VARIATIONS IN TEMPERATURE OF THE ARC.

(a) With current.—It is generally accepted, since Violle so stated, that the temperature of the arc is independent of the current, and this temperature is assumed to be the boiling point of carbon. There are, however, at least two reasons for which we should expect this temperature to vary with the current. As the current is increased there will be a tendency to superheat the viscous carbon layer from which the vapor boils, even though this vapor does not have a higher temperature than the normal boiling point, and as it is this viscous layer which is observed, variations of current above a certain limit should be accompanied by changes in temperature. Again, with low current a smaller area is heated, so that it will be more cooled by conduction. An examination of the observations from which it has been inferred that the arc temperature is independent of current seems to indicate that this conclusion is unwarranted, for no observer has published a series of results sufficiently concordant in themselves or of sufficient number to enable him to state with certainty whether or not the effect exists. This has been due largely to the tediousness or inadequacy of the methods employed.

The constancy of brightness was first announced as probable by Rossetti in 1878, and Violle was the first to state as a result of his own experiments that "the brightness of the positive carbon is rigorously independent of the electric power expended to produce the arc, changing from within the limits 10 amperes at 500 watts to 400 amperes at 34000 watts." Carbons of 3.5 cm diameter were used for the high currents, but no details of observations are published nor the precision of his spectrophotometric method, which is certainly sensitive, though it would be expected that any effect for very high currents would be neutralized, in part at least, by the larger carbons used. Furthermore, results with carbons of varying size and quality are not comparable. Although Violle showed undoubtedly that with carbons of different sizes adapted to carrying currents of from 10 to 400 amperes, there is no considerable change in temperature, yet it would seem that he did not show conclusively that for a given sized carbon there is no variation of temperature with current for the brightest portion of the positive crater.

Wilson and Gray found that changing from 14 to 25 amperes "the temperature then appeared to be a little higher than with the smaller indicate an exact

current.

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Later experiments

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a Violle: J. de Phys. (3), 2, p. 545; 1893.

equality of temperature." They do not give any data, but their published observations on the arc temperature indicate that it would be difficult to detect variations by their method.

Wanner states that "changing the current one and a half times (15 to 22 amperes) remains without influence." Wanner's published results for a given kind of carbon are few in number (four) and vary over 90° under the same conditions, so that any differences due to current changes might be masked.

Our experiments on the variation of arc temperature with current were first made with a Holborn-Kurlbaum pyrometer, which is peculiarly well adapted for these measurements, as it is readily sighted, and thus the wandering of the brightest spot on the crater can be easily followed. A very small photometric area is employed, and observations may be taken rapidly within intervals of a few seconds.

In order to secure a good-sized image of the crater, so as to facilitate the photometric measurements, the instrument, provided with auxiliary lenses and suitable absorption glasses, was placed as near as possible (12 to 25 cm) to the arc, which was mounted as previously described. The current from a 120 volt storage battery was varied without the observer being aware of the actual changes, and to render the settings of the pyrometer as unbiased as possible an additional rheostat in its lamp circuit was also worked independently of the observer. No observations were taken on a hissing or humming arc, nor until the arc burned normally after changing current, and the conditions of constant length of arc and constant P. D. across the are were very closely maintained, the latter being measured with a Weston voltmeter; the value of the P. D. was about 65 volts. Two observers obtained practically identical results, which are here summarized.

A few observations were also taken with a current of 40 amperes, which indicated that the effect persists with increasing current density to the limit that the auxiliary apparatus would stand.

The precision with which this determination can be made on a single carbon with the Holborn-Kurlbaum instrument is shown by the observations of June 23, 1904, namely, that the probable error of the mean in any one of the three series on that date is less than 3°, and no photometric observation with a current of 15 amperes was as high as the mean value for 30 amperes. Whatever may be the best value for the arc temperature, this value is apparently a function of the current when the P. D. across the arc is a constant and the arc is burning normally.

If the current is kept constant and the P. D. varied, it is necessary to vary simultaneously the length of the arc; therefore, temperature results obtained by this method of varying the power are not directly comparable, as the length of the arc is a variable which is not easily eliminated quantitatively.

It does not seem that our finding a small temperature change with current can be explained on physiological grounds, due to contrast in light intensities entering the eye, since with the smallest current used the image of the hottest part of the crater was many times larger than the image of the filament of the comparison lamp. To further test this point we determined the difference in temperature with a Le Chatelier optical pyrometer provided with auxiliary lens and a very homogeneous red glass before the eyepiece. A number of consistent observations indicate that changing the current from 15 to 30 amperes causes a rise in temperature of about 70°. With this instrument the eye does not receive light except through a 1 mm2 opening, so that the effects of the surrounding field can not influence the eye.

(b) With the material of carbons.-Wanner finds a difference of about 170° in changing from cored to retort carbon, the former giving a low value, and our experiments also show that the kind of carbon used will influence the apparent temperature of the arc. The homogeneous carbons described above gave us results 40° lower than with a very pure graphite furnished by the Acheson Company. This result was obtained both with the Holborn-Kurlbaum and Le Chatelier optical pyrometers.

In commercial carbons the presence of salts seems to facilitate the arcing, and with large currents a steadiness can be had which can not be approached with pure graphite carbons. It appears that the arc temperature, as determined with commercial carbons, is lower than the point obtained for pure carbon.

(c) Effect on the arc as a standard of light.-These questions are of interest in connection with the proposed use of the radiation from a definite area of the brightest part of the crater of the + carbon of the electric arc as a standard source of light. If the variations in temperature are as great as indicated in our experiments, a variation of current from 15 to 22 amperes (corresponding to a temperature variation of 40° C. in the temperature of the arc) would correspond to a variation in the photometric intensity of several per cent. Even with the same current and the same carbons our results appear to show relative time changes of photometric intensity that seem considerably greater than the experimental errors and which may be due to varying shape of the carbons and changes in current density, as well as variations in the composition of the material. While it would be possible to define the current, it would not be as easy to control the form of the crater and the current density in the region from which the light is to be taken.

Another difficulty in the above method of defining a light standard arises from the variations that may result from the use of different kinds of carbon, as shown above. The experiments of Wanner indicate an enormous change in the intensity of light due to this cause.

Blondel recognized the objections to the use of a screened area of the positive crater as a primary standard of light and recommended its use as a secondary standard for arc photometry. He found the nature of the carbon to be important in determining the absolute brightness (of a square millimeter); thus for five different qualities of homogeneous carbon an average value of 158 candles was found, the extremes being 150 and 163. With cored carbons he obtained values lower than 130 candles for the maximum brightness.

CONCLUSION.

A résumé of the estimates of the arc temperature that have been discussed in the preceding pages is given in the table on the next page. From this table it will be seen that the photometric methods based on the extrapolation of Wien's equation show that the "black body temperature of the arc" (pure graphite) is at least 3750 abs., so that its true temperature must be higher than this; it is not possible to state how much, in the absence of more definite knowledge concerning the departure of carbon from black body radiation. In the light of the best evidence that is at present available it would seem that the true

a Blondel: Proc. Int. Elec. Congress, Chicago, 1893.

temperature of the hottest part of the positive carbon is between 3900° and 4000° absolute.

Pure graphite gives a temperature not over 50° higher.

If we are justified in assuming that the high values found by Le Chatelier and by Féry, using photometric methods, are satisfactorily explained by the reasons we have advanced, a comparison of the results contained in the above table will show, when we consider the experimental difficulties and uncertainties that may enter due to varying conditions of the arc (such as current strength, length of arc, quality of carbon, etc.), that the results obtained, dependent as they are on the extreme extrapolation of different laws, are in quite satisfactory agreement, and diminish somewhat the doubt which is always present when we must venture beyond the domain of experiment.

The value obtained by Féry for the "black body temperature" of the arc, by making use of the Stefan-Boltzmann law for the total radiation of a black body, is in most satisfactory agreement with the results obtained by Wanner, dependent on the extrapolation of the WienPlanck relation, and is nearly identical with our own photometric determinations based on the same relation. It is interesting to note in