As far as I can see no contradiction exists between our understanding and the properties of photo-electric action observed by Mr. Lenard. If each energy quantum of the exciting light releases its energy independently from all others to the electrons, the distribution of velocities of the electrons, which means the quality of the generated cathode radiation, will be independent of the intensity of the exciting light; the number of electrons that exits the body, on the other hand, will, in otherwise equal circumstances, be proportional to the intensity of the exciting light. 
We expect that limits of validity of these rules will be similar in nature to the expected deviations from Stokes' rule.
In the preceding it has been assumed that the energy of at least some of the energy quanta of the generating light is transferred completely to a single electron. If one does not start with that natural supposition then instead of the above equation one obtains:
For cathode-luminescence, which constitutes the inverse process of the one just examined, one obtains by way of analogous consideration:
For the materials investigated by Mr. Lenard PE is always significantly larger than Rβν, as the voltage that the cathode rays have had to traverse to generate even visible light is in some cases several hundred, in other cases thousands of volts. 
Ionization of Gases by Ultraviolet Light
We have to assume that in ionization of a gas by ultraviolet light always one absorbed light
- P. Lenard, l. c. p.150 und p. 166-168.
- P. Lenard, Ann. d. Phys. 12. p.469. 1903.