:66 



NA rURE 



[August 8, 1901 



Volatilisation can only take place at the surface of contact 

 between the vapour-film and the positive carbon. When that 

 surface is smaller than the cross-section of the end of the carbon 

 it must dig down into the solid carbon and make a pit. The 

 sides of the pit, however, must be hot enough to burn away 

 where the air reaches them, hence there is a race between the 

 volatilisation of the centre of the carbon and the burning of its 

 sides that determines the shape of the carbon. When the arc 

 is short, the air cannot get so easily to the sides of the pit, hence 

 it remains concave. When the arc is long, the burning of the 

 sides gains over the volatilisation of the centre, and the surface 

 of volatilisation becomes flat, or even slightly convex. 



The peculiar shaping of the negative carbon is shown to be 

 due to its tip being protected from the air by the mist and its 

 sides being burnt away under the double action of radiation 

 from the vapour film and conduction from the mist, to a greater 

 or less distance, according to the length of the arc and the cross- 

 section of the vapour-film. 



It is shown that if the crater be defined as being that part of 

 the positive carbon that is far brighter than the rest, then the 

 crater must be larger, with the same current, the longer the arc, 

 although the area of the volatilising surface is constant for a 

 constant current. 



By considering how the cross-section of the vapour-film must 

 vary with the current and the length of the arc, it is found that 

 its resistance/ must be given by the formula 



h , k + mt 



where /;, /J and m are constants, / is the length of the arc, and 

 A the current. This is the same form as was found by measuring 

 the P. D. between the positive carbon and the arc by means of 

 an exploring carbon and dividing the results by the corresponding 

 currents. Hence the existence of a thin film of high-resisting 

 vapour in contact with the crater would not only cause a large 

 fall of potential between the positive carbon and the arc, exactly 

 as if the crater were the seat of a large back E M.F. , but it 

 would cause that P. D. to vary with the current and the length of 

 the arc exactly as it has been found to vary by actual measure- 

 ment. 



The Apparent " Negative Resistance." 



As nearly all the current flows through the vapour and mist, 

 the surrounding flame being practically an insulator, the resist- 

 ance of a solid carbon arc, apart from that of the vapour, must 

 depend entirely on the cross-section of the mist. To see how 

 this varies with the current, images of an arc of 2 mm. were 

 drawn, with the purple part — the mist — very carefully defined, for 

 currents of 4, 6,8, 10, 12 and 14 amperes. The mean cross- 

 section of the mist was found to increase more rapidly than the 

 current, consequently its resistance]diminishes more rapidly than 

 the current increases. As the formula for the resistance of the 

 vapour film shows that it too diminishes faster than the current 

 increases, it follows that the whole resistance of the arc does the 

 same, and that consequently the P.D. must diminish as the 

 current increases. Hence if 5V and 5A be corresponding incre- 

 ments of P.D. and current, 5V/5A must be negative, although 

 the resistance of the arc is positive. 



It is found, from the above measurementsof the cross-sections 

 of the mist, that the connection between ;«, the resistance of the 

 mist, and the current, is of the form, 



If lu varies directly with the length of the arc, then 



Adding this equation to (i), we get 



for the whole resistance of the arc, which is e.xactly the form 

 that was found by dividing direct measurements of the P.D. 

 between the carbons by the corresponding currents. Hence 

 there is no reason why this ratio should not represent the true 

 resistance of the arc. 



NO. 1658, VOL. 64] 



Under ivhat circumstances 5V/5A measures the True Resistance 

 of the Arc. 



When the current is changed it takes som.e time for the vapour 

 film to alter its area to its fullest extent, and still more time for 

 the carbon ends to change their shapes. All the time these 

 changes are going on the resistance of the arc, and, consequently^ 

 the P.D. between the carbons, must be altering also. Both 

 these, therefore, depend, not only on the current and the length 

 of the arc, but also, till everything has become steady again, i.e. 

 till the arc is *' normal " again, on how lately a change has beerk 

 made in either. At the first instant after a change of current, 

 before the volatilising area has had time to alter at all, SV and 

 5A must have the same sign, just as they would if the arc were 

 a wire, but as the volatilising surface alters, the sign of 5V 

 changes. If, therefore, a small alternating current is applied 

 to the direct current of an arc. it will depend on the frequency 

 of that current whether SV/SA is positive or negative. Wher> 

 the frequency is so high that the volatilising surface never changes- 

 at all, SV/SA will measure the true resistance of the arc 

 unless it has a back E.M.F. which varies w'ith the alternating 

 current. 



The measurements of the true resistance of the arc made i[>. 

 this way by various experimenters have given very various results, 

 because probably the frequency of the alternating currents em- 

 ployed has been too low not to alter the [resistance of the arc. 

 A curve is drawn showing how the value of 5V/5A with the same 

 direct current and length of arc varies with the frequency of the 

 alternating current, and it is pointed out that even if the arc has 

 as large a back E.M.F. as is usually supposed, the ^rj/t- resistance 

 cannot be measured with an alternating current of lower frequency 

 than 7000 complete alternations per second. 



The exact conditions under which the true resistance of the 

 arc can be measured in this way are examined, and the precautions 

 that it is necessary to take to ensure the fulfilment of these con- 

 ditions are enumerated. 



The Changes introduced into the Resistance of the Arc by the Use 

 of Cored Carbons. 



A core in either or both carbons has a great effect on both 

 the P.D between the carbons and the change of P.D. that 

 accompanies a given change current. It lowers the first and 

 makes the second more positive, i.e. gives it a smaller negative 

 or larger positive value, as the case may be. It is pointed out 

 that this might be due to the influence of cores either on the 

 cross-section of the arc or on its specific resistance, or on both. 



To see the effect on the cross-section, enlarged images were 

 drawn of 2 mm. arcs with currents increasing by 2 amperes 

 from 2 to 14 amperes, between four pairs of carbons, + solid — 

 solid, + solid - cored, + cored - solid, + cored - cored. 

 Two sets of images were drawn with each pair of carbons — the 

 one immediately after a change of current, to get the "non- 

 normal" change, and the other after the arc had become normal 

 again. The mean cross-section of the mist was calculated in 

 each case, and its cross-section where it touched the crater was 

 taken to be a rough measure of the cross-section, of the vapour 

 film. 



It was found that the mean cross-section of the mist with a 

 given current was largest when both carbons were solid, less 

 when the negative carbon alone was cored, less still when the 

 positive alone was cored, and least when both were cored. 

 Coring either the positive carbon alone, or both carbons, had 

 the same eft'ect on the cross-section of the vapour film as on that 

 of the mist, but coring the negative alone only diminished this 

 cross-section immediately after a change of current, but not 

 when the arc had become normal again. Hence it was deduced 

 that if the cores altered the cross-sections of the arc only they 

 would increase its resistance, and, consequently, the P.D. 

 between the carbons. As they lower this, however, they must 

 do it by lowering the specific resistance of the arc more than 

 they increase its cross-section. The vapour and mist of the 

 core must therefore have lower specific resistances than the 

 vapour and mist of the solid carbon. 



When it is the positive carbon that is cored, all the vapour 

 and mist come from the cored carbon. When the negative, they 

 come from the uncored carbon, and it is only because the 

 metallic salts in the core have a lower temperature of volatilisa- 

 tion than carbon that the mist is able to volatilise these and so 

 lower its own specific resistance. 



The effect of a core in either carbon, or in both, must depend 



