ON THE SPECIFIC GRAVITY OF SULPHURIC ACID. 5 
Table II. continued. 
Hydrate of 
sulphuric 
add in 
100 parts. 
Acid void 
of water 
in 
100 parts. 
Spedfic 
gravity 
calculated. 
Difference between tlic observed 
and calculated specific gravity 
according to 
Formula 1. 
Formula 2. 
21 
17*124 
1*14819 
— 
0*00019 
0*00066 
20 
16*308 
1*14080 
+ 
20 
_ 
11 
19 
15*493 
1*13345 
45 
_ 
30 
18 
14*673 
1*12614 
— 
154 
_ 
1.55 
17 
13*862 
1*11888 
— 
238 
_ 
226 
16 
13*046 
MII65 
— 
265 
_ 
238 
15 
12*231 
1*10H6 
— 
256 
_ 
220 
14 
11*416 
1*09731 
_ 
201 
150 
13 
10*600 
1*09019 
— 
149 
_ 
89 
12 
9*785 
1*08310 
— 
220 
_ 
152 
11 
8*969 
1*07604 
— 
174 
iOO 
10 
8*154 1 
1*06901 
— 
81 
_ 
3 
9 
7*339 
1*06201 
— 
61 
+ 
20 
8 
6*523 
1*05501. 
— 
64 
+ 
18 
7 
5*708 
1*04809 
— 
39 
+ 
42 
6 
4*892 
1*04116 
— 
66 
+ 
a 
5 
4*077 
1*03426 
— 
66 
+ 
5 
4 
3*262 
1*02737 
— 
57 
+ 
5 
3 
2*446 
1*02051 
+ 
9 
60 
2 
1*631 
1*01366 
+ 
34 
72 
1 
0*815 
1*00682 
+ 
58 
+ 
78 
If the differences A in the fourth column of the above table are squared, 
the sura of these squares will be found = 0’(X)0102088, and consequently the 
mean error is equal to O'OOI 244, and the probable error of a Blnele observa¬ 
tion = 0*00084. 
If aU the uncertainties and difficulties these observations arc subject to 
are taken into consideration, it is hardly to be supposed that tliis error is 
greater than the unavoidable errors of observations, and I believe therefore 
>at the first five terms of the series formula 1 with sufficient accuracy express 
this part of lire’s experiments. 
logarithmic formula has some advantages in the 
PP icanoii, I have as a comparison also calculated the same seventy obser¬ 
vations according to the formula 
.. . logs = a!s,.(2.) 
an oan the most probable value of the constant 
a = 0*3515280 + 0XX)021O2. 
The sum of the squares of errors is = 0*000052053, consequently the 
*?S ® " = 00008685. 
tn between the values of s observed and calculated according 
nf fL** are written in the fifth column of the above table. The sum 
the8quarcsoferror8wiUbefound=0*000618695; consequently the mean 
rror according to this formula = 0*00299, and the probalile error of a single 
observation 0-00202. 
