MEASURING DRY MASSES WITH INTERFERENCE MICROSCOPES 227 



Equations (8.9) and (8.10) yield: 



Now, (n — n')e equates the path difference d between a light ray (1) 

 passing through the cell and another ray passing next to it. Then: 



Since the constant K is known, the dry mass of the cell can be derived 

 by measuring its surface s and the path difference d it originates in 

 relation to the medium encompassing it. The measurement of d is 

 made by a two-wave interference microscope, e.g. Dyson's or a full- 

 duplication polarizing interference microscope. The method applies 

 to uniform objects within which d has a well-defined constant value. 

 However, measuring the dry mass of a non-uniform object is feasible 

 by observing the zones where S is constant. The dry mass and area 

 of such zones is computed by means of formula (8.12) and the total 

 dry mass is derived by adding the elementary dry masses, d =f(x, v), 

 showing the d variations in terms of the coordinates .v and v of a point 

 of the cell's surface can be plotted. The total dry mass is derived by 

 computing graphically the integral: 



The measurements carried out using this method apply likewise to 

 transparent objects enclosing no liquid. Reverting to Fig. 8.20, the 

 object of thickness e and index // has a density q and a mass M = soe. 

 Since the path difference originated by the object is 6 = {n — n)e, 

 then: 



M=-^— . (8.14) 



{n-n')lQ 



Provided the following be known: the index /?, the area s and density o 

 of the object and the index n' surrounding it. its mass M is determined 

 by measuring, with an interference microscope, the path difference b 

 it gives rise to. 



