QUANTITATIVE ANALYSIS BY MEANS OF THE MICROSCOPE 213 



specifications as to proportions of sand, gravel and cement 

 and further whether the material was properly mixed and wetted. 



Estimation of Molecular Weights by Micrometric Measure- 

 ments. - Barger l has described a most ingenious micrometric 

 method whereby the molecular weight of a substance may be 

 determined, providing a large enough amount of the material 

 for weighing upon an analytical balance is available. 



A solution is made of known weight content of the substance 

 whose molecular weight is sought. A second solution of known 

 strength is also made of a substance of known molecular weight. 

 Drops of these two solutions are introduced alternately into a 

 thin-walled capillary tube having a bore whose diameter is from 

 i to 2 millimeters. The tube should be 6 to 8 centimeters long. 

 Between the drops which occupy a space about i to 3 milli- 

 meters long there must be air spaces equal to approximately 

 twice the lengths of the drops. The first and last drops should 

 be those of the standard and from two to three times the length 

 of the intermediate drops. After the drops are in place the 

 capillary tube is sealed at both ends. The tube is then laid 

 upon an object slide and cemented in place with Canada balsam 

 or other sutiable medium, the slide is then immersed in water 

 in a suitable shallow vessel and placed under the microscope. 

 By means of a micrometer the lengths of the drops are deter- 

 mined and recorded in scale divisions but not in absolute units. 

 After standing for about an hour measurements are again made. 

 Owing to differences in vapor pressure, some drops have increased 

 in length; others have decreased. 



The theory of the method is thus described by its author: 

 " Each drop is placed between two others of a different solution, 

 and can evaporate on either side into a small air-chamber. 

 This chamber is soon saturated with vapor, which can condense 

 freely on the drops. If the vapor pressures of the two solutions 

 are equal the evaporation will equal the condensation, and there 

 will be no change in volume of the drops. If, on the other 

 hand, the vapor pressures are unequal, there will be a gradient 

 of vapor pressure in the air spaces; some drops will therefore 



1 Barger. J. Chem. Soc. (London), 85 (1904), 286. 



