Sec. 8.6] INDIRECT METHODS FOR MEASURING DEUTERIUM 271 



where Ad 2 o = mole fraction of D 2 



AS = d\\ — 1 relative to D free water 



8.6. Free Float. Several methods of varying the upward buoyant force 

 exerted on a body immersed in a liquid have been sufficiently developed to 

 serve as extremely sensitive methods for measuring small differences in 

 density. These differ among themselves chiefly in the manner in which 

 the effective density of a glass bulb is varied with respect to the solution 

 in which it is immersed. 



Most successful with regard to the degree of accuracy 

 attained is the method of Lamb and Lee [3,46]. A small 

 piece of soft iron is sealed in the bulb and a copper solenoid 

 wound around a beaker containing the sample. The pas- 

 sage of current through the solenoid produces a magnetic 

 force that causes the bulb to sink. At the bottom, the 

 bulb makes contact with a platinum electrode. The cur- 

 rent is then adjusted just enough to break the contact, and 

 a reading is taken on a milliammeter. The greater the 



density of the liquid, the greater is the current required to j . ,' ° a 



... ii r use d in free-float 



balance the upward buoyant force. An accuracy of methods. 



1 X 10 -7 in Ad was obtained by the original method and 



the extremely high accuracy of ±2 X 10 -8 in Ad with subsequent 



improvements. 



Another method [4-6] uses a float (Fig. 57) weighted with mercury, A, 

 and depends upon varying the temperature and determining that critical 

 temperature at which the float will neither rise nor sink. Precise ther- 

 mometry is basic to the method inasmuch as a change of 0.001°C will cause 

 the change from rising to sinking. A change of 1 X 10 -6 in density changes 

 the equilibrium about 0.006°. A plot of equilibrium temperature against 

 density gives almost but not quite a straight line. 



A somewhat more convenient method employs the Cartesian diver prin- 

 ciple in which the temperature is held constant but the hydrostatic pressure 

 on the system is varied [7-10,13]. A float similar to the one in the previous 

 method (Fig. 57) is sealed in a tube connected to a pump and manometer 

 system. The sample is distilled in vacuo into the tube containing the float. 

 It is practical to adjust the density of the float to correspond to that of water 

 at 4.58°C, at which temperature the thermal expansion of water is equal to 

 that of pyrex glass and small temperature fluctuations produce no appreci- 

 able change in the relative densities. The float is mounted in a well-stirred 

 thermostat maintained at 4.58°C by the flow of water through the ther- 

 mostat. The flow of water is regulated by a valve operated by a thyratron 



