272 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 8 



control system. If the float is more compressible than water, a rise in pres- 

 sure increases its relative density and causes it to sink. The motion of the 

 float is observed by a wide-field telescope with a scale in the ocular. The 

 equilibrium pressure is deduced from the rate of drift at pressures a little 

 low and a little high. With the pressure set at this value, the float will 

 remain stationary for as long as 15 min. In one of the setups of this general 

 type [13], a pressure change of 1 cm of mercury corresponded to a density 

 change of 0.376 X 10 -6 . The method has been used for measurement of 

 deuterium concentrations below 0.03 per cent, and a difference of 0.0002 

 atom per cent of deuterium can be determined, corresponding to a change in 

 density of 2 X 10~ 7 [48]. 



Like the pycnometer method, these buoyancy methods have the dis- 

 advantage of being tedious and not readily adaptable to rapid determinations. 



8.7. Falling Drop. In the falling-drop method the density of a sample of 

 water is determined by measuring the rate at which a drop of the sample 

 falls through an immiscible liquid of slightly lower density. This liquid, 

 the reference medium, is contained in a tube mounted vertically in a ther- 

 mostatically controlled water bath. The drops are formed with a mechanical 

 micropipette, and the rate of fall is determined by timing the interval that 

 elapses while the drop falls the distance between two fiducial marks on the 

 tube. 



For low velocities, the rate of fall is determined by a number of factors as 

 related in Stokes' law 



(miqav = j>gKa 3 (d — d )g 



where tj = viscosity of medium 

 a = radius of drop 

 v = velocity of drop 

 d = density of drop 

 d = density of medium 

 g = acceleration due to gravity 

 In order to obtain accurate and reproducible determinations of the density 

 from the rate of fall, it is essential to choose a medium, drop size, and operat- 

 ing temperature that will give falling times short enough for convenience 

 but with sufficient spread to give the required sensitivity over the range of 

 densities that will be encountered and to keep these factors constant. 



The originators of this method used a mixture of bromobenzene and xylene 

 as the medium [11,12]. By varying the proportions of these substances one 

 can obtain mixtures having a wide range of densities. The differential 

 vaporization that occurs, however, causes the composition of the mixture to 

 change from day to day. Keston et al. [14] introduced the use of 0-fluoro- 

 toluene, which has a density convenient for measuring deuterium oxide con- 



