STATE GEOLOGIST. 241 
Hydraulic Modulus Method. —A method of calculation generally 
used in Europe depends on the so-called hydraulic modulus, which may 
be stated as follows: 
Per cent. calcium oxide 
—— 
Per cent. silica+-per cent. alumina-_per cent. ferric oxide 
That is, the content of calcium oxide should be twice as great as the 
sum of the percentages of silica, alumina and ferric oxide. The permis- 
sible variations range from 1.8 to 2.2. This formula is much cruder 
and more inaccurate than the Chatelier formula, as it does not discrim- 
inate between the three constituents in the denominator, for the require- 
ments of the formula would be met just as well by a highly aluminous 
clay or a silicious iron ore. However, it gives a readily available check 
on the other method, provided a suitable clay is being used. The sum 
of the three constituents, silica, alumina and iron is briefly called “sili- 
cate’ ==s: The lime contents we let==c and the modulus ”. It a clay 
contains s parts of silicate, and c parts calcium oxide, the latter requires 
cn parts of silicate, which is to be subtracted from the s parts of silicate. 
The remaining parts of silicate, s—(c—n), require 1 times as much lime, 
or n[s—(c=n)] parts of calcium oxide. 
If the limestone contains s, parts of silicate and c, parts of lime, 
the former requires again n.s., parts of the latter, so that there are avail- 
able only c,—n.s, parts of calcium oxide. We know, however, that the 
clay requires n[s—(c—n) | parts of lime,and hence as many parts of lime- 
stone must be taken as will furnish the required number of parts of 
caustic lime or the ratio must be: 
€ 
(GS ==) (CLS, ) 
n 3 
This gives the formula: 
€ 
Limestone n(s—-—-) n.s—c 
n 
Clay C;—n.s,  C,—T.s, 
To illustrate:* A clay contains 63 per cent. of silicate and 25 per 
cent. of calcium carbonate=14 parts of calcium oxide. ‘The limestone 
contains 10 per cent silicate and 87.5 per cent of carbonate 49 parts of 
caustic lime. If the modulus is to be 2, the proportion of limestone and 
clay to be used is: 
Limestone 2X(63—1I4) 112 3.86 
Clay Tee 10) 29 I 
This method of calculation is not recommended for general use. 
*Schoch, Moertelmaterialien, p. 90. 
16—S. G. Bull. 3. 
