ox THE SPECIFIC GRAVITY OP SULPHURIC ACID. 9 
tains two atoms of water, and by degrees more water is added, the volume of 
the mixture suffers its greatest contraction, not as formerly, when It contains 
thre^ atoms of water for one atom of dry acid, but when its composition is 
one atom of dry acid and 7'5 atoms of water. Again, if the acid employed 
contains three atoms of water, the maximom of contraction will arrive when 
the mature has eleven atoms of water. That this is the case by every degree 
of dilution of the sulphuric acid will he seen in the following manner. Add 
to a diluted acid which eontamsy parts of dry acid, am! which has the spe- 
cific granty 4 so much water that one part of the mixture contains p parte 
of dry acid, then the mean specific gravity S, which the mixture would have 
It no contraction had taken place, is equal to 
1 
when, as formerly, 
S = 
* = 
1 -ap’ 
a'-I 
^p' 
Now, if 8 denotes the true specific gravity of the mixture, the contracted or 
s 
true volume is equal to — when the sum of the volumes of both componenta 
of the mixture are put equal to 1. As S is equal to s for the two extreme 
values,^ and/) = 0, and I have already proved that « is greater than 
I^ior all values o{p which are between the limits 0 and p', so it is clear that 
must have a minimum, or in other words, t/iatfor evenj diluted sulphuric 
acid ^hiclt^ misred mVi more water, tUre exists a maximum of contraction. 
lable lir. contains the values ofp'ands' corresponding to the several 
fromTL^^'**^*^” column, and the values of log a'deduced 
Table III. 
Acid employed. 
s'. 
loga-. 
SOj + laq 
0*81540 
1*8485 
9-7504616 
bOj 4 - 2 aq 
0-08833 
1*7613 
9-7979235 
SOj + 3aq 
0-59553 
1-6324 
9-8132605 
SO 3 4 - 4a(i 
^ * 
0-52478 
1*53333 
9-8213832 
hUj 4- 5an 
0*46905 
1*40179 
9*8283366 
SO 3 + 6 sq 
0*1.2402 
1*40749 
9*83428(14 
SO 3 4- 7aq 
0*38689 
1*36487 
9*8SiH64-l- 
SOj 4 - 9aq 
0*32921 
1-30219 
9*8481292 
SO 34 - I 2 aq 
0*26906 
1-24083 
9*8581.424 
“Oj + 15aq 
0*22748 
1-20049 
9*8657871 
quentlv the a dilution where p is less than 0*57, and where c 
tliivp eniployed for one equivalent dry acid contains more 
1 nts water, the specific gravity can be expressed by the foi 
ivh J. j Ip'^ -f- cp^ + dp*, 
coi^equently^"'^ ^ ’'’alues already determined in the equations < 
j.- - _J_ 
^ (1 — op) (1 + _|. 1^‘t ^ cp^ dp*y 
