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 ^ 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), 86 (1904), 286. 
