330 The Astronomer Royal on the Numerical Eocpression 



may be entirely put out of sight in the succeeding investi- 

 gations. 



2. If we compare the course of changes, in bursting, in two 

 boilers, a large one and a small one, we see that the order of 

 changes is the same in both ; but that to reduce the tempera- 

 ture of a large body of water by a certain number of degrees 

 a large volume of steam must escape, whereas, to reduce the 

 temperature of a small body of water by the same number of 

 degrees, it will suffice that a smaller volume of steam (smaller 

 in the same proportion as the bulk of water) escape. Thus it 

 will appear that the whole volume of escaping steam at a given 

 pressure, and the whole destructive energy of the steam, are 

 proportional to the bulk of water. 



3. For measure of the destructive energy of the steam, we 

 must suppose the simplest and most easily measurable case — 

 namely, that the steam, in expanding, drives a piston along a 

 uniform cylinder. It is necessary to ascertain the value of the 

 pressure F when the steam has expanded so far as to have pushed 

 the piston to the distance x : then the measure of the total energy 



is fe.F, the integral being taken from the point where the piston 



was in contact with the water to the point where the excess of 

 pressure of the steam above atmospheric pressure =0. 



4. In the case of gunpowder fired in a cannon, where the 

 weight of the ball and its velocity on emergence are found by 

 experiment, the energy of the gunpowder as acting on the ball 

 will be thus found. The pressure at distance y being F', acting 

 on a ball whose weight is W, and g being the numerical measure 

 of the acceleration produced in one second of time by gravity 

 (^ = 32*1908 if the unit of measure is the English foot, or 

 = 9*8116 if the unit is the French metre), v being the velocity 

 at distance y, and V the whole velocity acquired, then the acce- 

 leration is ~r, and therefore *>-j- = rJf, t; 2 = ^fe. F', and 



V 2 = total integral ^?^dy . F'= ™ x total energy, whence the 



W.V 2 



total energy = — ^ — . And if w be the weight of the gun- 



W V 2 



powder, the energy of one unit-weight of gunpowder = ^— : — • 



5. Several years ago (before 1849) I had desired in this way 

 to compare the destructive energy of steam from a bursting 

 boiler with that of gunpowder • and I had requested the assist- 

 ance of my friend Professor W. H. Miller of Cambridge (to 

 whose knowledge of the progress of accurate science in every 



