202 THE INERTIA OF THE CONNECTING ROD — MACGREGOR. 



and therefore if P' be the vahie of P, calculated on the 

 assumption of a massless connecting rod, requisite to produce a 



given ti, 



P'(p/s)-S = 0. 

 Hence 



P - P' ^tmv-^'^US'-^.) 

 p do p 



If, therefore, the ordinates of ff be increased in the ratio of s/p, 

 we obtain a curve giving the values of P— P' to the same scale 

 as that on which f gives the values of S' — S. We may obvi- 

 ously obtain the P — P' curve from the S' — S curve, by a process 

 similar to that by which we obtained the curve v v from the 

 curve VV above. 



The portion of the literature of graphical methods which is 

 accessible to me is very small ; and I am not at all sure that the 

 above method is new. I have been led to submit it to the Insti- 

 tute by finding, in so recent and so authoritative a work as that 

 of Prof. A. B. W. Kennedy, on the Mechanics of Machinery (1886), 

 a graphical method of solving the above problem which appears 

 to me to be erroneous. Prof. Kennedy obtains the curve v ?; in 

 the way shewn above, and then, after pointing out that it is not 

 what is known as a " velocity curve to a distance base," he pro- 

 ceeds to treat it in the way in which a curve to that kind would 

 be treated in order to obtain from it a force curve, though with- 

 out justifying this course. He thus obtains a graphical construe, 

 tion for solving the above problem, which is inconsistent with that 

 given above, and which seems to me to give inaccurate results. 



