122 Southern's Formula for the Elasticity of Steam. 



The following formula will be found to give the elasticity 

 belonging to a given temperature, and vice versa, with a suf- 

 ficient degree of accuracy for most purposes, within the range 

 of the experiments, at least, from which they have been formed. 



Let t = temperature, e = elasticity, in inches of mercury ; 



T = ^ + 52, and E = e-— , ?« = 94.250,000000. 



Then T^'^ ^ 

 = ill 



5-14 



-/£??« = T* 



But as the calculation is most easily performed by loga- 

 rithms, let L signify the logarithm of the quantity to which it 

 is prefixed : then 



5-14 LT-10'97427 = LE 



LE+ 10-97427 



5-14 



= LT. 



The following table shows the observed elasticities, those 

 derived from calculation by the formula, and the differences 

 of the two, which appear to me to be as small as can be ex- 

 pected, taking a general view. 



I believe it is now generally considered that the tempera- 

 ture 212° is that of water boiling when the barometer is at 30 

 inches instead of 29-8 ; and if in the above algebraic expres- 

 sions the following alterations be made, the results from the 

 formulae will correspond with the adjustment of that point, 

 and fully as well with the experiments generally. 



Let T = ^ + 51*3; the index of the power and of the root 

 be 5-13, instead of 5'14; and m = 87344,000000. So the 

 two last equations will be : 5-13 LT— 10*94 123 = LE; and 



LE+ 10-94123 T rr, 



5^ -^^' 



