Notices respecting New Books. 475 



one skilled in its use. The amount of drawing required for the 

 complete investigation of any one arch seems very great. PL v. a, 

 the finished (?) result for an arch, is so complex a whole (although 

 several preliminary drawings are omitted from it) as to require 

 great care for its comprehension; and even it seems (arts. 214, 219) 

 to be only a part of what is required. 



Among practical details, it is laid down (art. 121) that "an arch 

 ought to be wholly in compression." Now this principle is ob- 

 viously right for masonry ; but there can be no occasion for applying 

 it to iron or steel arches (as in art. 183) : this would surely be a 

 waste of power. 



The theory of earth -pressure given, depending on the " angle of 

 repose " and frictional stability, is complex and difficult (covering 

 23 pages before application to retaining walls). The " angle of 

 repose " is an item which in many cases can hardly be said to be 

 known at all, so that mathematical refinements are of little use. 

 Rankine's theory (which is much simpler) seems good enough for 

 such imperfect data. 



There are numerous references to foreign works on geometry 

 and graphic statics ; the influence of these is obvious in the diction. 

 The author is thoroughly at home in the practical application of 

 graphic methods ; but for a didactic work the mathematical render- 

 ing might be improved. Thus there is occasional obscurity in the 

 explanations, e. g. props, xxxix., xlii., and arts. 80, 161, 223 : results 

 to be derived as the fourth term of a proportion are commonly pre- 

 sented as [ a : b : : c : — ) a mere identity ; the insertion of the 



name or symbol for the required fourth term would be more useful 

 (e. g. in aiding its discovery in the diagrams). There is also a cer- 

 tain looseness of expression, e. g. moments termed forces (pp. 113, 

 139), the use of the term " centre of gravity " of forces (pp. 268, 

 274) : also of notation, e. g. in use of symbols A and d, 2 and \ 

 (passim), and of — in geometry (pp. 363, 364) ; also of analysis, 

 e. g. omission, removal, or change of variables under summatory 

 symbol (pp. 162, 268 ; 150, 275, 277 ; 281) ; these latter mistakes 

 generally correct themselves in the final results. There are also 

 two mistakes in the geometric theorems. Thus, Poncelet's condi- 

 tion of projectivity (prop, xxxii.) is stated in too general terms 

 without due limitations, and the example given is non-projective. 

 Again, in the proof of Pascal's theorem (prop, xlvi.), the conic and 

 its inscribed hexagon are projected into a circle and inscribed 

 hexagon with opposite sides parallel and one pair equal (which is 

 not generally possible) ; and it is stated that " the points of the 

 hexagon joined two and two concur in a point P " (and they actu- 

 ally do in the figure in consequence of its being a regular hexagon), 

 which is not generally true. 



Several minor points might be improved (in a new edition). 

 Thus there is hardly enough lettering on some of the diagrams for 

 their easy comprehension ; and in many cases the symbols given are 



