metaUk Conductors and their Resistance to Electric Currents. 21 



air's cooling power, which, like m, is constant, and therefore = ms. Equation 

 (3) then becomes 



mO'^ - e (rp - ms) =p, 



which, combined with fi^ = 2m0 — n, gives 



From the series in air and in vacuo already referred to, it appears that s = 

 0.2822 ; it may, therefore, be neglected, and then 



Substituting this in (4), we obtain 



, 5 + 2r0 /r/5 + 2r0x2 1 ' 



Whence it appears, that though fx and increase, e'"' is confined in narrow li- 

 mits, ranging from 0.105 to 0.268, while 6 passes from to infinity. 



Since the loss of heat must equal its production, we have me^ + sniB 

 as A C'-, or, 



e- + sO = qAC\ 



and as s is small, 6 = v^(qAC'). Hence the highest temperature attained is 



as the current, not as its square ; and also as the square root of the resistance. 



Kwe tabulate an equidistant series of 0, and compute for each the values of 



^-Mx. /"' _/ „„^ ^x (l + e""') X i/(2m) 



' 2m ~-'' u ' ~^' ^"^ assume i/= \ x V'{2m), 



the equation (6) gives 



g/, l + e-"' 



,±j" 



T = ^- 1 



e-JU) x'+Q- 



Now taking any two observed values of 7*, where A and C are known, we 

 have the ratio of the 0s ; assuming one the other is known, and the other 

 quantities can be taken from the table. A few trials of this kind show that 



