82 BELL SYSTEM TECHNICAL JOURNAL 



received energy from the molecules which they have struck. They 

 must therefore have struck molecules which were not originally in the 

 state of lowest energy, or "lowest state" for short. Such a mole- 

 cule might have been in the lowest state, until some antecedent quan- 

 tum came along and gave it energy, lifting it into a higher state; the 

 second quantum then undid the work of the first, taking away the 

 energy which the first had given and being shifted as far towards higher 

 as the former towards lower frequencies. It does not seem likely that 

 this double process occurs often, although pairs of lines with equal and 

 opposite shifts are reported in several cases. Much more commonly, 

 in all probability, the molecules which at any moment are in other 

 states than the lowest are there because of the interchanges of energy 

 which are always taking place between the particles of substances in 

 thermal equilibrium. The laws of thermal equilibrium are such, that 

 if in a substance at room-temperature the molecules have one or more 

 excited states differing from the lowest state only by fractions of a volt, 

 quite an appreciable fraction among them are at any moment in one 

 or another of those states. The higher the temperature, the greater 

 this fraction; in consonance with which fact it is observed, that the 

 warmer the scattering liquid the more prominent are these "anti- 

 Stokesian" lines. 



The shifted lines, in the light scattered at right angles to the primary 

 beam (the only direction which has been utilized to any extent), are 

 partially polarized. The electric vector is stronger in the direction 

 perpendicular to the primary beam than in the direction parallel to it, 

 as one would expect. The degree of polarization varies enormously 

 from one shifted line to another, and may be either greater or less 

 than that of the unshifted lines. Cabannes thought it to be constant 

 for lines shifted by the same amount from different primary lines, but 

 the ampler data of Carrelli do not seem to bear him out. 



The test for "coherence" of the shifted light, which is made by 

 bringing the scattering substance near to the state of "critical opales- 

 cence" where the irregularity of the arrangement of the atoms is 

 greatest — the shifted lines should brighten pari passu with the un- 

 shifted, if their light is coherent — has been made by at least four 

 people (Raman, Bogros and Rocard, Martin); but the results are 

 oddly discordant. 



One more most valuable service of the shifted lines remains to be 

 mentioned. In the foregoing pages I have stressed the fact that some 

 of them are known to agree, that is to say their frequency shifts are 

 known to coincide, with the frequencies of lines of the infra-red spec- 

 trum of the scattering substance. But there are cases in which the 



