Level of No Strain in a Cooling Homogeneous Sphere. 299 



further could be gained in resolution of groups of spectral 

 lines, on account of the real width of the lines themselves, 

 caused by the lack of homogeneity in the radiations which 

 produce them. The results of the preceding investigations 

 show that, while this is very far from being true with present 

 gratings, such a limit undoubtedly exists. The accordance 

 between the measured widths of eighteen lines shows, further, 

 that this broadening of lines in a rare gas can be fully 

 accounted for by the application of Doppler's principle to the 

 motion of the vibrating atoms in the line of sight, and indeed 

 furnishes what may be considered one of the most direct 

 proofs of the kinetic theory of gases. 



The form of the ultimate components of all the groups of 

 lines thus far examined is found to agree fairly well with an 

 exponential curve, <f){x) = e~ a2x2 , which shows that the distri- 

 bution of velocities cannot vary widely from that demanded 

 by Maxwell's theory. 



If the limit above mentioned were due solely to the motion 

 of the molecule, and the radiating substance could be rendered 

 luminous while its temperature was very low, it might be 

 possible to observe interference-phenomena with difference of 

 path of many metres. But it must be considered that, since 

 every vibrating molecule is communicating its energy to the 

 aether in the form of light-waves, its vibrations must diminish 

 in amplitude ; consequently the train of waves is no longer 

 homogeneous even though the vibrations remain absolutely 

 isochronous, and the result is a broadening of the line and 

 limitation of the difference of path at which interference is 

 visible. 



XXXI. Note on the Level of No Strain in a Cooling Homoge- 

 neous Sphere. By M. M. P. Rudski, Privat Docent in the 



University of Odessa *. 



[This note relates to the geological theory of the formation of 

 mountains which is based on the fact that, when a sphere cools and 

 contracts, the stratum which contracts most rapidly is situated 

 below the surface, and accordingly the superficial layers are com- 

 pressed and crumpled. This theory is developed in a paper by 

 Mr. Davison and in a subsequent note bv Professor Darwin in 

 Phil. Trans. Eoy. Soc. vol. clxxviii. (1887) A. pp. 231-249. It has 

 been urged against this theory that the level of no strain lies too 

 near the surface to explain the formation of mountains. But 

 M. E-udski here shows that if the initial temperature be not uni- 

 form, the level of no strain will lie deeper. Such an hypothesis 



* Communicated by Professor G. H. Darwin. 



