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solid, and for two solid carbons respectively. The former show conditions approaching those found when using both carbons cored. But beyond a certain current strength all the arcs pass through a condition of unstable equilibrium, and no length can be found where the voltage will remain constant for all currents, plainly demonstrating one of the advantages of using cored carbons. When both carbons are solid no length of arc gives even approximately constant voltage with varying current and a quiet arc. The constant voltage beyond the unstable condition is for hissing arcs. With cored carbons the voltage is from 3 to 6 volts less than with solid carbons, owing to the greater volatility of the electrode.
Resistance of the Arc. — If the current is kept constant the resistance of any arc increases with its length. With solid carbons the ratio is a linear one as shown by Fig. 262, and nearly so for cored carbons as given in Fig. 263.
As explained before, if the current is variable, the resistance of the arc stream proper varies inversely with the current. Therefore, the apparent resistance of the arc, which is the quotient of the volts and amperes, may be expressed by the formula,
R = x + al,
where x is some quantity varying inversely with the current and a is a constant. Multiplying both sides by the current / we have
IR = xl+ all.
IR = E and xl is composed of a term varying inversely with the current and one directly proportional to it, so that we may substitute a constant m for it. We may also substitute a value n for the product al, so that the voltage E at the arc is
E = m + nl.
The most probable values of these quantities for good solid carbons seem to be those obtained by Duncan and Rowland for good pure carbons, namely, m = 40.6 and n = 40, where / is the length of the arc expressed in inches.
Watts at Arc If the current is kept constant the watts
increase in a linear ratio with increase of arc length as shown by Fig. 264. If the arc length is constant and the current increases, the watts will vary in a similar manner, as shown by Fig. 265.
Hissing Arc When an arc is shortened, or its current increased until it hisses, the voltage drops 10 to 20 volts, and stays constant even when the current varies greatly (Figs. 260 and 261), for which no satisfactory explanation has been afforded.
Photometry of the Arc. — The chief source of light in the arc is the intensely heated crater, which gives about 85 per cent of the total light. The arc proper, or flame between the electrodes, is almost non-luminous, giving only about 5 per cent, while the tip of the negative carbon gives about 10 per cent. Owing to the form and arrangement of the carbons, as shown in Fig. 258, most of the light is thrown down when the positive carbon is above, as it usually is. The exact distribution varies with the current, carbons, and other conditions ; but the general distribution of light from a continuous current arc is shown in Fig. 266. The lengths of lines drawn from the arc to points on this curve represent the relative candle-power at different angles. It is evident from this diagram that it is possible to obtain various values for the candle-power of the arc according to how the measurement is made. As a matter of fact, candle-power is actually measured in four different ways:
Candle-Powers. — 1. The mean horizontal candle-power, usually the smallest of the four, being the average in all directions in a horizontal plane.
2. The mean hemispherical candle-power, usually greater than the last, which is the average obtained by making measurements in all directions and angles below the horizontal, showing the average value of the illumination thrown downwards.
3. The mean spherical candle-power, determined in a similar