Notices respecting New Books. 299 



reasoning and expression; nor will they, making due allowance 

 for the difficulty of the undertaking, be in any way disappointed. 

 It is not an easy task to teach even the first principles of me- 

 chanics to those of whom only a knowledge of Arithmetic, a little 

 Geometry, a few rules of Mensuration, an aptitude in the use of 

 compasses, scale, and protractor, and enough Algebra to solve a 

 simple equation are demanded. Yet the author has performed 

 this task in a manner which shows that with him teaching is an 

 art of which he is an accomplished master. It is true that now 

 and then he is obliged to omit or postpone the proofs of certain 

 important theorems which involve a knowledge of Geometry and 

 Trigonometry not possessed by beginners. In the parallelo- 

 gram of forces (art. 37), for instance, the student is told to find 

 the resultant by construction. That the resultant is the diagonal 

 of a parallelogram of which the two given forces are adjacent sides, 

 is assumed to be true — the reason of the rule being given in a sub- 

 sequent chapter (137), to which, however, no clue is given. And 

 this seems a suitable place, in our notice of Mr. Twisden's book, 

 for remarking that a work containing so much matter (far more 

 than at first sight appears) ought certainly to be furnished with a 

 copious index. 



That the centre of gravity of a triangle is the intersection of the 

 three straight lines which join the vertices to the middle points 

 of the opposite sides, is a proposition also given without proof 

 (art. 18), showing that the little Greometry which Mr. Twisden 

 requires of his readers does not even extend to the proof of so simple 

 a theorem. In art. 18 (b) we are told that " any area may be 

 conceived to be made up of a number of parallel straight lines," 

 a conception which must be inconsistent with the young geo- 

 meter's notion of a straight line. By use of the principle of limits 

 in finding the centre of gravity of the surface of a triangle, this 

 inconsistency would certainly be avoided. 



The book consists of eight chapters, the first five of which are 

 made as simple as possible. Each chapter is followed by a collec- 

 tion of excellent questions, not less than four hundred altogether 

 being given in this manner. Besides, nearly two hundred complete 

 solutions of useful and interesting problems are scattered through- 

 out the book, invaluable to those who study without a teacher. 



There are also Tables of Specific Gravities, Moduli of Elasticity, 

 Tenacities, and Eesistances to Compressions. 



We recommend the book to the notice of that numerous class 

 for whom it is specially intended — those who must know mechanics 

 and yet possess but little mathematical knowledge — to Students, as 

 being suitable to the curriculum of the University of London, and 

 to all Teachers, on account of the always clear, and often ingenious, 

 developments of the most important parts of the subject. 



