the Nature of Spectra. 81 



tude of the individual numbers) we lay down for a base 

 the mean length of path of the hydrogen molecule at 0° 

 (L = 194. 10 -7 centim.) and the mean velocity of the same 

 at the same temperature (c = 1698 . 10 2 centim.), we get 



L 194.10-7 



T = 



1698.10 s 



1-14 xlO" 10 second. 



The two quantities T and t agree relatively so well with one 

 another that at all events the assumption is not inadmissible 

 that the aether particles on the sodium atom may accomplish 

 undisturbed, on the average, as many as 50,000 vibrations. 

 This investigation shows, at the same time, that we need not 

 in all cases conceive of the vanishing of interferences as pro- 

 ceeding from a widening of the lines of the spectrum. 



The measuring of the high interferences must also furnish 

 us with a means of determining the amplitude of the aether- 

 vibrations, and therewith the density of the aether. If the 

 length of path in which a particle undergoes no disturbance 

 be, say, x millimetres, if the number of the vibrations executed 

 upon this path be m, then the motion is disturbed just at the 

 commencement of the mth vibration ; the m vibrations, for 

 which there is no reason that they should all be perpen- 

 dicular to the progressive motion of the molecules, are dis- 

 tributed equally over x millims. ; the mean magnitude of the 



x 



amplitude in that direction amounts to — millim. 

 x m 



The distance upon which the molecules undergo no disturb- 

 ance it must be possible to determine by heating the gas under 

 different pressures to the same temperature, and determining 

 the number of the interferences. The length of the molecular 

 diameter, S, is independent of the pressure. But if at the 

 density 1 the mean distances of the molecules are A millim., 



they are -^ millim. at the density \ ; the numbers q and q lf 



however, of the resulting undisturbed vibrations are deter- 

 mined by 



A-S . 

 q= -yjjr and q 1 — 



if T denotes the duration of a vibration, and V the velocity of 

 translation of the molecules. Hence, if q and q 1 be known, 

 A and S follow immediately. 



The available data are nevertheless not yet sufficient for 

 carrying out these calculations, the principle only of which is 



