388 Mr. W. J. M. Rankine on the Expansive 



6. The theorems discovered by Mr. Sylvester now afford the 

 means of greatly extending the art of designing structures by 

 transformation from structures of more simple figures ; for they 

 obviously give at once the solution of the question — given the 

 figure of a structure which is balanced and stable under a load dis- 

 tributed in a given way ; given also any perspective or homalogra- 

 phic projection of that figure ; to find how the load must be dis- 

 tributed on the transformed structure in order that it also may be 

 balanced and stable. 



7. This is not the first instance in which theorems of pure 

 science have proved to be capable of practical applications unex- 

 pected, perhaps, by their discoverers. 



LVIT. On the Expansive Energy of Heated Water. 

 By W. J. Macquorn Rankine, C.E., LL.D., F.R.SS.L.fyE.* 



AS the question of the quantity of mechanical energy which 

 a given weight of water, heated to a given temperature, is 

 capable of exerting in the act of partially evaporating without 

 receiving heat until it falls to a given lower temperature, has 

 been raised in connexion with recent researches as to the burst- 

 ing of steam-boilers, I may point out that the complete solution 

 of that question for any given liquid, together with a numerical 

 example in the case of water, is given under the head of Propo- 

 sition XVII. of a paper on Thermo-dynamics, which was commu- 

 nicated by me to the Royal Society in December 1853, read in 

 January 1854, and published in the Philosophical Transactions 

 for 1854. 



That solution is expressed by the following formula (page 161, 

 equation 65) : 



Energy exerted by each pound of fluid 



= K{| 1 -/^1 + hyp. log J)}; . . . (1) 



in which K denotes the dynamical value of the specific heat of 

 the liquid, being the product of its specific heat expressed in 

 the ordinary way by " Joule's Equivalent ;" 



t x and t% the initial and final absolute temperatures, — the abso- 

 lute zero being 274° C, or 493°*2 F. below the melting-point 

 of icef. 

 Another equation (equation 63 of the paper) gives the follow- 



* Read to the Institution of Engineers in Scotland. Communicated by 

 the Author. 



t In the original paper the absolute zero of heat was assumed to be 

 272^° C. below the melting-point of ice. The-value now adopted, 274° C, 

 is deduced from later experimental data. 



