HALL. — THERMAL AND ELECTRICAL EFFECTS IN SOFT IRON. 607 



above the mean temperature of the inner guard-ring, all relating to the 

 region between the cross-sections a and e, 



0.0848 -r- S.32 = 0.0134 calorie. 



The difference between this estimated outflow, per degree difference 

 of temperature in the neighborhood of 218° C, and the corresponding 

 outflow in the neighborhood of 100° C, 0.0184 and O.Olol, respect- 

 ively, is too large, apparently, to be readily attributed to mere errors 

 of measurement. On the other hand, one may well doubt whether the 

 coefficient of thermal conductivity of a packing of asbestos fibre really 

 increases by 33 per cent in the rise of temperature from 100° to 218°, 

 though we are unacquainted with any experiments upon this point 

 except our own. We have already stated that the fibre was loosely 

 packed, 1 gram, in, let us say, 15 cu. cm. It is easy to make the 

 density of such packing several times as great as this, and the ques- 

 tion has arisen whether there may not have been considerable currents 

 of air through our loosely placed fibre and whether the increase in 

 facility of lateral heat transmission with rise of temperature may not 

 have been due to the part played by such air currents. In this state 

 of doubt one naturally asks whether the coefficient of lateral outflow of 

 heat at either temperature is consistent with the results obtained by 

 previous experimenters on the thermal conductivity of fibrous materials. 



Assuming that our lateral outflow is due to conduction proper, we 

 can make from our data a tolerable estimate of the coefficient of thermal 

 conductivity of the packing. Thus, examining Figure 2, we see that 

 no heat should flow across the vertical between Gi and Gn. Accord- 

 ingly, a gives heat to the half-ring Gi Gi6 Gn only. The length of 

 this arc, along the centres of the guard-ring bars, is approximately 

 7 TT cm., 22 cm. It is evident that a, with a given difference of tem- 

 perature between it and the guard-ring, sends less heat to this arc 

 than it would send to the same length of arc bent to a radius equal to 

 the distance, about 4 cm., from the centre of a to the centre of the 

 nearest guard-ring bar, Gie. On the other hand, it is evident that a 

 gives out more heat to the half-ring in the actual case than it would 

 give to the same half-ring, with the same difference of temperature, if 

 it were placed at the centre of curvature of the ring, the radius of which 

 is 7 cm. We can, therefore, make no very large mistake in assuming 

 that, for a given difference of temperature, the lateral outflow of heat 

 from a is equal to that which would occur between a and a guard-ring 

 arc 22 cm. long, having a radius of curvature equal to i (4-f- 7) cm., 

 a being at the centre of curvature. A point of some doubt just here 

 is, how large a part of the circumference of a we should consider as 



