150 



KINEMATICS. 



[271. 



To fix the ideas, let 4 I (Fig. 68) be the horizontal middle 

 position of the beam of a beam engine; 4 is fixed and i describes 

 an arc of a circle of radius 4 I =#. We might place a counter- 

 beam 3 2 of equal length turning about the fixed end 3 so as to 

 be in its middle position parallel to 4 I and so as to make the 

 connecting link I 2 nearly vertical. The middle point of i 2 

 would then describe a looped curve whose central portion does 



Fig. 68. 



not differ very much from a straight line; connecting this 

 middle point with the piston rod, the problem would be solved. 

 But the introduction of the large counter-beam 3 2 in the 

 position indicated above would be very inconvenient. To reduce 

 the size of the mechanism the counter-beam 3 2 is placed nearer 

 to 41, into the position 3^2', and the parallelogram 1567 is 

 introduced, the piston rod being attached at 7. Owing to the 

 property of the linked parallelogram (Art. 266), the point 7 has 

 a motion similar to that of the point of intersection of 4 7 with 

 5 6 ; it describes therefore approximately a straight line. The 



