212 
ELEMENTARY CHEMICAL MICROSCOPY 
size by the number of fragments and the specific gravity of the 
fiber. 
Quantitative microchemical methods with reference to the 
handling of minute amounts of material and weighing on a 
Nernst micro balance; the titration of tiny volumes of liquid; 
the measurement of tiny volumes of gas, etc., which do not 
require the application of the microscope need no discussion here, 
since we are dealing solely with the application of the micro¬ 
scope to the solution of chemical problems. ^ 
Volume and Weight Per Cents from Area Measurements. — 
The quantitative analysis of heterogeneous material in thin sec¬ 
tions through the determination of the areas occupied by the 
different components, as ascertained from their images when 
seen in the microscope, has long been employed by petrologists. 
The process is briefly as follows: The outlines of the areas of 
the component under consideration, in a given field of the micro¬ 
scope, are traced upon coordinate paper by means of a drawing 
camera; the value of a square of the paper is ascertained with 
a stage micrometer as hereinbefore described. The areas of the 
tracing may then be computed or may be accurately determined 
by means of a planimeter. Or the preparation may be photo¬ 
graphed with a coordinate (net-ruled) ocular in place, the value 
of the rulings in the image ascertained in the usual manner and 
the areas of the different component-sections in the photogrpah 
computed.^ 
From the computed areas, volume per cents may be calcu¬ 
lated, and knowing the specific gravities of the components, 
weight per cents are easily ascertained. 
This method of quantitative microscopic analysis has recently 
been applied by Johnson to the examination of concretes. He 
has shown ^ that it is a simple matter to ascertain, whether, in a 
given concrete structure, a contractor has complied with the 
1 See Doiiau, Die Arbeitsmethoden der Mikrochemie, Stuttgart, 1913. 
Pregl: Quantitative organische Mikroanalyse, Berlin, 1917. 
2 For further details as to rock analysis and for bibliography see Johannsen, 
Petrographic Methods, p. 290. See also Coghill and Bonardi: Quantitative 
Microscopy of Pulverized Ores, Tech. Paper 211, Bur. Mines. 
^ Eng. Record, Mar. 1915. 
