130 Notices respecting New Books. 



Chapter vi. the principle of work, here we have an account, with 

 examples, of Rocking Stones, which it will be remembered the 

 author has also treated in his Rigid Dynamics. In Chapter vii., 

 on forces in three dimensions, we have an account of much that 

 is given in Sir R. S. Ball's work on screws, and which will put 

 the student into a position to profit by a study of that treatise. 

 Chapter viii. is devoted to graphical statics and the consideration 

 of Maxwell's and Cremona's theorems. Centres of gravity fill up 

 Chapter ix. ; and the fullest treatment we have met with of strings 

 occupies Chapter x. The machines are rapidly gone through in 

 Chapter xi. The fact of the text being grounded on successive 

 annual courses of lectures readily accounts for Dr. Eouth's great 

 skill in meeting the difficulties which occur to students, and the 

 result is a work which few will be able to pass over without loss. 

 The practice has been kept up of referring "each result to its 

 original author." It is a pity one cannot do this for so many of 

 the beautiful problems in which the College papers abound. The 

 printing matches the text, but two figures (pp. 58 & 275) are 

 incorrectly drawn. "We have noticed only five small mistakes 

 besides the few pointed out in the errata. The only evidence of 

 haste appears to be in the numerous cases towards the end of the 

 book where after questions we have "May Exam.," " Coll. Exam.," 

 " Tripos Exam.," and the like, whereas in the greater part of the 

 work we have, as we ought to have, the " year " or the name of 

 the .College. 



The Foundations of Geometry. By Edwakd T. Dixo:n". 

 (Cambridge: Deighton, Bell, & Co.', 1891 ; pp. viii + 143.) 



Mb.Dixos" in the treatise before us does not provide milk for babes, 

 but strong meat for adult geometers. So he does not enter upon 

 "the question whether beginners could readily be brought to under- 

 stand his book or not." This inferior matter is postponed until his 

 preseut reasoning is admitted to be sound. We have read all 

 with great interest and can certainly commend the " foundations " 

 to authors, teachers, and all other students of geometry, bar the 

 babes, for in it they will find many valuable suggestions and acute 

 criticisms. The author has rightly stated that " the crux of my 

 theory lies in my definition of direction, for it has been chiefly 

 owing to the want of such a definition that all previous attempts 

 to make use of direction in Elementary G-eometry have failed." 

 We give here the implicit definition of Direction : " (a) a direction 

 may be conceived to be indicated by naming two points, as the 

 direction ' from one to the other.' (b) If a point move from a 

 given position constantly in a given direction, there is only one 

 path, or series of positions, along which it can pass. (Such a path is 

 called a ' direct path,' and a continuous series of points occupying 

 all positions in it, is called a ' straight line.') (c) If the direction 

 from A to B is the same as that from B to C, the direction from 

 A to C is also that same direction, (d) If two unterminated 



