173 



X. ON THE GENERAL THEORY OF THE STEAM ENGINE. 



BY THE EDITOR. 



THE mechanical relations of the steam engine, or the principles upon which the power is 

 transmitted from the cylinder, are of a simple and elementary nature. To discuss them it is 

 only necessary to have recourse to the properties of the crank and the well understood 

 mechanical powers, the lever, the wheel and axle, and the inclined plane. In every combina- 

 tion of the ordinary mechanical powers, supposed to be divested of friction, the transmission 

 of force follows the well-known law that the efficient power is of precisely the same value at 

 each point, understanding the efficient power to be the force of resistance multiplied into the 

 velocity. Thus the effect produced, or the effective power, is measured by the weight moved, 

 or resistance overcome, multiplied by its velocity : the moving power is similarly measured 

 by its force multiplied by its velocity ; and these powers would in all cases be equal, were it 

 not for the effects of friction. To preserve distinctness, we shall designate the pressure by the 

 term pressure or force, and the effect produced, or the force multiplied into the velocity, by 

 the term power ; the former of these may likewise be called the statical, and the latter the 

 dynamical value of the force. These terms being agreed upon, it follows that in every machine 

 composed of the ordinary mechanical powers, the quantity of power developed, or the dyna- 

 mical effect of the force, would be the same at all points ; that the power, by such arrange- 

 ment, is transmitted without any change in its value, except it be such as is caused by the 

 loss resulting from friction. It would be easy to show that this principle is universal, or, in 

 other words, that it applies to every possible combination of machinery ; but this is quite 

 unnecessary for our present object, though it may perhaps not be out of place to make a few 

 observations on the nature of the crank, in addition to what has been stated in the present 

 work at page 228. 



I. ACTION OF THE CRANK. 



In the annexed figure let C D = r be the 

 length of the connecting rod; O D = p the 

 radius of the crank; the angle (D O E) de- 

 scribed = a ; the velocity at C = v ; the velocity 

 of D = v', and the distance (A C) described 

 = x. Then, the perpendicular D G = p sin. a ; 



C G = ^/ r 2 p 2 sin. 2 a ; O G = p cos. a ; C O = >/ r 3 p 2 sin. 2 a + p cos. a ; A O = r + p, 

 and therefore the value of A C, or A O C O, is 



x = r + p (>/r 2 p 2 sin. 2 + p cos. a) 



= p (1 - cos. a) + (r - V r* - p 2 sin. 2 ) (1). 



z 



