QUANTITATIVE ANALYSIS BY MEANS OF THE MICROSCOPE 199 
preted as evidence that the material in question is abnormal, 
of inferior (or superior) grade or sophisticated. From the mag¬ 
nitude of the variation of the ratio found from that in the stand¬ 
ard or from the standard unit used, the percentage composition 
of the powdered material may be calculated.^ 
In microscopic quantitative analyses we may (i) ascertain 
the ratios to each other of the different components present and 
compare these ratios with those obtained on known standards, 
or (2) compare preparations made from the material of unknown 
percentage composition with preparations containing the same 
components in known amounts, the standards used in the com¬ 
parison having been carefully prepared in the laboratory; or 
(3) we may, by micrometric measurements compute the areas 
(or employ a planimeter) and thus obtain a clue to the percentage 
composition since volume per cents are to each other as the areas, 
and from the volume per cents weight per cents may be computed 
if the specific gravities of the components are known: these 
relations can be ascertained as described below; or (4) in the 
case of mixtures solidifying from fusion where the melt on 
freezing has been found to give rise to phases sufficiently char¬ 
acteristic in appearance yet differing according to the percentage 
composition, the recognition of these crystalline phases will 
serve to indicate the probable composition of the mass. 
The last method (4) is restricted to materials such as alloys 
or related substances. An expert, knowing the characteristic 
appearance following certain treatments, is able, on studying 
materials of known components but of unknown percentage, to 
decide upon the probable proportion of the chief constituents 
without the necessity of a quantitative analysis. This type of 
analysis by means of the microscope can be practiced only by 
experts after long study and investigation and cannot therefore 
be here discussed. 
lA thorough discussion of this sort of microscopic quantitative analysis with 
many illustrative examples will be found in: Schneider: Microbiology and Micro¬ 
analysis of Foods, p. 92. Blackiston’s Son & Co., Philadelphia, 1920. Or in: 
“ Microanalysis of Powdered Vegetable Drugs,” by the same author. Second 
Ed. p. 141. Blackiston’s Son & Co., 1920. 
