366 NOTE TO CHAP. H. [APPENDIX. 



NOTE TO CHAPTER H 



14. The reader will observe that in Chapter I. we had given 

 forces acting at certain points of a given frame, and we found 

 by simple resolution of forces the strains in the pieces of that 

 frame. In Chapter II. we have given forces acting in certain 

 directions, and having assumed the strains, we find the equi- 

 librium polygon or frame, which, having its angles on these 

 force directions, and having these strains, will hold the given 

 forces in equilibrium. Thus in Figs. 12 (b) and (c), PI. III., of 

 the text, by choosing a pole and drawing lines to the forces in 

 the force polygon (a), we virtually assume the strains which 

 are to act upon our frame. Then lines parallel to these strains 

 in (i), forming a polygon whose angles are upon the forces, 

 must give us the frame which holds these forces in equilibrium, 

 provided we close the polygon by a line and apply at the ends 

 forces which balance each other horizontally, and whose com- 

 ponents parallel to the resultant of the forces balance the 

 forces. 



Thus the polygon maficdenm is a frame along whose 

 sides the forces S S^ etc., act, and whose reactions at the sup- 

 ports in and n must then be a o and 5 a, as given in (a). 



This frame keeping the same pole, that is, the same strains 

 we may put anywhere in the plane, its angles being always on 

 the forces, and its sides always respectively parallel, though 

 varying in length according to the position assumed. 



We might also have assumed different strains, that is, taken 

 a different pole, and constructed a different frame; but evi- 

 dently the end reactions will not be altered, and will be always 

 equal to a and 5 a, as given in (a). 



The peculiarities of the frame thus obtained are, as we see 

 further on, that its end sides always intersect upon the result- 

 ant of the forces ; its depth is always proportional (for paral- 

 lel forces) to the moment at any point ; its area to the moment 



