If the roots of the discriminant (3A) are complex, a case which often arises in practical applications, one may write (3A) in two forms: and where When (6A) and ( 8 A ) are combinedWhen ( PREVIOUS WORKThe early studies of thermal diffusion were made in the single-stage, convection-free apparatus in which separations are very small. In 1938 Clusius and Dickel ( I ) devised the thermal diffusion column which acts as a multistage device and thus greatly magnifies the possible separations. In 1939 Furry, Jones, and Onsager ( 2 ) and, independently, Debye (3) published theories to explain the behavior of the column. A number of investigations followed which demonstrated the approximate validity of the theory of the column for gases.