of immersion must be defended by means of screens (Fig. 59) from the influence of the source of heat, so that the bar beyond A may be heated by conduction of heat, and by nothing else.

By means of thermometers plunged into small holes drilled in the bar, and kept by some fluid metal in metallic contact with the bar itself, the temperature of each part of the bar was accurately ascertained. An auxiliary bar LM, hung in the room sufficiently far from the source of heat, served to determine the temperature of the room. Deducting this from the temperature of the various parts of the bar AB, the difference will represent the excess of temperature of each part of AB due to the source of heat at A, and by having a sufficient number of thermometers a curve of temperature DE may be obtained, of which the ordinate AD represents the excess of temperature at A, the ordinate CF the excess at C, and so on. At the point E, where this curve cuts the bar, there is no excess of temperature; that is to say, E and all points beyond it are virtually unaffected by the source of heat at A.

272. Now it is clear that heat is constantly flowing outwards across any section of the bar CC', but since by hypothesis all parts of this bar have attained a constant state with respect to temperature, the flow of heat across CC' does not increase the temperature of the bar beyond CC'; what then does it do? A little consideration will shew that it is all spent in radiation and convection of hot air from the heated surface of the bar beyond CC'.

If, therefore, we are able to estimate the value of this radiation and convection for each portion of the bar beyond CC', the integral of this effect will represent the flow of heat across CC', which, as we have just now seen, is entirely carried off by radiation and convection.

273. Suppose that by this means we have been able to

ascertain the flow of heat across CC'. Now let cc represent another cross section of the bar a little (but very little) further off than CC' from the source of heat, and let CF denote the temperature of the first section, and of that of the second, the difference between these two temperatures is therefore 4F, while the distance between the two sections is of; our units of temperature and length being denoted by equal lines.

Hence if we imagine the sectional area of the bar to be denoted by unity, according to Art. 270, we shall have—

Flow of heat across CC' conductivity >

=

OF

of

conduc

tivity tan Ff = conductivity x tangent of the angle denoting the downward slope of the temperature curve at the point F;

and hence

flow of heat across C C

conductivity

tan Ffo

(1)

274. In this experimental investigation it is therefore necessary to determine two things: in the first place, we must have the means of drawing a true temperature curve; and secondly, we must be able to estimate the whole loss of heat due to radiation and convection united past any section CC', since this, as we have seen, will represent the flow of heat outwards past the same section.

We have already stated how, in this investigation, the curve of temperature was determined by means of thermometers plunged into small holes in the bar, and we shall now proceed to shew how the amount of heat carried off by radiation and convection united past any given cross section CC' was determined. For this purpose a smaller but otherwise similar bar LM (Fig. 59) was heated to a temperature at least equal to the highest temperature of the bar AB. A thermometer P plunged into a small hole in

the centre of this bar gave the velocity of cooling at the various temperatures of the bar.

It is clear from what we have already said (Arts. 228, 229) that the velocity of cooling of such a bar really denotes the rate at which heat is momentarily carried off by radiation and convection united from the bar at the various temperatures of observation, and a little reflection will convince us that by making use of these observed velocities of cooling we may be able to estimate the amount of heat carried off momentarily from all portions of the similar bar AB by radiation and convection united, since we know by the curve we have drawn the temperatures of the various parts of this bar.

Having thus estimated the amount of heat carried off by convection and radiation united from the surface of the bar AB past any cross section CC', we can find at once its equivalent or the flow of heat past this same section.

Knowing therefore this flow of heat, and being able to determine by means of the curve of temperatures the tangent of the angle denoting the downward slope of the temperature curve at any point F, we are able at once from the expression (1) Art. 273 to determine the conductivity at any section CC'. 275. It will be observed that this process is entirely devoid of any theoretical assumption with regard to the laws of radiation and convection, and that it may even be employed for the purpose of finding whether the conductivity of the bar AB varies from one point to another, or whether it is constant throughout. If this be constant throughout, then the expressions for the conductivity found by the process above described for two different sections CC', GG' will be the same. On the other hand, if the conductivity be not constant, but vary with the temperature, then the expression found for one cross section CC' will be different from that found for another section GG', since the temperatures of these two sections are different.

276. It was mainly with the view of ascertaining whether the thermal conductivity of wrought iron varies with the temperature that Professor Forbes made these experiments, and we will state the result obtained in a future paragraph. In the meantime, let us state the results obtained by other observers for the comparative thermal conductivity of the

various metals.

M. Despretz was one of the first to make experiments on the subject, his instrument of research being a bar with thermometers plunged into it at different intervals from the source of heat. After him MM. Wiedemann and Franz investigated very carefully the relative conductivity of several of the most important metals. They operated with thin bars, and the temperature of these bars at the various points was ascertained by means of a thermo-electric arrangement.

Their results are embodied in the following table.

We are probably furnished in this table with very good determinations of the relative conductivity of these different metals. The same remark ought however to be made here that was made on a former occasion, when a table of the

linear dilatations of different metals was given, namely, that difference in quality makes probably a very considerable difference in conductivity; and there is reason to think that the relative conductivity of pure copper is considerably greater than that here given. This table gives however only the relative conductivity, and to complete our information we require to know the absolute conductivity of some one metal. One or two observations of absolute conductivity have been made. M. Peclet has determined the absolute conductivity of lead by finding how much heat was conveyed across a plate of this substance whose two sides were kept at unequal temperatures.

Principal Forbes, in connection with the experiments already described, has likewise determined the absolute conductivity of wrought iron. In his experiments conductivity was expressed in terms of the amount of heat as unity which is required to raise the temperature of one cubic foot of water by one degree Centigrade. It expresses the amount of heat reckoned in such units which would traverse in one minute across an area of one square foot a plate of iron one foot thick with the two surfaces maintained at temperatures differing by 1° Centigrade. According to these experiments, the conductivity at o° Centigrade of one of his bars was .01337, while that of another bar was only .00992. This discordance was probably due to a difference in the quality of the iron of

the two bars.

277. Variation of thermal conductivity with temperature. We have already mentioned that the main object of Principal Forbes in his research was to ascertain if the conductivity of an iron bar varies with its temperature. The method employed has already been described; it only now remains to mention the results. There were two square bars; the side of the one being 1 in., while that of the other was I in.