April i8, 1901] 



NA TURE 



Few points in this book call for adverse criticism. In 

 determining the motion of the frame consisting of tangent, 

 normal and binormal at any point of a curve, it would be 

 clearer to introduce the curvature and torsion into the 

 general formulas for moving axes as measures of small 

 rotations, and it would be more convenient to make a 

 positive torsion correspond to a positive rotation (in this 

 connection the English reader may be warned that the 

 term " rechts-gewunden " is applied to what we should 

 call a "left-handed" screw). It is surprising that no 

 general method is given for expanding the coordinates in 

 powers of the arc ; the employment of these expansions 

 very much simplifies the investigation of osculating helices 

 and of the osculating cone, and can hardly be objected to 

 on the ground of being a " Kunstgriff." 



The book is written in a very pleasing style, with that 

 light and clear touch which we are accustomed to as- 

 sociate with French writers, and except in one or two 

 instances the analysis is very judiciously handled. For 

 soundness it leaves nothing to be desired and its incom- 

 pleteness is only an incentive to deeper research into the 

 subject. Specially commendable are the careful explana-" 

 tions of points which are usually slurred over. A distinct 

 feature is the introduction of imaginary quantities at an 

 early stage and the discussion of exceptional cases that 

 arise in connection with minimal lines and curves. The 

 whole book is pervaded by the ideas which are associated 

 with the name of the author's great master, Sophus Lie. 



The type is clear and good, misprints seldom occur, and 

 the figures are excellent. The practice of giving two or 

 three orthogonal projections instead of one figure in 

 perspective is much to be commended as a means of 

 conveying exact information and of training the student 

 to build up a mental conception of a figure in three 

 dimensions. 



The second volume, which is promised in the course of 

 next year, will be awaited with the greatest interest. 



R. W. H. T. H. 



OUR BOOK SHELF. 



Les Phenomenes electriques et leurs Applications. By 

 H. Vivarez. Pp. vi +574. (Paris : Carre and Naud, 

 1901.) Price Fr. 15. 



M. ViVAREZ's book covers almost the whole field of 

 modern electrical practice in a manner which is neither 

 too technical nor too popular. The daily increasing 

 applications of electricity in the industries and arts 

 render such a book valuable in two ways. In the first 

 place, it should appeal to the ordinary engineer, manufac- 

 turer or man of science who finds himself obliged to make 

 use of electricity in some way or other, and who can 

 turn to its pages for general information on the subject. 

 Secondly, the electrical engineer is generally obliged 

 nowadays to become a specialist in some particular 

 branch of his profession, and is liable, in consequence, to 

 get out of touch with other branches with which it is 

 desirable he should have a general, if not a detailed, 

 acquaintance. Such he can obtain from a book of this 

 kind. M, Vivarez has set out with the object of supply- 

 ing the wants of these persons, and also, doubtless, the 

 want of the intelligent amateur who is anxious to keep 

 pace with modern industrial progress, and he has, we 

 think, succeeded admirably in his endeavour. He has 

 produced a book which is thoroughly readable and 

 interesting, and is not at all overladen with calculation or 



NO. 1642, VOL. 63] 



technical detail. Perhaps in some cases he has shown 

 rather a tendency to skip over the less interesting parts 

 at a sacrifice of clearness, as, for example, in the section 

 on units. This may not be of much importance to the 

 electrician who will have obtained his fundamental con- 

 ceptions elsewhere, but it is a great disadvantage to the 

 non-electrical reader, who can never properly understand 

 the subject unless his knowledge of the groundwork be 

 sound — a truth he is himself too prone to ignore. 



In a book of this kind a great deal depends on 

 the proper proportioning of the space allotted to the 

 various subjects considered. On the whole, M. Vivarez 

 has divided his space very fairly, though he has given 

 rather an undue preponderance to the more modern 

 "engineering" developments. More space should, we 

 think, have been devoted to telegraphy, which is at once 

 the oldest and the most important application of electri- 

 city ; electrochemistry and metallurgy are also treated 

 somewhat too briefly. We looked in vain, also, for any 

 description of vacuum tubes ; their omission is unfor- 

 tunate, seeing of what value they have become to man- 

 kind since Rontgen's discovery. The X-ray may have 

 passed rather from the hands of the electrician to those 

 of the surgeon, but it remains, all the same, an important 

 " phenomene electrique." 



The most interesting portions of the book, to our mind, 

 are the historical parts. M. Vivarez has given a brief 

 historical account of all the important developments, and 

 has carried this to the extent of even giving a short 

 history of the industrial employment of coal. These 

 historical summaries are both interesting and valuable, 

 the more so as this is a side of science too frequently 

 neglected. Is it because the development is so rapid 

 that the history cannot keep pace with it, or, as we are 

 inclined to believe, because of the natural antipathy of the 

 average engineer to anything that tends to be literary ? 

 In any case, there can be no doubt that many engineers 

 will be found ignorant, not only of the works, but even of 

 the names of the men who have made their profession, and 

 for this reason we would recommend the book before us 

 to the student of electrical engineering ; it will show him 

 the importance of the work of the man of science, and 

 may bear useful fruit in inducing him to read original 

 papers. 



The Agricultural Changes and Laying Down Land to 

 Grass. By R. H. Elliott, 2nd edition. Pp. xii+ioi. 

 (Kelso: J. and J. H. Rutherford, 1901.) 

 Mr. Elliott has for some years been pursuing a system 

 of agriculture on his estate in Roxburgh, the essential 

 feature of which is that he secures a thick turf by the 

 use of heavy seedlings of the stronger grasses and other 

 pasture plants, and after half a dozen years or so humus 

 has accumulated to such an extent that the land may be 

 put through a course of tillage cultivation without the 

 use of any fertiliser but artificial manures. The seed- 

 mixture that he uses is characterised not only by its 

 abundance, but also by the fact that it contains the seeds 

 of such out-of-the-way plants as burnet and chicory. 

 Mr. Elliott is a firm believer in the ameliorative influence 

 of deep roots on the subsoil, and certainly his pastures 

 yield a large amount of food. He claims that the tem- 

 porary leys secured under his system are much more 

 profitable than "our two great enemies, turnips and 

 cereals," and our national statistics show that many 

 farmers are of the same opinion. The system has, no 

 doubt, answered well in the comparatively cool and 

 humid atmosphere of the Cheviot uplands, but whether it 

 is capable of successful adoption in the drier dristricts 

 of England is another matter. As Mr. Elliott has not 

 put his system into competition with the ordinary 

 methods of management of temporary grass land, it is 

 impossible to say whether it is an improvement on 

 general practice or not. Be this as it may, it does not 



