Mechanics of Luminosity. 387 



Methods of determining the Quantity b. 

 37. Although the phenomena of phosphorescence in Bal- 

 main's luminous paint led to no result in the determination of 

 the quantity h, there are a series of other phenomena which 

 render possible a conclusion as to its magnitude. The results 

 to be thus obtained are brought together in the following. 

 The value of b finally given in each case is in round numbers, 

 since the question can only be as to its order of magnitude. 

 We make use of the equation on p. 337. 



h=\og(j^j(t\oge). 



(a) The observations of interference-bands with a large 

 difference by Michelson and Morley * show that in the case 

 of sodium, bands are visible with a difference of 200,000 wave- 

 lengths ; we may therefore conclude that after the time 

 which corresponds to the performance of 200,000 vibrations 

 in the case of sodium light, the energy of the vibrating mole- 

 cule has not yet sunk to ^ ; for otherwise the difference in 

 intensity of the two interfering pencils of rays emitted at the 

 beginning and end of this time would be too great for the 

 occurrence of still visible interference. That a great number 

 of oscillations may take place undisturbed and without great 

 decrease in intensity is shown by the occurrence of sharp 

 lines in the spectrum, since the vibrations which cause them 

 can only occur upon the free path between two impacts, for 

 so long as the vibrating molecules occupy their opposed 

 spheres of action irregular vibrations are produced. From 

 the experiments of H. Ebert| it follows that the increase in 

 number of luminous particles in the unit volume is almost 

 the only cause of the widening of lines, a sure sign that the 

 modes of vibration become more complicated in consequence 

 of the impacts of molecules of the same kind. 



If we take the wave-length of sodium as 0*0 3 6 millim., the 

 oscillation period as 1/(5 x 10 14 ) seconds, we have the follow,, 

 ing equation : — 



POOOOO 



J* = iJo = J e 5xioi4 = j oe _4xio-ioa. hence ^ = 1-74 xlO 9 . 



The actual value is no doubt smaller, since no doubt more 

 than 200,000 vibrations occur without disturbance. 



(b) Herr FeddersenJ has observed oscillating discharges 



* Michelson and Ed. Morley, Sill. Journ. [3] xxxiv. p. 421 (1887). 

 t Wied. Ann. xxxiv. p. 85 (1888). 

 \ Pogg\ Ann. cxvi. p. 132 (1862). 



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