January 21, 1909J 



NA TURE 



in 



traffic, absence of noise, and ease in cleaning and 

 repairs. 



The second of the books under notice is a third 

 edition, the first having been published in 1S94. The 

 aim of the author is 



" to give a brief discussion, from an engineering 

 standpoint, of the principles involved in highway 

 work, and to outline the more important systems of 

 construction, with a view to forming a text which 

 inav serve as a basis for a systematic study of the 

 subject." 



The edition now published has been largely revised, 

 and professes to represent the best recent practice in 

 highway work in the United States of America. 



The book is divided into eleven chapters, two of 

 which deal with " country roads," the information in 

 which may be of ser\'ice in our colonies and in new 

 countries. The other chapters treat of road economics, 

 drainage of streets and roads, macadamised roads, 

 road foundations, brick pavements, bituminous 

 pavements, stone and wood-block paving, and city 

 streets. The information given is practical and 

 useful, and covers very much the same ground as 

 the book previously noticed. In the first chapter the 

 author refers to statistics obtained by the Road 

 Enquiry Office of the United States department con- 

 cerning the cost of hauling farm produce to market, 

 with the view of basing upon the figures obtained some 

 conclusion as to the average saving resulting from 

 the improvement of roads. The general conclusion 

 arrived at appears to have been that, where the sur- 

 face of an earth road is macadamised, the load that 

 can be transported by the same number of horses may 

 be doubled, if the earth road be dry and level; but 

 where it is in a wet and rutty condition the load may 

 be increased four- or five-fold. In many instances the 

 economic advantage to an agricultural district may, 

 by allowing the hauling to be distributed over the 

 whole season, amount practically to a saving equal to 

 nearly the entire cost of hauling by permitting the 

 work to be done at times when other work is 

 impossible. 



With regard to the use of oil for preserving the 

 surface of macadamised roads and for the prevention 

 of dust, the author fully confirms all that is said in 

 Prof. Morrison's book. The quantity of oil used, 

 according to the author's experience, is about the 

 same as that given by him. The results obtained by 

 this process are deemed so satisfactory that the use of 

 oil is largely extending. 



The author refers to the use made by the French 

 road engineers of tar, either as a sufrace dressing or 

 as tar macadam for the purpose of eliminating dust. 

 It has been found that the cost of maintenance of 

 roads so treated is considerably reduced, the dust 

 nuisance is minimised, and the life of the road pro- 

 longed. The quantity of tar used for dressing the 

 surface averages about one-third of a gallon to a 

 square yard. The application of the tar is made 

 about once in two years. At the recent road confer- 

 ence held at Paris, the conclusion was arrived at that 

 tar-spreading on the surface of macadamised roads, 

 when [iroperlv carried out, is an effective means of 

 NO. 2047, VOL. 79] 



preventing dust, and that i' also protects the road 

 surface against the destructive action of trafHic 

 generally, and specially of motor-cars driven at high 

 speeds. The tarring of the main roads, where this 

 system has been carried out in this country, has also 

 been found to be very effective in preventing dust. 



VVRE .4A'D .4Ar.4LFT/C.4L GEOMETRY. 

 (i) Modern Geometry. By C. Godfre}' and A. W. 



Siddons. Pp. xvi-l-162. (Cambridge: University 



Press, 1908.) Price 45. bd. 

 (2) The Analytical Geometry of the Conic Sections. 



By the Rev. E. H. .'Vskwith, D.D. Pp. xiv-t-443. 



(London : A. and C. Black, 1908.) Price 7^. 6d. net. 

 (i) ' I 'HIS book is an interesting introduction to the 

 -L ideas and methods of modern geometry so far 

 as required for the special examination in mathematics 

 for the ordinary B.A. degree at Cambridge. It deals 

 with certain properties of triangles and of groups of 

 circles, with chapters on harmonic section, pole and 

 polar, similitude, inversion, orthogonal projection and 

 cross-ratios, with a glimpse at the principle of duality 

 both in a plane and in space, but not dealing much 

 with the properties of conies except in the interesting 

 chapter on orthogonal projection. There is a good 

 table of contents, and an index which is of great 

 assistance in finding where any subject is treated. 



The book contains a number of theorems, but is 

 written largely on the heuristic principle, as in many 

 cases proofs of theorems are left to the reader, and 

 in some cases important theorems are to be found 

 only among the examples; e.g. the fact that if 

 (AB, CD) = (AB, DC) the range is harmonic seems 

 only to be given in Ex. 525 on p. 124. Such examples, 

 which are mostly in thick type, must be treated as 

 additional theorems. 



The method of selection of theorems, especially in 

 the early part of the book, is not easy to understand. 

 Thus, two trigonometric properties of a triangle are 

 given, viz. rt/sin A = (^/sin B, &c.,anda- = d^ + c--2/iccos A, 

 why is not obvious, as they are contained in any 

 trigonometry. It seems a pity that the latter formula 

 is not proved straight from Pythagoras instead of 

 being merely borrowed from Euclid, Book ii. It would 

 be much more instructive, and would illustrate the 

 use of signs in dealing with segments of a line as 

 discussed in the authors' first chapter. 



The great charm of the book lies in its suggestive- 

 ness and in the excellent collection of examples, many 

 of which are arranged so as to lead up to the theorems 

 following them. The conciseness of the book will 

 probably prevent it from being the sole text-book, but 

 on the other hand will be of great use in fixing the 

 student's attention on the leading theorems of the sub- 

 ject, and in enabling him to master them. The 

 authors avoid any use of imaginary points, evidently 

 thinking them unsuited for beginners. 



(2) This fascinating book is the most complete text- 

 book on the subject since the great work of Dr. Sal- 

 mon. It is too difficult to be read as a first book, but 

 for more advanced students and for a university course 

 it is likely to be the standard book. The order in 



