metallk Condwtors, and their Resistance to Electric Currents. 1 7 



pressed by equating to cypher the differential equation, whicli expresses the 

 rate of coohng for a differential section of the wire in function of the time 

 Calhng ^ the distance of a point from the extremity of the wire, y the excess of 

 Its temperature above the surrounding medium, and /(^), /(y), the heatin<. 

 power of the current, and that cooling one which depends on its surface and on 

 the surroundmg media, the differential equation becomes 



= H.fiy)-I.fiy).^, 



The integral of which will determine y the temperature at^r. 



The heating power of a given voltaic current is known to be proportional to 

 the resistance which it overcomes ; but in all the experiments which have es- 

 tabhshed these laws, the change of resistance which I have been considering, was 

 overlooked, because the conductors were kept at a comparatively low tempe- 

 rature. It might, therefore, be a question, whether the resistance to be used 

 IS the intrmsic (that at a given temperature) or that increased by heat It is 

 easily proved to be the latter by means of the apparatus (fig. 3) A is a 

 thin jar, in whose neck are cemented copper 

 wires terminating in the binding screws C, C. 

 Their other ends are connected by platinum 

 wire,W, of ^V inch diameter, and 5,4 inches 

 long. Over the wire is inverted another jar, 

 B, formed of thin tube. If water be now 



poured in, B acts as a diving-bell, and the wire 

 W is in contact with air. Passing a current 



through it, it may be intensely heated, and its 



resistance of course increased; but the heat 



which it gives off is employed in heatbg the 



glass and water by which it is surrounded, and 



can be measured by a thermometer immersed 



in the water. At low temperatures Newton's 



law of cooling is exact, and, therefore, the 



rise of the thermometer is proportional to the 



thermic power of tlie current. 

 VOL. xxn. 



Fig. 3. 



A single result will be sufficient. The jar 



