ERBIUM SALTS. 



61 



between the maxima of the deviations of the dispersion curve vary directly 

 as the square root of the absolute temperature. 



If this law is true then the size of the bands is proportional to the 

 mean speed of translation of the molecules. Schonrock * has shown that 

 the width of bands in a gas results not only from the Doppler effect due to 

 the kinetic motion of the gas molecules, but also from collisions. Colli- 

 sions determine the sudden and fortuitous variations in the phase, amplitude, 

 and direction of motion of the electrons, and prevent the light that is being 

 emitted or absorbed from being homogeneous. The size of the bands is 

 then a function of the mean length of the wave-trains emitted between 

 collisions. If d is the width of the band between the positions where the 

 intensity of light is half the maximum, and r is the length of the train of 

 waves emitted between collisions, then: 



1.39; 2 = 1.39Vm == ^V T_ 

 tit izvL L L V M 



u is the mean speed of translation, L the mean free path, v the velocity of 

 light, A is a constant, M the molecular weight, T the absolute temperature; 

 L = l 2 /p 2 Vlrc, I is the mean distance between the centers of molecules; 

 p is the distance between two molecules at the time of their collision. 



If the same mass and volume of a vapor has its temperature raised, I 

 and p are but slightly changed, so that the width of the bands should vary 

 as the square root of the absolute temperature. The above theory applies 

 to a gas. The width of the bands of solids can not be explained on the 

 Doppler-Fizean principle, but may be due to the extremely numerous 

 shocks of the molecules. The fineness of the erbium bands may then be due 

 to the union of several atoms into big molecules having a very small velocity 

 of translation. If the molecules are large the collisions will be less numerous. 



In a later paper Becquerel 2 gives some values for the terms which 

 appear in his equation giving the refractive index. It should be stated 

 here that dispersion equations differ considerably according to the assump- 

 tions made in their calculation. 



TYSONITE. 



From the changes of Ih, the dielectric coefficient, with changes in tem- 

 perature, Becquerel considers that the increase in intensity of the bands 

 when the temperature is lowered is not only due to a narrowing of the 

 bands, but also to an increase in the total amount of energy absorbed as 

 the dielectric constant is increased. Let us assume that e = 3.4 (10)~ 10 . 



1 Ann. Phys., 20, 995 (1906); 22, 210 (1907). 



2 Le Radium, Nov. (1907). 



