Vol.. 7, 1921 
MATHEMATICS: G. A. MILLER 
325 
in the work function of the surface, so that more of the electrons present 
may escape; 3 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. Miixer 
Department of Mathematics, University of Iixinois 
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 cate- 
gories. First, those which can be obtained by transforming all the sub- 
stitutions 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 trans- 
forming G by substitutions on its own letters, which transform G into 
