Rotatory Steam-Engine. 53 



which the crank revolves, — so that, in producing this effect, 

 the motion of the piston is just so much slower than the mo- 

 lion of the crank, as the power on the crank is less than that 

 on the piston ; so that here again we have a dynamical equiva- 

 lent of a greater force and a slower motion to a higher velocity 

 with a less force. 



As the piston descends and the pressure increases, it will be 

 observed that the velocity of the piston increases exactly in the 

 ratio of its effect on the crank ; so that, at the instant when the 

 pressure on the crank and piston is equal, their velocities are 

 also equal, and during the subsequent decrease of pressure on 

 the crank, the velocity of the piston diminislies in the same 

 ratio. The motion of the piston is not therefore an uniform 

 but a variable motion, its velocity varying according to the 

 pressure on the crank ; and the two dynamical effects are not 

 only equal in ultimatum, but they are equal at every instant of 

 time ; and if, on the other hand, the motion of the piston had 

 been uniform, the motion of the crank must have been a vari- 

 able quantity, as it is represented in Fig. 6, a case which does not 

 occur, and would be unsuitable at once to the nature and laws 

 of matter, and to the practical application of mechanical power. 



It appears therefore, 1. That the mean pressure on the crank 

 during the whole revolution, is less than the pressure on the 

 piston just in the proportion in which the space moved over by 

 the latter is less than the space described by the former, so that 

 the total of all the power in the one is equal to the total of all 

 the effects in the other ; 2. That the steam is not at all ex- 

 pended at the neutral points, and that its expenditure is at 

 every point exactly proportioned to the power it gives out in 

 useful effect; 3. That the velocity of the motion of the piston 

 is in the ratio of the force acting at each instant on the crank. 



These conclusions, here derived from obvious and elemen- 

 tary views of the relations of position and velocity, are origi- 

 nally deduced from the same data, by the more rigid method 

 of the calculus. In the numerical exemplification I have en- 

 deavoured to give here of that more correct process, I have 

 been compelled to select only a few points in the circuit, and 

 the result is only approximately correct ; but as the same might 

 obviously be done at any point, the result is equally satisfac- 

 tory. 



