474 Notices respecting New Boohs. 



stress-diagrams sometimes imperfectly " reciprocal " to the original 

 — a slight disadvantage. ]S"o. iii. is Clerk-Maxwell's beautiful pro- 

 cess : this is the simplest and easiest of the three ; its simplicity 

 seems to depend on the complete reciprocity of the stress-diagram 

 with the original figure. Methods i. and ii. might have been omitted 

 with advantage, and more space given to the last. This Chapter 

 is illustrated by numerous* well-chosen examples. The three pro- 

 cesses therein are really a graphic solution of the " conditions of 

 equilibrium" among the forces at each section or joint; as there 

 are thus only two equations for each section or joint, the magni- 

 tudes of two stresses can be found for each section or joint. Thus 

 the problem is indeterminate for a frame at any of whose joints so 

 many bars meet as to require the determiuation of more than two 

 stresses thereat. This is actually the case with two of the frames 

 (figs. 49 and 51) for which finished stress-diagrams are given with- 

 out comment. Some explanation is surely wanted in the text as to 

 how this indeterminateness (which is inherent in both) is to be met. 

 One of these (No. 51) is solved in Eankine's ' Civil Engineering,' 

 art. 576, by a method of dissecting the complex Truss into partial 

 Trusses, which bridges the difficulty by (tacitly) assuming the inter- 

 action of the partial Trusses. 



In Clerk-Maxwell's process for Frames under dead load the 

 graphic methods probably appear at their best ; but with moving 

 load the greatest stress in each bar occurs with a different state of 

 load, thus involving a tolerably complete special diagram for each 

 bar, greatly increasing the work and the intricacy of the finished 

 drawing. 



In investigating the stability of Retaining "Walls and Masonry 

 Arches, again, the graphic methods have decided advantage over 

 computation : this arises partly from the fact of the cross-sections 

 being solid, so that the limit within which the centre of pressure at 

 each joint should fall is easily known to be the middle third. The 

 tracing of lines of pressure and resistance therein is well ex- 

 plained and illustrated. 



In the case of the Arch, however, one difficulty (indeterminate- 

 ness) has not been adequately met. In general many lines of 

 pressure and resistance could perhaps be traced within the " core " 

 or admissible limits (the middle third) ; and the question is, which 

 is the true line '? The author says, " the true line of pressures is 

 that which is nearest the axial line" (art. 181); this seems 

 doubtful. Moseley's Principle of Least Resistance gives a means 

 of locating it so that the passive resistance required at the spring- 

 ing shall be the least : this seems sound for rigid material ; but its 

 applicability to non-rigid material is not so clear. 



Of all the processes given, the applications to Continuous Beams 

 and the Elastic Arch are naturally the most intricate. These are 

 masterly specimens of the power of graphic work in the hands of 



* There are several lines wrong in lower part of fig. 57 b. 



