3i 8 APPLIED SCIENCE 



as the general condition of being in equilibrium under the force 

 applied at the joints. The manner of proceeding which seems 

 most easy is to draw, first the polygon without friction, and 

 then to sketch a modified polygon having its sides tangent to 

 the friction circles, or making the stated angle with the joints. 

 The sides of this trial polygon intersect at certain points which 

 may be called trial points. When the friction circles are not 

 very large, it is easy, by the exercise of a little judgment, to 

 draw the trial polygon so as to make these trial points agree 

 very closely with the true points of intersection, even at the 

 first attempt. Then, referring the loads to the trial points, we 

 draw a new polygon and reciprocal figure, Figs. 36 and 36a, as 

 for the frame without friction. If this second polygon has sides 

 which make the stated angle with the joints, the problem is 

 solved. Otherwise, a second selection of corrected trial points 

 must be made, and a third trial polygon drawn : it will seldom 

 if ever be necessary to make a third trial. We thus get a 

 dynamic frame which truly represents the directions of the 

 forces at every joint in the actual machine, and this frame will 

 be called the complete dynamic frame of the machine, or the 

 loaded dynamic frame with friction. The resistance which can 

 be overcome by a given effort 1 in the driving link, is shown by 

 the line 6 in the reciprocal figure 36a, which has been used as 

 an auxiliary in drawing the loaded dynamic frame, and this 

 resistance will be the actual resistance which could be overcome 

 by the given effort in the given machine, under the given con- 

 ditions as to speed, friction, mass, and weight. 



29. Application of the Method to an ordinary Horizontal 

 Single-acting Steam-Engine. In Fig. 37, p. 321, let the lines b and 

 c represent the centre lines of the connecting rod and crank of an 

 engine, while the line a represents the direction of the motion 

 of the piston. Let the line / represent the direction and position 

 of the resistance overcome ; and let this resistance be represented 

 as in previous examples by a stress between d and c. Let the 

 lines L a , L 6 , L c , and L d represent the loads on the elements a, 

 &, c, and d of this engine, where d is the bed-plate, it being re- 

 membered that these loads must be such as would balance one 

 another ; in other words, L d , the resultant reaction due to the 

 foundation, must be the equilibrant of the three others ; L f is 



