The appearance of the terminals is shown in fig. 18, given by Mrs Ayrton (_Proc. Inst. Elec. Eng._ 28, p. 400); a, b represent the terminals when the arc is quiet, and c when it is accompanied by a hissing sound. The intrinsic brightness of the positive crater does not increase with an increase in the current; an increased current produces an increase in the area of the luminous crater, but the amount of light given out by each unit of area of luminous surface is unaltered. This indicates that the temperature of the crater is constant; it is probably that at which carbon volatilizes. W. E. Wilson (_Proc. Roy. Soc._ 58, p. 174; 60, p. 377) has shown that at pressures of several atmospheres the intrinsic brightness of the crater is considerably diminished. [Illustration: FIG. 18.] [Illustration: FIG. 19.] The connexion between V, the potential difference between the terminals, and l, the length of the arc, is somewhat analogous to that which holds for the spark discharge. Fröhlich (_Electrotech. Zeit._ 4, p. 150) gives for this connexion the relation V = m + nl, where m and n are constants. Mrs Ayrton (_The Electric Arc_, chap. iv.) finds that both m and n depend upon the current passing between the terminals, and gives as the relation between V and l, V = [alpha] + [beta]/I + ([gamma] + [delta]/I)l, where [alpha], [beta], [gamma], [delta] are constants and I the current. The relation between current and potential difference was made the subject of a series of experiments by Ayrton (_Electrician_, 1, p. 319; xi. p. 418), some of whose results are represented in fig. 19. For a quiet arc an increase in current is accompanied by a fall in potential difference, while for the hissing arc the potential difference is independent of the current. The quantities m and n which occur in Fröhlich's equation have been determined by several experimenters. For carbon electrodes in air at atmospheric pressure m is about 39 volts, varying somewhat with the size and purity of the carbons; it is diminished by soaking the terminals in salt solution. The value of n given by different observers varies considerably, ranging from .76 to 2 volts when l is measured in millimetres; it depends upon the current, diminishing as the current increases. When metallic terminals are used instead of carbons, the value of m depends upon the nature of the metal, m in general being larger the higher the temperature at which the metal volatilizes. Thus v. Lang (_Wied. Ann._ 31, p. 384) found the following values for m in air at atmospheric pressure:--C = 35; Pt = 27.4; Fe = 25; Ni = 26.18; Cu = 23.86; Ag = 15.23; Zn = 19.86; Cd = 10.28. Lecher (_Wied. Ann._ 33, p. 609) gives Pt = 28, Fe = 20, Ag = 8, while Arons (_Wied. Ann._ 31, p. 384) found for Hg the value 12.8; in this case the fall of potential along the arc itself was abnormally small.