Intelligence and Miscellaneous Articles. 79 



doubtless be very mediocre, especially on account of the sparks 

 given by the commutators. We constantly employ here, as a source 

 of electricity, an excellent Gramme machine moved by steam- 

 power. This machine consumes only one horse-povi^er, and pro- 

 duces a light equal to 100 Carcel burners, quite sufficieut for all 

 lecture-experiments. — Comptes Rendus de VAcademie des Sciences, 

 May 14, 1877, tome Ixxxiv. pp. 1084, 1085. 



ON THE DISTRIBUTION OF TEMPERATURE IN THE CONDUCTING- 

 WIRE OF A GALVANIC CURRENT. BY HEINRICH STREINTZ. 

 If a galvanic current is led through a wire, the temperature of 

 the wire rises until the stationary condition enters — until, namely, 

 in every corporeal element of the wire exactly as much heat is ex- 

 cited as is carried off through the surrounding particles to the sur- 

 face and through this into the environing medium. 



Leaving out of consideration the ends of the wire, the calculation 

 is a problem of the plane. If Jc denotes the conducting-power for 

 heat, u the temperature at an}^ point of the cross section, the ex 

 pression 



represents the amount by which the heat brought to a surface- 

 element from the circumjacent elements exceeds that which is car- 

 ried away. 



According to Joule's law, the quantity excited during the same 

 time by the galvanic current is 



lui^ doc dy dt. 

 For the stationary state the sum of the two expressions must be 

 equal to nil ; hence 



du^ dht , T_ r| . J ivi^ 



dx^ dif- ' Ic ' 



As integral of the equation, we obtain 



i* = A— -r^ + Blognr. 



Since, for obvious physical reasons, B must be = 0, only A 

 remains to be determined. Given the surface- temperature r of the 

 wire, and calling its radius a, then 



M=r-^^(a2-r2) (L) 



But if for T the coefficient of the eoctemcd heat-conducting power 

 H be substituted, the condition-equation 



('}}!:) +A(^,-U)_,=o, ;.= ^, 



\drJr=a h 



is added, in which U denotes the temperature of the surrounding 

 medium, and we obtain 



u = \J+^^a+\(a^-r^) (II.) 



