of Thermo-electric Phenomena, 531 



dition, the available energy would have a minimum (and therefore 

 a stable) distribution if the temperature fell along a logarithmic 



curve, or if — - oc#: it is therefore to be assumed that this is the 

 clx 



case. But from this it follows, since — = 0, that the thermo- 

 metric conductivity - must vary inversely as the absolute tem- 

 perature, k by itself nearly does, but not quite, (8) ; so we get 

 a law for the variation of specific heat per unit volume with 

 temperature, viz. 



a H & Art 



aa:pfcd=-'— — - (9) 



This is tolerably constant, or the curve runs almost parallel to 



the axis of 0, for ordinary ranges of temperature : it attains a 



2 

 maximum about when 6=^ — — , and it has points of inflexion 



log_.a L 



2 -*- \/2 



about when 6 = — = , the three temperatures referred to 



log a ? r 



being -196°-4, -10°«8, +174°'8 Centigrade, if the value of 

 a were 1*0077 ; but a very small change in a would obviously 

 cause great alteration in these temperatures. 



One may write a tolerably close approximation to a for ordi- 

 nary values of 6 thus : 



^"m (log a) 2 '(3 + log a)* " * * ^ 10 ^ 



I have put p into (9) with no other justification than to get rid 

 of it from k, (whose h contains it) so as to leave nothing but 

 the atomic weight m in (9), except a universal constant H, this 

 H being proportional to ma, the atomic heat. 



§ 26. In saying, as we did in § 21, that the cord remains 

 stationary under the combined oscillatory motions of the but- 

 tons, we have assumed that the friction of a button is symme- 

 trical as regards right and left ; that is, we have assumed that the 

 buttons are not notched so as to be rougher when sliding over 

 the cord one way than when sliding the other way, as an ear 

 of rye-grass would be. If this condition were not satisfied, 

 the simple to-and-fro oscillations of the buttons would confer 

 a progressive motion on the cord. Possibly the condition is not 

 satisfied in some crystalline bodies, like tourmaline : and this 

 would account for their internal polarity; for since the crystal is 

 an insulator, the cord will be displaced by the unequal friction 

 only so far as the dielectric elasticity will permit it, and the result 

 will be a state of strain inside the crystal and a difference of 

 potential between its opposite faces. In time the potentials of 



2 M2 



