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It will be observed that the radiation-constant is practically the same as that derived from his cylinder results*, while the value of c is rather less.
Experiments on spheres (both of 2 centim. radius) have also been made by MacFarlanet and extended by Bottomley+, both using the same enclosure, which was of "large dimensions" (Bottomley).
Extrapolation from Péclet's results for a sphere of 2 centim. radius in his enclosure gives :
Using his formula.
Using formula given above.
MacFarlane's results for a blackened sphere (Péclet's were dull) give 000238 for 0° excess. Bottomley's results give about 000260 for 0° excess, showing that the formula derived from Péclet's results is roughly applicable here.
Bottomley also experimented on the same sphere in a spherical enclosure of 5 centim. radius. If the formulæ
hitherto given in this paper were applicable to this case, the emissivity ought to increase with decrease of radius of enclosure. Bottomley's results show a marked decrease. The value at 17° for 0° excess is not more than 00011 after correcting approximately for temperature.
Since the true radiation was determined separately it is possible to find the value of "c" for these experiments,
Péclet endeavoured to estimate the radiation independently by means of a thermopile, and deducted it from the total emission to obtain the aireffect. The value he obtained was only 0000072 for 0° excess, a value so much smaller than received values that I have ignored it entirely, and dealt only with the total effect.
+ D. MacFarlane, Proc. Roy. Soc. 1892.
J. T. Bottomley "On Thermal Radiation in Absolute Measure," Trans. Roy. Soc. 1892.
Place against these the values obtained from cylinders :
In order to throw light on this question, I have started experiments, in conjunction with Mr. Eumorfopoulos, on cylindrical rods in cylindrical enclosures of different radii. Experiments made so far are as follows:
A brass rod 483 centim. radius has soldered on it two thermoelectric junctions of iron and german-silver at a distance apart of 10 centim., each of which is part of a couple whose other junction is kept cold in a water-pot. The rod is heated at one end by steam until the steady state of temperature is attained, and the ratio of the temperatures (reckoning from enclosure temperature as zero) of the two junctions is measured successively with different water-jackets embracing the rod.
The general arrangement is shown in fig. 2 (p. 277). Tap-water is passed through the water-jacket at such a rate that its temperature as it enters is sensibly the same as when it leaves the jacket. This temperature is read by a thermometer, as also are the temperatures of the cold junctions. Then either the junction at A and its corresponding cold junction, or the junction at B and its corresponding cold junction, can be connected to a potentiometer, and the thermoelectric E.M.F. in each case determined.
The potentiometer was standardized from time to time by a Clark's cell which is so connected (switches not shown) that the same galvanometer does for all three operations.
The ratio of the thermoelectric E.M.F.'s is approximately the same as the ratio of the excess temperatures of the points
A and B after it has been corrected for slight differences of temperature between the two water-baths and the waterjacket. Two jackets have been employed so far, and compared with each other and with the bar unjacketed. In this last case the bar is merely shielded from the ruder form of draught by brown-paper screens.
The results are given in the subjoined table:
The values of emissivity here given have been calculated from the formula
kr [log O1-log 0s],
•4343 × x
Phil. Mag. S 5. Vol. 39. No. 238. March 1895. U
in which a=10 centim., and the value of k taken is that determined by Mr. Eumorfopoulos for the same rod by Ångström's method, viz. 2386. The emissivity is therefore in each case an average value for the range of temperature between the two points. The actual temperatures were ascertained by standardizing the thermoelectric couples in water-baths of known temperatures.
The above results are also shown plotted in fig. 3. An
Variation of Emissivity of Cylindrical Brass Rod with the Radius of its Cylindrical Enclosure.
elastic curve (bent steel lath) has been made to pass through the two results for definite dimensions and extended provisionally by a dotted line so as to rise asymptotically to the highest value. It is unsafe to rest too much upon these few results : more will need to be obtained before the law of variation can be stated with certainty: the following paragraph must be considered therefore as merely provisional. Take the two definite values and also (by interpolation) the value for an enclosure of 2.54 centim. radius (that employed by Messrs. Ayrton and Kilgour) and find the values of "b."
The value derived from A. and K.'s results at 60° is
047 × 10-3. As their thin wires blocked up the enclosure less than the thick rod here employed, it is natural that the value obtained from them should be greater than that given
The formula which I have given for a cylinder appears to hold through a far wider range than that given by Messrs. Ayrton and Kilgour. Take for example their formula for a wire at 100°. The emissivity for it can never (for any radius) fall lower than
Calculating from my formula we get
for a rod of 483 centim. radius at 100°. On reduction to 60° it becomes about
which is much more within sight of the value 000154 which is obtained from fig. 3. Considering the violent nature of the extrapolation here made, the agreement is probably as close as could reasonably be expected.
i. That the theoretic assumption made in this paper gives results which are accordant through a wide range of radius of rod with experimental results obtained under similar conditions as regards enclosure: and in this respect is far superior to the usual assumption which gives no account whatever of variation of the value of emissivity with radius.
ii. That if the freedom permitted to convection effects be varied, as it will be if the enclosure be changed, it is necessary to consider the convecto-conduction constant as varying with the changed conditions according to a law which can only be found by a complete series of experiments made with enclosures of different dimensions.
iii. I conclude that the enclosing boundary is as important a factor in determining the value of the emissivity as the size of the body itself: and that therefore in any collection of data (such as Everett's) it is very necessary to specify the exact nature of the enclosure in which the experiments were conducted; and, further, that all determinations that have been made of this constant and published with imperfect description of all the boundaries are of little scientific value. Finally, I must express my thanks to Prof. G. C. Foster for kindly advice and suggestions given from time to time in connexion with this matter.
University College, London,