proceedings: philosophical society 373 



ordinates be selected in pairs sjanmetrically located in the integration 

 interval. The formulas of Cotes, Euler, and Gauss may be derived as 

 special cases. 



The paper was discussed by Messrs. Sosman, White, and Burgess. 



A third paper, by P. D. Foote and F. L. Mohler, on Ionization and 

 resonance potentials for electrons in vapors of magnesium and thallium, 

 was presented by ]\Ir. Mohler. (Illustrated by lantern slides). Since 

 mercury, magnesium, cadmium, and zinc belong to the same family, 

 one might expect that the behaviour of electrons in vapors of these four 

 elements should be somewhat similar in character. The single line 

 spectrum of mercury is known to be excited at the resonance potential 

 of 4.9 volts. Work of Tate and Foote reported at the Chicago meeting 

 of the Phj^sical Society, shows that the resonance potentials for cad- 

 mium and zinc obey the quantum relation hv = Ve, where v is the fre- 

 quenc}' of tli£ single line spectrum. Hence, one would expect the single 

 line spectrum of magnesium to follow a similar relation. 



The present writers have employed the method of Franck and Hertz 

 for determining the resonance potential of electrons in magnesium vapor 

 and Tate's modification for determining the#ionization potential. The 

 mean of data so far obtained gives 2.65 volts for resonance and 7.75 

 volts for ionization with an accuracy of possibly 0.1 volt. The theo- 

 retical values on the basis of X = 4,571 and 1,622 are 2.70 volts and 

 7.75 volts, respectively, while the single line spectrum at X = 2,852 

 would require a resonance potential of 4.3 volts.' This experiment 

 combined with the confirmed results on the other metals in the same 

 group suggests that the single line spectrum of Mg is X = 4,571 rather 

 than X = 2,852. Evidence was obtained in the present work for a 

 series of double points in the current-potential curves similar to those 

 found by Tate and Foote for zinc, but further work now in progress is 

 required properly to interpret these subsidiary points. 



The resonance and ionization potentials for electrons in thallium 

 vapor have been measured by the method described in earlier papers, 

 with the modification of the use of a hot equal potential surface instead 

 of a hot wire as a cathode. The cathode was similar in principle to 

 that used by Goucher and consisted of a platinum (or better, a nickel 

 cylinder) insulated from a helix of tungsten wire inside, which was used 

 as the heater. Ionization occurred at an applied potential of 6.6 volts, 

 which when corrected for the initial velocity observed as 0.7 volts 

 gives the final value for the ionization potential of 7.3 volts. The thal- 

 lium spectrum is characterized by a set of doublet series. The reso- 

 nance potential of 1.07 volts is given within experimental errors by the 

 quantum relation hv — eV when v is the frequency of the stronger 

 line (X = 11,513) of the first doublet of the principal series. The theo- 

 retical value of the resonance potential computed on this basis is 1.07 

 volts. We believe this is good evidence that the single line spectrum 

 of thallium is X = 11,513. 



We were unajDle to detect any sign of ionization accompanying reso- 

 nance or any resonance due to the line X = 13,014. If thallium acted 



