198 THE INERTIA OF THE CONNECTING ROD — MA.G iRE^iOR. 



example, representing, on some convenient scale of distances, the 

 length of the arc AqA in Fig. 1. Let the ordinate AL represent, 

 on some convenient scale of velocities, the velocity of the crank- 

 pin in the crank pcjsition represented by A (Figs. 1 and 2.) A 

 smooth curve, VV, drawn through L and a sufficient number of 

 points similarly determined, gives the velocity of the crank -pin 

 in all crank positions. As seen above, if the moment of inertia 

 of the fly-wheel be sufficiently great, it will be practically a 

 straight line ; if not, it will be a known curve. 



The value of the velocity, V, of the crank-pin being known 

 for all positions of the crank, the velocity, v, of the above for- 

 mula may be obtained at once ; for, as the rod is instantaneously 

 rotating about 0, we have 



y = ^^• = k. 



S 



To tind the value of v corresponding to the crank position A, 



cut off from A A,, produced (Fig. 2), AE and AF representing 



on any scale k. and s respectively (obtained as on p. 196 and from 



Fig. 1) ; join FL, and through E draw a line parallel to FL and 



intersecting AL in M. Then we have 



AM = AL'^,= V~. 

 AF s 



Hence AM represents v to the same scale as AL represents 

 F; and M is therefore a point on the curve which gives the 

 values of v for all crank positions. Other points may be simi- 

 larly determined, and a smooth curve, v v, may then be drawn 

 through them. Its form is roughly indicated in Fig. 2, which is 

 not, however, drawn to scale. It will obviously touch the VV 

 curve at the crank position ^4i, (Figs 1 and 2), the rod in that- 

 position having a motion of translation only (0 being at an 

 infinite distance). In all other crank positions between A(^ and 

 An its ordinates will be less than the ordinates of the VV curve. 

 Obviously the lines FL and EM need not be actually drawn in 

 the above construction ; it is sufficient to mark their end points. 

 From this curve we may And the values of vdv/dc for all crank 

 positions. Thus for the position A : — Let N be a point on the 

 curve V v, near M. From M and iV draw MQ and NQ parallel to 



