APPENDIX.] NOTE TO CHAP. I. 355 



and two strain diagrams the larger for vertical reactions, the 

 smaller for inclined reactions. 



This last brings out the force polygon in perhaps a clearer 

 shape than before. The weights 1 to 7 being laid off down- 

 wards, the two reactions must always bring us back to the 

 starting-point, and thus close the polygon in this case a trian- 

 gle, in the preceding case a straight line, and in the case of Fig 

 6, Art. 10., Chap. I., a true polygon. Both strain diagrams 

 illustrate the check we have upon the accuracy of the work. 

 The second half should be perfectly symmetrical with the first, 

 and the lines Y It, and points k in each should coincide. 



We have here also to notice a point which in roof trusses is 

 of frequent occurrence, and may, if not noticed, cause diffi- 

 culty. 



"We have already observed in Art. 9, Chap. I., that we can 

 always find the strains in the pieces which meet at an apex, 

 provided only two are unknown. Now in the strain diagram 

 to Fig. IV., we readily determine the strains in Xa, Y a, X J, 

 a b, Y c and b c successively, and arrive finally at apex 2, where 

 we have the two known strains in X b and b <?, and wish to find 

 the strains in three pieces, viz., X d, d h and c h. At first sight 

 this seems impossible. If, however, we assume that the pieces 

 of the frame can take only strains of a certain kind, as, for 

 instance, h d only tension, and not compression, the problem is 

 perfectly determinate. This assumption is easily realized in 

 practice. Thus if h d is a rod of small diameter, it cannot 

 act as a compression member at all. Moreover, the strain 

 of tension in h d must evidently be precisely equal to that in 

 b C, already found. We have then to form a closed polygon 

 with the weight at 2 and the known strains in X b and b c, whose 

 other three sides shall be parallel to Xd, h d and c h respec- 

 tively, and in which, moreover, the strain in h d shall be equal 

 to that in b c, and where both these strains must be, when the 

 polygon is followed round according to rule, tensile. We have 

 evidently, then, in accordance with these conditions, only the 

 polygon 2X6?A<?X, thus finding the point d, from which 

 we can now proceed to find e, etc. The points a, 5, d and e are 

 evidently in the same straight line parallel to c h. This point 

 is one of importance, and the reader should carefully follow 

 the above remarks with the aid of the Fig. 



The strain diagram thus constructed shows us many facts 

 23 



