of Thermo-electric Phenomena, 529 



the two are the same in homogeneous material, the experi- 

 mental value of the resistance is probably too great in the case 

 of crystalline metals like antimony and bismuth, or even per- 

 haps iron. And as regards mercury, its molecular motions 

 cannot be all oscillatory like those assumed in the hypothesis, 

 but must have much of their energy in the form of whatever 

 motion is characteristic of liquidity. 



§ 24. Now the researches of Dulong and Petit have indi- 

 cated the true law of cooling to be 



0=p(* e -l), (3) 



where p is a constant depending on the nature of the sub- 

 stance, and a is a number usually stated to apply to all sub- 

 stances and to be equal to 1*0077. As, however, this is only 

 an experimental number, I shall take the liberty of assuming 

 that in general both p and a vary with the substance, but that 

 the value of a is always very close to unity. 



Equations (2) and (3) combined give us the law according 

 to which the electrical resistance of a body varies with the ab- 

 solute temperature, viz.: — 



Jmp a 9 — \ ... 



r= . s- (4) 



I shall denote the constant — — by the letter h for shortness, 

 and shall occasionally use (4) in the expanded form — 



r=« + 00 + 70 8 + ».., .... (5) 

 where 



« = Aloga, M^' y=h^§^,&c. 



The series is very converging, because a is so near 1 ; thus if 

 a = 1*0077, log e a= *0076; and the first two terms will in many 

 cases suffice. 



Digression. 



§ 25. In Balfour Stewart's * Heat,' page 207, it is shown 

 from the theory of exchanges that the internal radiative power 

 of a transparent substance is proportional to the square of its 

 index of refraction, because a small cone of rays issuing nor- 

 mally from some small area inside the body will spread out at 

 the surface into a cone of larger angle, the ratio between the two 

 solid angles being obviously fj?, so that to maintain equilibrium of 

 temperature the internal radiative power must be /j? times that 

 of the surface of the enclosure exposed to the plane surface of 

 the body. There is no ground for denying an index of refrac- 



PJdl. Mag. S. 5. No. 14. Suppl. Vol. 2. 2 M 



