232 Mr. J. W. Peck on the Steady 



values of the emissivity 0*0003 and 0*0002 respectively. The 

 temperature difference of radiating surface and medium is 

 here supposed not to exceed a few degrees, so that the 

 Newtonian law of cooling is applicable. 



Thus for any substance to which it is proposed to apply 

 the Fourier solution there are four lengths to be taken account 

 of, viz. the semiradius (a/2), the thermal length modulus (L). 

 the geometric mean of these two, and the length of the bar (Z), 

 In experiments on a series of these substances a proper pro- 

 portioning of the bars so as to give the ratios a/2 : L, and 

 \/ ttL/2 : 1, the same for all will give the same degree of 

 approximation in all the cases. Of course it is to be noted 

 that the equations (6) above would not now be applicable, 

 innsmuch as they assume equality of radius of the bars under 

 comparison. But the modified forms are easily arrived at 

 and are not much more complicated. 



The next point is the numerical values which should be 

 assigned to these two characteristic ratios. According to 

 Lord Kelvin (Encyc. Britann. Article " Heat," § 78), for an 

 iron bar the Fourier solution may be applied with safety for 

 all radii up to 5 cms. Beyond this the radial temperature- 

 gradient would become perceptible, and therefore the solu- 

 tion inapplicable. Taking this as a basis, the characteristic 

 fraction a/2 : L is 1/224. With the refined thermoelectric 

 measure of temperature now available, this value should cer- 

 tainly not be exceeded. As to the second ratio a A*alue of 1/5 

 is sufficient ; for if the length of the rod is H\e times the 



- o 



value of v* La/2, the ratio of the cold end temperature to the 

 hot end temperature is 1/148, and therefore the end radiation 

 is negligible for all ordinary experimental methods of heating. 

 It will be seen from the above table that the first criterion 

 is satisfied for most of the metals for bars say up to 5 cms. 

 in radius, though for the metals of inferior conducting power 

 the point would become of importance with refined measure 

 or temperature. It is moreover impossible to diminish the 

 radii of the bars in the same proportion as their thermal 

 length moduli, so that the error becomes increasingly great 

 as we descend the list, and when we come to the non-metals 

 is sufficiently large to vitiate the method altogether. For 

 example, Despretz *, in the account of his experiments, states 

 that the law of the drop of temperature in geometrical pro- 

 gression is not well satisfied for lead and the inferior metals. 

 He used square bars of edge 2*4 cms., and blackened or 

 varnished the surfaces ; so that for bismuth, say (assuming 



* Ann. de Chimie et de Physique, t. xxxvi. p. 422 (1827), 



