On Stationary Waves in Water, 97 



and any line of the series 1*5$— mpj, where m > 2, is neces- 

 sarily excited at the sacrifice of l"5s — 2/>>. 



Above a certain voltage the intensity of any line per unit 

 number of electrons reaching the anode attains a saturation 

 value, in agreement with the quantum hypothesis, which 

 requires that the number of quanta radiated be proportional 

 to the number of collisions, and hence (approximately) to the 

 number of electrons present. 



Curves are given showing the relative intensities of the 

 prominent cresium lines at various voltages. The ratio of 

 intensities of the components of the first doublet of the 

 principal series X8521/X 8943 is constant and equal to 1*5 from 

 1-5 volts to 120 volts. 



The ca?sium arc of the type employed does not rectify 

 alternating current of 120 volts. 



Sodium and potassium occurring as an impurity of the 

 caesium similarly exhibited the single-line or doublet spectrum 

 l"5s — 2p| below their respective ionization potentials. 



Only two types of inelastic impact between electrons 

 and atoms of the alkali-metal vapours occur, at potentials 

 known as the resonance and ionization potentials and given 

 by the quantum relation 7iv = eV, where v=l'5s—2p 1 and 

 v = l'5s. 



Bureau of Standards, 



Washington, D.C., 

 January 14, 1920. 



VIII. Stationary Waves in Water. By A. R. Richakdson, 



Imperial College of Science and Technology *. 



ALTHOUGH the subject is of very great practical im- 

 portance, and has received much attention at the 

 hands of engineers and experimentalists, very few exact 

 solutions have been obtained of problems involving the flow 

 of a liquid under gravity. 



In this paper some exact solutions are obtained, and 

 existing results are linked together through a differential 

 equation which forms the subject of the first part. Amongst 

 the problems discussed is that of the flow over a weir, and 

 an approximate calculation is made of the constants which 

 appear in the Francis formula. 



* Communicated by the Author. 



Phil. Mag. S. 6. Vol. 10. No. 235. July 1920; H 



