58 
THE NATURE AND 
[sect. II. 
steam at that temperature and density 4137 atmospheres; and in the uncertainty 
both as to what the actual expansion of water would be in such high temperatures, 
and the decrease of its modulus, it is more prudent to be within than beyond the 
limit. But at or near the temperature 1150°, the rule will cease to be of any use, 
because then it is simply the expansive power of compressed water; and it varies 
as the quantity of water expands by a given change of temperature. 
Having thus far explained the methods by which the rules have been obtained, it 
only remains to give them the most simple form for use, with illustrative examples. 
88. Rule i. To find the force of steam from water in inches of mercury, the 
temperature being given. 1 * * * 
consequently as the § power of the volume. Hence, if e be the expansion, the original bulk being 
unity, and m the modulus, it must be 
- , = the modulus at any expansion e; 
(1+0* 
and consequently (by art. 85.) 
1 : e : : 
m 
(Ï+Ôi 
m e 
0+7)§ 
the force of compression capable of retaining the fluid in its original state of density. 
The expansion varies as the expanding power of heat, and as the temperature; hence it will be 
as the power of the temperature ; and it must be 0 at 40° : consequently, A (t—40)8=<?, and as 
from 40° to 212° it is found to be -04333, we have § log. (#—40) — 5-08909=e; which suggests 
the following Rule :—Subtract 40 from the temperature ; under the logarithm of the difference, 
write its one-third part twice over, and add all three up ; from the sum subtract 5-08909, and the 
remainder will be the logarithm of the expansion. 
The agreement of this formula and rule with experiment is showm in the following table :— 
Temperature. 
Expansion by 
formula. 
Expansion by 
experiment. 
Temperature. 
Expansion by 
formula. 
Expansion by ' 
experiment. 
40° 
0-00 
0-00 
400° 
0-1484 
64 
0-00159 
0 00133 
800 
0-5155 
102 
0-00791 
0-0076 
1150 
0-9693 
212 
00433 
0-04333 
1171 
1-0000 
In the equation for the force at 1150 degrees of temperature, we have 
me 22100 x-9693 roo , . , 
5 = — = 6925 atmospheres, 
(1+e) 5 (1-9693)1 
1 Mr. Southern’s Rule, which applies with considerable accuracy up to very high temperatures 
and pressures, is in substance as follows :— 
Add 51°-3 to the temperature, and multiply the logarithm of the sum by 5*13 ; from the pro 
duct deduct 10-94123; then, finding the natural number answering to the remainder, and 
increasing it by one tenth, the result will express the required pressure in inches of mercury.