Components of an Igneous Rock — Williams 41 
rock. This is accomplished by A. Rosiwalt by successive ap- 
pUcation of an eye-piece micrometer to each of a series of 
lines on the cover glass of the section. The width of eacli 
grain crossed by the line is recorded in micrometer divisions 
from which the relative cross sections of the minerals can be 
deduced. Uniformity in direction or any specified system of 
drawing these lines for measurement is shown by Rosiwal 
to be unnecessary. They may be curved or irregularly 
drawn over the section so long as the stipulation is fulfilled 
that, in order to obtain the correct relations of the mineral 
constituents in a rock, a distance at least 100 times the aver- 
age diameter of the grains must be covered. For a uni- 
formly crystallized rock a rectangular network of lines will 
answer. Or, two or more series of parallel lines intersecting 
at oblique angles give equally concordant results. 
To calculate from data obtained in this way the quanti- 
tative relations of the minerals it is assumed by Rosiwal 
that these measurements represent average diameters and 
that the ratio between them is the same as between volumes. 
Percentage composition is thus expressed in terms of the vol- 
umes of minerals. (These are of course readily transferable 
to weight percentages by multiplying by the specific gravi- 
ties of the minerals.) 
Dr. Julien has since called attention to the fact that 
wliile concordant results may be obtained by this method, 
the diameters are by no means proportional to volumes 
whether the grains are conceived as cubical or spherical ; 
and that the true composition can be based only on the cube 
of the diameter, d, in the case of generally cubical grains 
and on that function of the diameter representing volume. 
.523d^, if they are spherical. In granitoid rocks that "have 
not suffered from shearing or other dynamic action, the 
grains may, according to this writer, be considered as pre- 
dominantly cubical or spherical according as they appear 
angular or have rounded outlines. Under this assumption it 
is clear the only true expressions for volumes are d^ and 
.5236d2 as stated. 
tUeber geometri-sche Gesteinsanalvp en. I'erh l\'ien Geol Reichs- 
anstalt. vol. -32, 1898, pp. 143-175. 
