360 The American Geologist. June, is99 
We have always V >v\ and further, according to the 
calculations of Lewinson-Lessing, we V>v. 
Therefore, starting with the oxides, when a compound min- 
eral (a silicate) forms in the magma, there results sometimes an 
increase and sometimes a diminution in volume, and the per- 
centage of this variation varies with the mineral. The greater 
the diminution of volume the greater the work produced, and 
consequently the greater the amount of heat disengaged. 
Therefore according to the principle of maximum wgrk, those 
minerals which diminish most in volume in forming ought to 
consolidate first. 
Suppose IOoF-^7' equals .r, and let j/ be the quantity of 
heat disengaged corresponding to the variation of volume 
X. We shall have j' equal f {x)\ but this function is not 
known. 
The author has calculated the value of V. v, v\ and V^v 
for a certain number of minerals, using analyses and specific 
weights comprised in Dana's Mineralogy of 1892, according 
to ^vhich he calculated the formulas of minerals. The atomic 
volumes and the specific weights of the elements were taken 
from the chemistry of Mendelejeff and from the tables of 
Landolt. 
Following is the table of these values ( F, v, v') includ- 
ing the specific gravit)- (5), reproduced from the author's 
text, p. 138. 
From this table the author concludes: T' > i> for the 
feldspars, leucite, nepheline, etc., and for the ferro-magne- 
sian elements V < v. That is to sa}', the latter on consoli- 
dation are accompanied by a diminution of volume, while 
the feldspars solidif}- with increase of volume (like water). 
For all minerals V < v ', but for the feldspars the diminution 
is less than 50 per cent., while for the ferro-magnesian ele- 
ments it exceeds 50 per cent. Now, according to the laws 
of thermo-dynamics, the point of solidification rises or falls 
with the pressure. 
