466 Notices respecting New Books. 



thing is arbitrary unless the reader knows more than he finds in 

 the book, whereas, if the author had gone back a single step, and 

 stated the connexion between Z and the moment of inertia of the 

 cross section, the reader would have seen that nothing more was 

 being assumed than certain geometrical results which are to be 

 found proved in many text-books*. On p. 54, and elsewhere, 

 Poncelet's formulae for approximating to *J (a 2 + b 2 ) are used, but 

 not a word is said to indicate the degree of approximation obtained 

 by them. When a student is informed that if a and b are un- 

 known he may write 0-83(a + 6) for /s/(a 2 -\- b 2 ), he certainly 

 ought to be told that in doing so he is liable to an error of rather 

 more than a sixth part of the whole, either in excess or defect. A 

 somewhat glaring example of a formula given without the needful 

 explanations occurs on p. 31, where, in an article on Continuous 

 Beams, the author gives the equation which expresses the " Theorem 

 of Three Moments :" he states in connexion with the equation that 

 the bending-moments at the extreme points of support are zero. 

 Now, if the reader happens to know more about the subject than 

 the author tells him, he will be able to understand the article, and 

 will see that as far as it goes it is quite correct. If, however, he 

 attempts to use the equation with no more information than the 

 book supplies, we should feel no certainty as to the result : e.g., 

 let the beam be supported on the two extreme points and an inter- 

 vening point (A, C, and B), and let the reader suppose that B is 

 gradually brought nearer and nearer to C ; when it reaches C he 

 will probably expect that as B is now at the extreme point the 

 bending-moment at it will be zero. The equation, how T ever, tells 

 him that it equals one fourth part of the moment of the weight of 

 the beam. The explanation of this seeming paradox would hardly 

 occur to him, viz. that when the beam is said to rest on three sup- 

 ports this means that when B and C are less than a certain dis- 

 tance apart the end of the beam must be pressed down on C, and 

 that when they come into coincidence the force by which this is 

 done must be infinitely great. Again, when the author states, 

 almost parenthetically, that the points of support are at the same 

 level, the unlearned reader is not likely to understand that the 

 sameness of the level is an essential condition of the truth of the 

 formula, and that a very small difference between the heights of 

 the points of support would render the equation quite inapplicable. 

 It would be easy to name cases in which a difference of no more 

 than an exceeding small fraction of an inch would completely alter 

 the conditions of the question. 



* On a subsequent page (p. 50) the relation is stated, but not iu such 

 a wav as to invalidate what is said above. 



