RECENT PROGRESS IN PHYSICS. 439 



For ;i = 0, this equation gives ^ = 0.78 ; for X = 49 it gives h = 

 0.476 ; for X = 147.7, h =z 0.267, &c., all of which values correspond 

 remarkably well with the above observations, so that we can consider 

 this equation as the expression of the actual relation between h and X. 



Dividing the numerator and denominator of this equation by 0.013, 

 we get 



7 _ 60 



'* - 76.9 + r 



In this form we find the greatest resemblance to the law of Ohm, 

 The discharge in these experiments had, in addition to the variable 

 length A of the interposed copper wire, to traverse the invariable part 

 of the circuit, in which the platinum wire of the thermometer was 

 comprised. 



Each increase of length in the circuit resists the rise of tempera- 

 ture, which is, in fact, inversely proportional to the length of the 

 circuit, as shown by the formula, if we assume that the constant part 

 of the cii-cuit acts like a piece of copper wire 76.9 feet long and 

 having the thickness of the interposed wire. 



The above value of h represents only a special case ; it may be gen- 

 eralized thus : 



h = 



t 



1 s 



- -\- k L +A 



& 



a 1 - , 



by substituting a' for v' and L for .-' Thus we have the same 



law here for the development of heat as for the magnetic effect of the 

 galvanic battery. 



Evidently L liere expresses the reduced length of the circuit ; that 

 is, it indicates how long a platinum wire should be, of the same 

 thickness as the interposed wire whose length is I, to give the same 

 value of retardation as the whole circuit, with the exception of the 

 platinum wire in the discharger having the length X. 



This last transformation, by means of which Riess' law of heating 

 gives a form perfectly similar to Ohm's law, Itiess has not presented 

 with his formula. In the beginning of his memoir he merely made 

 the general remark that the similarity of his results to the magnetic 

 effect of the galvanic battery was not to be overlooked, but without 

 presenting or proving it ; indeed, in his treatise he has intentionally, 

 as he says, avoided representations which might seem to refer to gal- 

 vanism, because the subject of electricity needs well founded experi- 

 ments more than theoretical disquisitions and analogies. 



Equation (1) brought into the general form is as follows : 



a 

 h =: 



from which Miess draws the following conclusion: 



