THEORIES OF DYEING 319 



this ratio being independent of the amounts of solute and 

 solvents originally taken, i.e. : 



c - K. 



• When the molecular complexity of the solute is not identical 

 in the two solvents, there is no constant ratio of distribution, 

 the ratios of the concentrations varying with the original 

 quantities present. There is, however, a somewhat more com- 

 plex function which in such cases takes the place of the simple 

 distribution ratio. If the molecular weight of the solute in one 

 is n times as great as its molecular weight in the other solvent, 

 then, at equilibrium, the nth root of the concentration in the 

 first solvent will bear a constant ratio to the concentration in 

 the second solvent, i.e. : 



c 



= K. 



This equation was first applied to dye solutions by Georgevics, 

 who studied the manner in which indigo-carmine distributed 

 itself between the dyed fabric and the dye-bath under different 

 concentrations. Silk was dyed in a bath containing indigo- 

 carmine and sulphuric acid. The amounts of silk, dye-stuff, 

 sulphuric acid, and water were varied separately and in pairs, 

 and the amount of dye-stuff remaining in the bath after the 

 process was estimated by careful colorimetric comparison with 

 the original solution. The difference gave the amount taken 

 up by the fibre. He found that 



C f 



#C. 



= K 



in which C w = amount of dye-stuff in 100 c.c. of dye liquor after 

 the process, and C f = the amount of dye taken up by 100 grms. 

 of silk. He further found that this ratio increases slightly 

 with increasing concentration, and drew the obvious inference 

 that, according to Witt's solid solution theory, these results 

 show that the molecules of dye in the dye-liquor must be more 

 complex than those in the fibre ! 



Later Georgevics and Lowy (1896) tried to show whether the 

 value of K depended at all on the chemical nature and physical 

 structure of the dyed material. They studied the behaviour 

 of cellulose in its two forms of fibre and powder. The latter 



