THE INERTIA OF THE CONNECTING ROD — MACGREGOR. 197 



/give an J- 1? curve. This may readily be done, either by the 

 ordinar}'^ process of graphical multiplication or by selecting 

 points in either curve which have ordinates of simple value and 

 multiplying by them the corresponding ordinates of the other. 

 The corresponding ordinates of the J- 1? curve are thus ol^tained, 

 and the curve may then be plotted. The quantity l m being a 

 constant, this curve, read to the proper scale, will also be a curve 

 giving the values of hnic/k'^ for all crank positions ; and the 

 tangent of the inclination to the axis of crank positions, of the 

 tangent to this curve at any point, is the value of *S' — >S for the 

 corresponding crank position. 



This process, however, is laborious, and the above equation 

 may be thrown into a form which gives a much simpler graphi- 

 cal treatment. For this purpose the two variable quantities, w 

 and h, are combined in one, the product, uk, being obviously the 

 velocity of any point rigidly connected with the rod and at a 

 •distance from equal to /.'. If we call this velocity v we have 



S' - S = if (hnv"-), 

 tie " 



dv 



dc 

 In this expression there is but one quantity, v, varying with c. 

 It leads, therefore, to a very simple graphical treatment. 



Let A^A., (Fig. 2) be the straight line or axis on which dis- 

 tances (c) traversed Ijy the crank-pin are represented, AoA, for 



