290 



THE HUMAN MOTOR 



When the displacements are very great they can be reduced 

 in any desired proportion i.e., I millimetre can represent 10 centi- 

 metres, or 1 metre, or even 1 kilometre. This is the principle 

 employed in a steam engine indicator : a curve is obtained of 

 which any one point represents both the position of the piston 

 (distance covered) and the pressure of the steam. The area of 

 the curve is the measure of the work done during the stroke ( 61) 

 of the engine. The shape of the curves obtained varies. Some- 

 times it is that of regular figures, such as a nght-angled triangle 

 (fig. 194) (R), a trapezium (T), an ellipse or circle (E,c), a segment 

 of a parabola (P), a sinusoidal curve (S), etc. The areas are 

 respectively as follows : right-angled triangle 



S = 



OB x AB 



Trapezium (fig. 195) : 

 S _AB+0? 



ft 



Semi-ellipse : 



7T X OA 



~ X AB (or AB') 



(fig. 196) ; 



m 



o o 



Fic.135. 

 Area of a trapezium. 



C X 



A * A 



FIG. 1%. 



Area of ellipse and circle. 



C X 



Semi-circle (fig. 196) : 



S =- 



x AB* 



Segment of parabola (fig. 197) : 



S = OA x AB 



