260 OF THE REGULATION AND [SECT. vm. 



541. CASE n. In a single engine with a crank the mean excess is half the 

 moving force ; hence, 



A = 80 P a 



or the rim of the fly wheel should be double that required for a double engine 

 with the same sized cylinder, or of twice the power. x 



542. COUNTER-WEIGHTS. If the beam of a single engine be balanced when at 

 rest, that weight which it is necessary to add or subtract, to cause the piston to 

 rise at the proper speed, is called the counter-weight. The excess of force of the 

 steam overcomes the friction of the parts, and the additional weight ought to be 

 sufficient to cause it to rise and acquire double the velocity of the engine, if it 

 freely accelerated during the whole stroke. If W be the whole weight of matter 

 moved, w = the counter-weight, and / = the length of the stroke, then 



64 ** 

 W + w 



or w = 



But (art. 342.) u s = 2-66 / ; v being for one second : hence, w = 0'2 W ; con- 

 sequently, the counter-weight should, with these proportions, be one-fifth of the 

 mass of matter it has to move, supposing the whole to be collected at the ends 

 of the beam; and it is most easily found by trial. The resistance of the water in 

 the pumps will reduce the accelerated to an uniform motion of half the final 

 velocity it would have acquired with no such resistance. 2 



OF REGULATING THE POWER OF ENGINES. 



543. An engine is frequently applied where the work to be done is not 

 constantly the same ; and when the machinery of a part of it is suddenly stopped, 



1 In single acting atmospheric engines a weight has been applied to the fly wheel, such that 

 its force to turn the shaft should be exactly half the force of the steam to turn it, and placed so 

 as to rise while the piston was descending, and descend during the rise of the piston. To find 



the weight, we have 



Pa 



w being the weight, and P the mean pressure on the piston. It is supposed to be applied to the 

 rim of the fly, and the section of the continued rim should be the same as for a double engine of 

 the same power. This mode is described in ' Fenwick's Essays on Practical Mechanics,' p. 39. 

 Woolf proposed to equalize the motion of an engine by a piston working in a cylinder; this, 

 however, has no other effect than a weight, while the friction and expense of construction are 

 considerably increased. See Nich. Journal, vol. vi. p. 218. and vol. vii. p. 134. 



2 Smeaton arranged his engines to make the returning stroke iu less time than the acting one. 

 (Reports, vol. ii. p. 360.) Watt states it to be generally agreed that the reverse should be the case. 

 (Robison's Mech. Phil. vol. ii. p. 99.) The reasons for making them equal are stated in art. 340. 



