of the Destructive Energy in Steam-boiler Explosions. 333 



Comparing this with the weight of the 22 cubic feet of water 

 alone, or 597*1 kilogs., it appears that the heated materials 

 extraneous to the water produce the effect of 146*1 kilogs. 

 of water. 



11. Assuming then that there are really 743*2 kilogs. of 

 heated water, the investigation of the destructive energy pro- 

 ceeds thus. To heat 743-2 kilogs. of water from 0° to 152°-84 

 requires 743*2 x 154*38 calories = 114740 calories) and this is 

 the quantity of heat for which we must account in every stage of 

 the expansion, when the steam is allowed to blow into a cylinder 

 and drive a piston before it. Now at any instant let w be the 

 number of kilogs. of water converted into saturated steam • T the 

 common temperature of the water and steam ; Qt the number of 

 calories required to heat 1 kilog. of water from 0° to T • \ T the 

 number of calories required to convert 1 kilog. of water at 0°into 

 steam at T ; P T the pressure of saturated steam at T in milli- 

 metres of mercury at 0° • K T the same pressure in kilogrammes 

 per square decimetre (all which are given for numerical values 

 of T by Regnault) ; V T the ratio of the volume of saturated steam 

 under pressure P T to the volume of the water at 0° from which 

 that steam is derived (which is given by Fairbairn's formula). 

 Then, forming the expressions for the number of kilogs. of water 

 and steam respectively, and multiplying each by its correspond- 

 ing number of calories, and equating the aggregate to the original 

 number of calories, 



114740= (743-2 -iv) xQ T + wx\ T . 

 From this formula, with any assigned numerical value of T, w 

 (the number of kilogrammes of water converted into steam) is 

 found in numbers. And V T , the ratio of the volume of the 

 steam generated to that of the water from which it is generated, 

 is taken in numbers from Fairbairn's formula. And a kilo- 

 gramme of water occupies one cubic decimetre of volume. There- 

 fore the volume of steam, in cubic decimetres, is w x V T , of which 

 w are left in the boiler to occupy the place of the expanded water ; 

 and the volume of steam expelled from the boiler is w x (V T — 1) 



in cubic decimetres, or y^— x (V T — 1) in cubic metres.] 



12. Suppose now that the steam in escaping enters a cylin- 

 der whose section is 1 square metre, driving a piston before it. 

 Let z be the distance to which the piston has travelled (the unit 



being the metre). Then s= ^~ x (V T ~1). And the pres- 

 sure of the steam on the piston (the unit being the kilogramme) 

 is 100 x K T . Therefore the two elements, the distance of the 

 piston and the pressure upon it, can be calculated numerically 



