58 



THE NATURE AND 



[SECT. u. 



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 ; 



m e 



and consequently (by art. 85.) 



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 f power of the temperature ; and it must be at 40 : consequently, A (/ 40)=e, and as 

 from 40 to 212 it is found to be -04333, we have f log. (t 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 shown in the following table : 



In the equation for the force at 1150 degrees of temperature, we have 



me _ 22100 x -9693 



(1-9693)* 



= 6925 atmospheres. 



: 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. 



