APPENDIX.] NOTE TO CHAP. I. 351 



"We can now at once take off the strains to scale in the vari 

 ous pieces. 



A comparison of our method with that given by Stoney for 

 the same case will be instructive, as illustrating the compara- 

 tive merits of the two. 



3. Character of tlie Strains in the Piece. One of the 

 most important points o.f our method is the ease and certainty 

 with which the character of the strains in the pieces may bo 

 determined. "We have only, as detailed at length in Chapter 1., 

 to follow round any closed polygon in the direction of the 

 forces, and then refer back to that apex of the frame where for 

 the moment we may happen to be. 



Thus for the peak, since we know that the weight acts down, 

 we follow down from X to Y, and then from Y to 1, and 1 

 back to X. Referring back now to the frame, and remember 

 ing that a force acting away from the apex means tension, and 

 towards, compression, we have at once Y 1 compression and 

 X 1 tension. 



Now for apex <z, since X 1 is tension, with respect to this new 

 apex, it must act away. We go round then from X to 1, 1 to 

 2, and 2 back to X, and then, referring these directions to the 

 corresponding pieces meeting at #, we have 1 2 compression 

 and X 2 tension. 



"We find thus all the outer flanges in tension, as evidently 

 should by simple inspection be the case. Also all the inner 

 flanges compression. As for the diagonals, they alternate, the 

 first being tension, the next compression, until we arrive at 4 5, 

 which we find to be also compression. 



A glance at the strain diagram shows how this comes about. 

 The line X 4 crosses Y 5, and thus gives us a reverse direction 

 for 45. 



In such a simple structure as the present, the character of the 

 strains would present no especial difficulty in any case ; but in 

 more complicated ones, the aid of such a simple and sure crite- 

 rion as the above is indispensable, and we have been thus even 

 prolix upon this point, the more so as it is not so much as 

 alluded to, as far as we are aware, in those few works which 

 notice the above method at all. 



4. There are other points which we may here illustrate by 

 our Fig. 



According to our first principle (Art. 3, Chapter I.), when 



