EECENT PEOGRESS IN PHYSICS. 407 



Ivires by a galvanic current is proportional to the square of the force 

 ')f current and to the resistance to conduction of the wire. We can, 

 herefore, put 



W =5^ Z . . , . 1.) 



ifhere W denotes the quantity of heat produced (within a given time) 



:n a wire, the resistance of which is I for the strength of current s. 



We may now consider W the quantity of heat which must be produced 

 lin a given time in the wire in order to make it red hot. If this 

 mire be replaced by one of the same metal and of equal length, but n 

 [times the diameter, its surface will also be n times as great, and this 



surface gives to the surrounding air — cceteris paribus — n times as 

 'much heat, and therefore n times as much heat, viz: w W, must be 

 'evolved in the thicker wire in order to produce the same appearance of 

 [red heat. But the resistance to conductions of the wire of n times 



igreater diameter is —7. Denoting by &' the strength of current 



jwhich makes it red hot, we obtain the equation : 



w W = 6'2 -4 . . . . 



n- 

 I therefore, W =- s'^ A 2) 



and by combining the equations 1) and 2) 

 s'- = n^ s^ 

 or s' = s V^-' 3). 



Thus, according to this reasoning, a current of 2.83 and 5.19 times 

 the strength should be necessary in order to make red hot, wires, the 

 diameter of which is twice or three times as great, while, according 

 to my observations, a two and three times stronger current proves suf- 

 ficient ; in short, instead of equation 3), according to my observations, 

 that of s' = w s holds good. The deviations are far too considerable 

 to allow of the supposition that they proceed from errors of obser- 

 vation. 



How this difference is to be accounted for I am at present unable to 

 decide. It is, indeed, conceivable that with thicker wires and an equal 

 strength of current the outermost stratum reaches so low a tem- 

 perature that the loss of heat is not greater than from thin wires, but 

 that towards the interior the temperature increases so rapidly that 

 the outer colder strata have no perceptible influence upon the appear- 

 ance of the wire. Small differences, too, are lost by the defective esti- 

 mation of ignition, and it is therefore to be expected that deviations 

 from the above law relating to the thickness will be found, when the 

 diameter is more varied than in these experiments. I intend to con- 

 tinue the investigation of this subject. 



The laws of ignition by the galvanic battery and by the discharge 

 of the Leyden jar differ entirely. While the strength of current must 

 be increased in equal, or at least nearly equal proportions to the 

 diameter, the charge in the Leyden jar has to be augmented in pro- 

 portion to the fourth power of it, if the degree of ignition is to be 



