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XXX.—Thermal and Electric Conductivity

Published online by Cambridge University Press:  14 March 2016

Tait
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Extract

The following paper contains the results of an inquiry which has occupied me at intervals for somewhere about ten years. It was carried out in part at the expense of the British Association, and I have already reported results to that body in 1869 and 1871. But these provisional reports referred to very short ranges of temperature only, and the experiments were made with faulty thermometers, for which I had not the corrections which had been carefully determined by Welsh at Kew.

The inquiry arose from my desire to extend to other metals the very beautiful and original method which Principal Forbes devised, and which the state of his health prevented him from applying to any substance but iron. Forbes' experiments gave a result so very remarkable, and (as it seemed to me) so theoretically suggestive, that I wished to extend them to other pure metals, and also, in one or two cases at least, to alloys.

I believe that Principal Forbes had at least two reasons for undertaking his investigations:—(1.) When he commenced his inquiry, there was no really accurate or trustworthy determination of the absolute conductivity of any body whatever for heat. (2.) FORBES had himself, in 1833 and subsequent years, pointed out a very remarkable analogy between the conducting powers of metals for electricity and for heat, and had shown that these were almost precisely proportional to one another—that is to say, that the list of the average relative conductivities of different metals for electricity differed, from that of their relative conductivities with regard to heat, certainly not more than did the several electric lists furnished by different experimenters, and certainly less than the corresponding thermal lists. Hence it was natural to suppose that temperature might have a marked effect on thermal conductivity, as it was known to have such an effect on electric conductivity.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 28 , Issue 3 , 1878 , pp. 717 - 740
Copyright
Copyright © Royal Society of Edinburgh 1877

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References

page 717 note * Proc. R S. E., i. 5.

page 717 note † Report B. A., 1852.

page 718 note * Trans. R S. E., 1860-61, and 1864-5.

page 719 note * Proc. R S., 1857 (June 15).

page 719 note † Pogg. Ann., 1862. Phil. Mag., 1863, i.

page 720 note * Proc. R, S. E.

page 720 note † Pogg. Ann., Band 118, 1863.

page 721 note * One of these interpolation methods is so easily applied, and (in consequence of the usual nature of the statical curves) gives results so fairly approximate, that it must be mentioned here as of great use if only in checking the results of the more complex calculations.

Let v 1, v 2, v 3, v 4, be the observed temperatures shown by the four thermometers, placed at intervals of three inches on the long bar. Let w be the number of degrees lost per minute by the thermometer in the short bar, when its temperature-excess above the air is nearly that of ½(v 2+v 3). Then the conductivity at the temperature ½(v 2 + v 3), in terms of the units employed in § 15 below, is very approximately

[This formula assumes third differences of v 1 to vanish.] With a single bar of 20 inches, or so, in length (with four or more holes three inches apart), to be used alternately for the statical and for the dynamical experiment (in the former with its free end artificially cooled), I believe that very fair determinations of thermal conductivity may be made in a few hours by the use of the above formula. Had I known this ten years ago I should not have undertaken the repetition and extension of Forbes' experiments under conditions exactly similar to his. But, on the other hand, had I not undertaken this work, I should probably not have fallen upon this simple method.

I believe that it may be found applicable even to stout wires or rods, the temperatures being observed by a thermo-electric process. Thus these determinations may be made for very rare metals, and also for substances of very low conductivity. I hope, with the assistance of a party of my Laboratory students, to get a large number of metals examined by this method during next winter and summer sessions.

page 723 note * Extract from a letter, Dr Stewart to Prof. Tait.

“Kew Observatory, 8th December 1868. …. “We have come to the conclusion that each instrument ought to go down as low as the freezing point.

“It is possible, no doubt, starting with an instrument that includes the freezing point in order to determine the graduation constants, and afterwards taking out some mercury, to produce instruments that begin to register only at high temperatures. But there is an element of uncertainty introduced in taking out the mercury, which may not only cause a constant error, but an error of scale value.

page 726 note * Jan. 13, 1879. In spite of the contents of § 11* now added, this is nearly true of my experiments, for the highest of the thermometer readings in the cooling bars were not used in the calculations.

page 730 note * It is interesting, however, to know that it can be transformed into

which differs only by the factor ϵф on the right from the equation for constant conductivity.