350 NOTE IT CHAP. L [APPENDIX. 



NOTE TO CHAPTER I. 



1. The method by the resolution of forces developed in 

 Chapter I. is so simple and easy of application, and its principles 

 are so few and self-evident, that we have not considered it ad- 

 visable to tax the patience of the reader by any great variety 

 of practical applications. A large number of such applica- 

 tions are to be found in a most excellent little treatise by 

 Robert H. JSow, entitled The Economics of Construction in 

 Relation to Framed Structures. There are, however, a few 

 important practical points of detail, and a few general consid- 

 erations, which we think it well to notice here, and to which, 

 in illustration of the remarks in Chap. L, the reader will do 

 well to attend. 



2. In PI. 1, Fig. I. (Appendix), we have represented the 

 "Bent Crane " given by Stoney in his Theory of /Strains, p. 

 121, Art. 200. 



"We assume the following method of notation. Let all that 

 space above the Fig. be indicated by X, and all that space 

 below by Y, and the triangular spaces enclosed by the flanges 

 and diagonals by the numbers 1, 2, 3, 4, etc. The first upper 

 flange is then denoted by X 2, the second by X 4, and so on. 

 So also the first lower flange is Y 1, the next Y 3, etc. The 

 first diagonal is then X 1, the next 1 2, the next 2 3, etc.* 



The flanges are equidistant, forming quadrants of two cir- 

 cles whose radii are respectively 20 and 24 feet. The inner 

 flange is divided into four equal bays, on which stand isosceles 

 triangles, and a weight of 10 tons is suspended from the peak. 

 The scale for this and all the Figs, of PI. I. is 20 tons to an inch 

 and 10 feet to an inch. Laying off, then, the weight X Y = 10 

 tons, we form, according to the method of Chapter L, the strain 

 diagram. It will be seen at once that all the lower flanges, Y 1, 

 Y 3, etc., radiate from Y, all the upper flanges, X 2, X 4, etc., 

 from X, and everywhere the letters in the one diagram indi- 

 cate the corresponding pieces in the other. 



* For this very elegant method of notation, we are indebted to the work of 

 B. H. Bow, above alluded to. 



