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The average relative coefficient is found from the normal equation

1059.4x=410.1 X 11040 T

x=0.00000350 The absolute linear coefficient of expansion is therefore

a= 0.0000045.

The comparisons were made on a Zeiss horizontal comparator, which allows a direct reading of 1.0u.

An attempt to obtain a fiber with a zero temperature coefficient by melting quartz and steatite together was unsuccessful. As soon as too much quartz is present the bead loses its transparency. If beads made of soapstone should not be clear, it is generally due to an excess of quartz in the substance. In such a case the addition of a small amount of magnesia or magnesium carbonate will clear up the bead. .

Inder of refraction of fused steatite.-Two small prisms were ground from steatite beads, and their index of refraction for sodium light determined by the method of minimum deviation. The instrument used was a spectrometer reading to half minutes. Table IV contains the results.


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Also for these determinations I am indebted to Mr. L. G. Hoxton.

From the above comparison we conclude that we have found in fused steatite a substance which shows all the characteristic properties of fuzed quartz. The method of drawing fibers from it is very simple, and since the substance is easily secured (an old jet of a gas burner will furnish a large number of fibers), these fibers may, with advantage, be used where economy of time is an important question. One more advantage lies in the easy handling of the fiber. While thick quartz threads break easily when bent, those of steatite may be bent considerably more without breaking.

Barnetta working with fibers from 0.005 to 0.007 cm in diameter did not detect any time effect upon the period. But I found a distinct effect with either quartz or steatite fiber. The quartz fibers became

a Barnett: loc. cit., p. 116.

more rigid in course of time, a behavior resembling that of metals. a Professor Carhart and the writerhave found, however, a decrease of rigidity in the case of phosphor bronze. Continued vibrations, especially of very large amplitude, seem to bave a distinct influence upon this "settling down” to a steady state, if such can be obtained.

Tests have been made concerning this time change in order to determine whether different specimens of quartz will differ in their behavior—mine contained quite a large amount of strontium-or whether the difficulties are to be attributed simply to the size of the fibers. Fibers were drawn from a stick of quartz glass (Heraeus). These show no time effect if the load is very small in comparison with the tensile strength, but the time effect becomes more and more pronounced the larger the load. After a fiber 0.02 cm in diameter had been vibrated for about a week with a load of 400 grams, the latter was removed and the fiber allowed to rest for a couple of days. It showed a partial return to the original state. It seems that the thickness of quartz fibers can not be increased beyond 0.002 or 0.005 cm without the loss of the desirable properties which make them so well adapted for very fine suspensions.

a Nichols and Franklin: Elements of Physics, I, p. 99.
6 Carhart and Guthe: Phys. Rev., 9, p. 292; 1899.



The comparison of the methods of extrapolation that must be resorted to in the estimation of extremely high temperatures is of growing importance in establishing a satisfactory tentative scale of temperature which is already required in many scientific and industrial operations.

In a study of the possibilities of the application of optical and radiation methods of pyrometry to the estimation of extremely high temperatures we have been led to compare a number of carefully calibrated optical pyrometers at the “temperature of the arc.

The early attempts to estimate the so-called temperature of the arc, or more precisely, the temperature of the hottest portion of the positive crater, were based on the extrapolation of empirical relations connecting radiation and temperature (Newton, Dulong and Petit, Rosetti, etc.), that were only applicable through very narrow ranges of temperature, and the results to which they have led are now only of historical interest.

The first important measurement was that of Le Chatelier, a who determined for a number of bodies the relation between the photometric intensity of the red light emitted and the temperature. The photometric measurements were made with his optical pyrometer, and the temperature measurements with the now well-known Le Chatelier thermocouple (platinum, platinum-rhodium 10 per cent). This empirical relation is based on experiments extending over the range 700° C. to nearly 1800° C. Le Chatelier found by the extrapolation of this relation (I=106.7 T T) for the temperature of the arc 4400° abs. The red light was obtained by passing the radiation through red glass, which probably lets through the shorter wave lengths at high temperatures, so that the measured intensity would increase more rapidly than the formula would indicate. This would act in the direction of making the result come out too high.


a Le Chatelier: C. R., 114, p. 737; 1892; J. de Phys. (3), 1, p. 185; 1892.

Violle « made an estimate of the temperature of the are by a calorimetric method. A small removable button of carbon on the end of the positive crater was dropped into the calorimeter. The specific heat of carbon was measured and found to obey a linear relation for a considerable range above 1000°, and the relation thus established was assumed to hold as far as the temperature of the arc. The final value found by Violle was given as 3875° abs. Among the great experimental difficulties of this method are those due to loss of heat by the button in falling to the calorimeter and to nonuniformity of heating. Violle investigated these by varying the height of fall and size of the button. In general criticism of this method it should be noted that the specific heat of most substances increases more rapidly as the temperature corresponding to change of state is approached than at low temperatures. Although the difficulties of this method are very great-as admitted by Violle--the result is nevertheless interesting as a determination by a method widely different from those usually employed, based on the extrapolation of relations connecting radiation and temperature.

Wilson and Gray made an estimate of the temperature of the arc by a method in which the radiation from the positive crater falling on one junction of a differential radiomicrometer was balanced by the radiation on the other junction from a known area of incandescent polished platinum strip, whose temperature was measured by its expansion after the principle of the Joly meldometer. The relation between the radiation of polished platinum and of platinum covered with copper oxide was then determined and the assumption made that the radiation from the carbon obeyed the same law as from the copper oxide, which is very nearly the case. Knowing then the apparent areas of the two sources of radiation, and knowing the relation connecting radiation and temperature, they could at once find the temperature to which the platinum strip would have to be raised to balance the arc if the apparent areas were equal. The result to which these experimenters were led was 3600° abs. In discussing this experiment which was admirably carried out it must be remembered that it was done at a time when the laws of radiation were not so well understood as they were a few years later. The method of measuring the temperature made use of in these experiments is capable of considerable precision. Their temperature scale is probably about 20 low at 1000°, inasmuch as the melting point of gold was taken as

a Violle: C. R., 95, p. 1273; J. de Phys. (3), 2, p. 545; 1893; C. R., 120, p. 868; 1895.

Wilson and Gray: Proc. Roy. Soc., 58, p. 24; 1895; Phil. Trans. A., 185, p. 361, 1894, for details of apparatus, same as used in estimation of temperature of the sun.

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