of the Heat-conducting Power of Mercury. 483 



is certainly not desirable; nevertheless even mercury possesses 

 a galvanic conductivity the variability of which is always very 

 apparent and sufficient for the intended investigation. And, as 

 regards the second, I do not think that disturbing currents are 

 to be apprehended if a rather narrow mercury-tube be taken 

 and, of course, heated from above in a vertical position. Even 



o 



with tubes of 37 millims. diameter, Angstrom* obtained normal 

 results for the heat-conduction of mercury. So much the more 

 could I hope to see no disturbances enter in the tubes employed 

 by me, which were about 1 centim. in diameter. 



§2. 



It was, then, my intention, with such mercury-tubes, to inves- 

 tigate simultaneously electrical conduction and the conduction 

 of heat in their dependence on temperature. I give, in the fol- 

 lowing, first, the general principle of the method, which is cal- 

 culated, by one and the same experiment, to bring into the ex- 

 pression the variability of the conducting-power as well for heat 

 as for electricity. 



Let us imagine a metallic rod heated (or a pretty narrow tube 

 filled with mercury heated from above), and at the same time a 

 powerful current passed through it. After the stationary condi- 

 tion has come in, the quantities of heat generated in any cross 

 section by the double action of the heat-conduction and the cur- 

 rent must be continually given up again outwards. According 

 to this, the following differential equation is formed. Let the 

 cross section q be at the distance x from the initial point and 

 have the temperature t while the temperature of the surrounding- 

 air is 6. Let the circumference of the cross section be p, the 

 outer heat-conducting capacity h, the current-intensity i. If, 

 then, R is the galvanic resistance for 0°, I put for the resistance 

 at t° R (1 -f ftt). This form of the variability of R with the tem- 

 perature is quite sufficient for our present purpose ; and more- 

 over, for mercury especially, it is in harmony with the experi- 

 ments of most experimenters. 



For the heat-conduction I likewise introduce the specific re- 

 sistance at 0°, and put that which holds for t° equal to r{\ -f ut). 

 Then, for the unit of time, 



_jl . g + !^i! R( i +/3/)=/7/ , (/ _0 ) . 



r{\-\-ut) dx 2 q K .. < 



If therein we put 



. const i 2 Rr , ,, phr 

 A = Q and 13 = - — > 



9 9 



* Pogg. Ann. vol. oxxiii. p. (JoS. 

 2 1 2 



