Notices respecting New Boohs. 473 



In application to Engineering great superiority is claimed for 

 graphic methods over computation. The practical applications are 

 skilfully and neatly worked out ; and the study of them is an intellec- 

 tual treat (not easy reading). The scope of the work is very wide : 

 Besultants of Forces, Moments, Centre of Gravity, Moments of 

 Inertia, and Stresses in Structures, e.g. in Frames, Beams (supported, 

 fixed, and continuous), Arches (rigid and elastic), Suspension- 

 Bridges, Betaining Walls, and Tunnels are all treated by graphic 

 methods. These processes are only meant to supersede computa- 

 tion : analysis is often used for their actual elucidation ; thus the 

 explanation of the graphic methods for the Elastic Arch covers 

 20 pages of a somewhat difficult analysis. 



In some cases the graphic methods have decided advantage, 

 chiefly when the work is simply a repeated application of the 

 theorem of the "polygon of forces ;" the diagrams of these are 

 simple and can be quickly drawn. But in cases where sums of pro- 

 duets are required (e. g. in moments of forces, moments of inertia, 

 &c), the advantage is not so clear : the process increases greatly in 

 complexity as the number of variable factors in each product in- 

 creases, the diagrams become intricate, and are finally a network 

 of lines (see fig. 65-i, fig. 143 pi. I, pi. va), requiring great skill 

 in their original preparation, and -not to be unravelled in after-ex- 

 amination without careful study. The risk of mistake in construc- 

 tion, not so much from inaccurate drawing as from mistaking one 

 point or line for another, in such a network must be considerable, 

 and quite analogous to that of numerical slips in computing. Even in 

 the simple case of the sum of the products of two factors, the result 

 would probably be got more quickly with a slide-rule or Crelle's 

 mutiplication-table than by the very neat graphic process given ; 

 but in the more complex cases of several factors computation would 

 surely be quicker. 



The processes given are by no means always the shortest. Thus 

 the determination of the pressures on the supports due to a single 

 load placed on a beam requires only the division of the line repre- 

 sentative of the load into segments inversely proportional to the 

 segments of the beam on either side of the load. This requires only 

 three lines for its complete graphic solution ; but the process given 

 (the same as for the general case of many loads) requires seven 

 lines. 



When several processes are available for the same purpose, it 

 would surely suffice to give the best, unless each has peculiar ad- 

 vantages in special cases, which should then be stated. Now, for 

 finding stresses in frameworks three processes are given, covering 

 66 pages. No. L, by " Method of Sections," requiring at every 

 section a preliminary reduction of the frame on one side thereof to 

 an ideal triangle and evaluation of the Besultant force thereon : 

 this is a difficult and troublesome process. This troublesome pre- 

 liminary is avoided in No. ii., the Method of Sections proper : this 

 is nearly the same in its application as No. iii., but gives rise to 



Phil. Mag. S. 5. Vol. 14. No. 90. Dec. 1882. 21 



