CONDUCTIVITY. 107 



tivity is no longer independent of the pressure but falls very rapidly 

 with it. In order, then, to determine the effect of radiation they re- 

 duced the pressure far beyond this limit, so that conduction was negligible, 

 and at such low pressure convection also vanished. This was borne out 

 by the fact that the loss of heat was the same wherever the thermometer 

 was placed in the enclosure. Radiation would be the same, while con- 

 duction, if it existed, would depend on the distance of the thermometer 

 from the walls. Gas was then admitted, but only to such a pressure, 

 that while conduction was active, convection had not yet come into play. 

 The radiation effect could now be allowed for, and it was found that be- 

 tween an upper limit of 150 mm., and a lower limit of 1 mm. for air and 

 9 mm. for hydrogen, the rate of cooling was quite independent of the 

 pressure, and they assumed that, within this range, convection did not 

 exist and that conduction was constant. Their result for hydrogen was 

 seven times that for air, as Maxwell had expected, and they estimated 

 the conductivities as 



Air .... -000048 



Hydrogen . . '000341 



Todd * experimented on the heat conducted through a layer of gas 

 between two horizontal metal plates. The upper one was the base of a 

 steam chamber, and was so maintained at 100 0. The lower was main- 

 tained at a constant temperature, about 10 C., by a stream of water 

 flowing against its under surface. The amount of water flowing in any 

 time and the difference of temperature at inlet and outlet gave the heat 

 absorbed by the lower plate. This heat was partly conducted, partly 

 radiated. Convection was eliminated by having the hot plate uppermost. 

 To understand the principle of the method let us suppose that the plates 

 are of indefinitely large area to eliminate edge effects. Let Q be the heat 

 received below per sq. cm. per second. Let K be the conductivity of the gas, 

 6 the temperature difference of its two surfaces x apart, and let R be the 

 heat received by radiation per sq. cm. per second. Then Q = R + K&/X. 

 But if x be varied R is constant, so that we have (Q-R)z = K0. 

 Plotting Q against x, we have a rectangular hyperbola with Q = R as 

 asymptote, and the curve will give this, and therefore K0 and hence K. 



Todd found for air K = 0-0000571, for carbon dioxide K = 0-0000411, 

 and for nitric oxide K = 0-0000888, all at 55 C. 



The subject of conductivity is one of which the mathematical develop- 

 ment based on certain assumptions has outstripped experimental 

 verifications. Fourier, the founder of the mathematical theory, in his 

 Theorie Analytique de la Chaleur, discussed many problems, such as 

 that of the motion of heat in bars, which have been made use of by 

 Despretz and succeeding experimenters, and of the motion of heat in 

 spheres, of which we have a special case in the earth. 



The reader will find an account of the problem presented by the 

 penetration of the sun's heat into the earth in Tait's Heat, p. 218, and a 

 sketch of Fourier's theory in Maxwell's Theory of Heat, 5th ed., p. 288. 

 * Proc. Roy. Soc., A., vol. Ixxiii. p. 19, 1909. 



