that from 5 it was raised to 15 turns, that is, made three times greater. 

 It was objected that the flame could disperse the electricity, but it should be 

 remembered that dynamic electricity is not so easily dispersed as common elec- 

 tricity. To render, however, the experiment free from such an objection, I put 

 the spiral in the focus of a large burning-glass, but then also a diminution of con- 

 ductibility took place, although the wire did not appear red-hot. I met afterwards 

 with an experiment of Sir Humphrey Davy, which proves the same conclusion. 

 If a wire be raised only to a dark-red color by an electric current, and any portion 

 of it be then raised to a white heat by a spirit-lamp, the remaining part of the wire 

 loses the red heat. The explanation of this fact is very obvious : the resistance of 

 the wire is increased in that portion by the heat of the lamp, and does not allow 

 the passage free to a sufiicient quantity of electricity to make it red. So that there 

 is no question that heat diminishes the conductibihty of wires* 



It is therefore beyond controversy that heat increases the resistance of conducting 

 wires, so that the real measure of resistance in Ohm's formula for a length of wire 

 = B will he B + x,x being a quantity function of the temperature produced by 

 the current in the wire. Now from the experiments of Becquerel [Archives de 

 EledricitS, No. 8, 1843), it appears that the quantity of heat developed by a cur- 



