Measurement of the apparent partial volume per mass

The quantity wt can be expressed in terms of (measured) masses per volume 

The difference ps — °p0 can be measured with the help of immersion scales (see Fig. 5.13). Let Fc be the volume of the cylinders, and the mass which has to be added in one side to maintain equilibrium. We then have pa-°Po = M/Va. 

However, the apparatus that gives the most precise measurement of ps — °p0 works in a completely different manner. This apparatus was devised by Kratky et al.13 It consists of a tube, one end of which is set in a vertical wall, and of a system which excites transversal vibrations of this tube (see Fig. 5,14). The tube is filled with solution. The tube-plus-solution device constitutes a system which has its own vibration pulsation to. The mass per volume of solution ps is obtained from the observed value of to. The whole thing can be compared to a vibrating beam and the elastic forces are practically independent of the solution. 

Both immersed cylinders have the same volume V. 

pulsation a is a simple function of the mass Jt of solution in the tube 

---