38 Dr. Tyndall on the Progress of the Physical Sciences : 



II. Thicker bars. 



Brass,' 



Tin, 



Lead, 



Rose's metal, 



Bismuth. 

 The foregoing results enable us, however, to give numerical 

 expression to the relative conductivity of the various bars. If a 

 metallic rod Nvith the transverse section O and periphery 7 be 

 heated at two points above the surrounding medium, and if the 

 temperature Vq, r„ Vc^ of three different points which are separated 

 from each other and a constant interval a be determined, then, 

 according to Fourier, we have the following relation : — 



Vo + v^ -«\/*Z , «v/^ 

 q=— =e ^ m + e ^ iq, 



where / denotes the interior, and h the exterior conductivity of 

 the rod. 



\/ ^y 1 



Setting e iQ=x, we have x-\ — =q, and 



n (log^)2 



In the experiments at present under consideration, the distance 

 «, and also the exterior conductivity h, are in all cases the same. 

 Further, the cross section of the bar is a circle ; and if its thick- 



7 1 

 ness =rf, we have -^= j. If two different bars, therefore, pos- 

 sess the conductivities I and /,, the thicknesses d and d^, and the 

 values X and x■^ calculated from the observed quotients q and q^, 

 we have 



d (log.r)2 

 f 1 — < . 



It is easy to see that a very small alteration of the quotient q 

 is sufficient to cause a considerable change in the conductivity I 

 calcidatcd from it. If, for example, the quotient varies between 

 the numbers2'032 and 2-035, the calculated conductivities change 

 from 152 to 166. Since, therefore, a small error of observation 

 carries along with it a large alteration of the calculated conduc- 

 tivity, the numerical values obtained from the qvxotients in 

 question must not be considered more than approximate. The 

 curves to which we have already refei'red the reader are certainly 

 calculated to give a more correct notion of the distribution 

 throughout the different bars than the numbers derived from the 

 application of the foregoing formula. Nevertheless, as a nume- 



