a b d FIGURE 1 Added space currents due to illumination of audion filament by red light. = (a) Filament heating current .65 amp.; (b) filament Equal added space currents caused by (a) illumination by red light; (b) increase of heating current. Added space currents due to illumination of audion filament by blue light. Filament heating currents = (a) .60 amp.; (b) .64 amp. ; (c) .70 amp.; = 0.1 second. in the work function of the surface, so that more of the electrons present may escape; or it may be a light induced change in the chemical nature of the surface. In any case there must be ascribed to the light produced change a temperature coefficient of speed of response. Some clue to the nature of the phenomenon may perhaps be obtained from a study of the growth and decay curves. They are not simple exponential curves such as would represent the charging and discharging of a condenser. If the reciprocal of the square root of the decaying current increment is plotted against time, the plots are very nearly straight lines for all temperatures (law of phosphorescence decay). Attention may be called to the fact that the growth and decay of current represented in the curves in figure 3 exhibiting slow response at low temperatures and quick response at high, are quite similar to the growth and decay of current in selenium under illumination, which likewise show a great variation of speed with temperature. This analogy suggests that the cause of the light effect in the oxide coated filament may be closely related to that which gives selenium its photo-sensitive properties. It should also be noted that the change of speed of response with temperature would be expected if one assumed the effect to be due to a chemical reaction. In view of the data presented it is believed that this photo-effect in thermionic filaments cannot safely be considered as evidence for a variation of the true photo-electric effect with temperature. We suggest the use of the term "photo-thermionic emission." 1 T. W. Case, Physic. Rev., 17, 3, p. 398. 2 E. Merritt, Ibid., 17, 4, p. 525. 3 Koppius (Ibid., Mar. 1921, p. 395) found with oxide coated filaments a decrease in the work function with increasing temperatures. GROUP OF ISOMORPHISMS OF A TRANSITIVE SUBSTITUTION GROUP By G. A. MILLER DEPARTMENT of MathemaTICS, UNIVERSITY OF ILLINOIS Read before the Academy, November 15, 1921 Let G represent any transitive substitution group of degree n. It is convenient to divide the possible automorphisms of G into three categories. First, those which can be obtained by transforming all the substitutions of G successively by each of its own substitutions. In this way the group of inner isomorphisms of G can be found and this group. is known to be an invariant subgroup of the group of isomorphisms I of G.. The second category consists of the automorphisms obtained by transforming G by substitutions on its own letters, which transform G into |