262 



NA TURE 



{Aug. 6, 1874 



passed the wider and higher would grow the tunnel in 

 which you were groping your way. The walls of the 

 tunnel would grow thicker at every step, and their thick- 

 ness and stoutness would tell you that you were already 

 in an artery, but the inside would be delightfully smooth. 

 As you went on you would keep passing the openings 

 into similar tunnels, but the further you went on the 

 fewer they would be. Sometimes the tunnels into which 

 these openings led would be smaller, sometimes bigger, 

 sometimes of the same size as the one in which you were. 

 Sometimes one would be so much bigger that it would 

 seem absurd to say that it opened into your tunnel. On 

 the contrary, it would appear to you that you were passing 

 out of a narrow side passage into a great wide thorough- 

 fare. I dare say you would notice that every time one 

 passage opened into another the way suddenly grew 

 wider, and then kept about the same size until it joined 

 the next. Travelling onwards in this way you would, after 

 a while, find yourself in a great wide tunnel, so big that 

 you, poor little corpuscle, would seem quite lost in it. 

 Had you anyone to ask, they would tell you that it was the 

 main artery of the arm. Toiling onward through this, and 

 passing a few, but, for the most part, large openings, you 

 would suddenly tumble into a space so vast that at first 

 you would hardly be able to realise that it was the tunnel 

 of an artery like those in which you had been journeying. 

 This you would learn to be the aorta, the great artery of 

 all ; and a little further on you would be in the heart." 



In conclusion, we are sura that there is no book which 

 could be more profitably placed in the hands of the youth 

 of both sexes, as a means of intellectual training and 

 general culture, than this small work of Dr. Foster's. It 

 possesses the advantage of combining precise reasoning 

 with information on a subject which is all-important in 

 every-day life ; a subject which, if more universally under- 

 stood, would lead to the adoption, by all, of means for the 

 healthy maintenance of life which are now as systemati- 

 cally ignored as they are misunderstood. The reader is 

 referred to Prof. Huxley's " Elementary Physiology " for 

 the discussion of many subjects which the space allowed 

 and the age of the pupils make it necessary to omit in the 

 work before us. 



OUR BOOK SHELF 



Expcsilioii Gi'omiinquc dcs propriHh gcrn'rah-s As 

 Coiirbcs. Par Charles Ruchonnet (dc Lausanne). 

 Troisifeme Edition, augmentce et en partie refondue. 

 (Paris, 1S74.) 

 Elements dc Calciil approximatif. Par Charles Ru- 

 chonnet. Seconde Edition augmentde. (Paris, 1874.) 

 We have read these works with interest and somewhat of 

 surprise : with interest because the subjects are fairly 

 interesting .and are treated in the well-marked style which 

 distinguishes the writings of French mathematicians ; 

 with somewhat of surprise that the subjects treated at 

 such length should have met with such a large circle of 

 readers as is indicated by the number of editions that 

 have been called for. The first work on our list esta- 

 blishes many general properties of curves by means of 

 first principles and by the use of infinitesimals. This 

 mode of treatment, so far as we know, is confined in our 

 own text-books to a chapter or two in Dr. Salmon's 

 works, and it would be hard to find more than he has 

 given in any other work. The author himself states that 



this elementary knowledge will carry the student through 

 the book with the sole exception that a more extended 

 acquaintance with mathematics is required for an article 

 devoted to the finding the distance between a curve and 

 its osculating sphere in the neighbourhood of the point 

 of contact. The author, too, claims the major part of 

 the demonstrations as his own, though in some cases he 

 has generalised results previously given, and in some 

 cases has established known properties in a novel way. 



The work is divided into two parts ; the first treating 

 of the tangency, curvature, and osculating circle of plane 

 curves : the second part treats of the analogous pro- 

 perties for non-plane curves, and deals also with the 

 polar surface, the osculating sphere, ruled surfaces, deve- 

 lopables, and the osculating helix. There are five pages 

 of plates containing eighty clearly drawn figures. 



The " Calcul approximatif" is concerned with num- 

 bers only. M. Ruchonnet considers that he has improved 

 upon the processes given by previous writers as regards 

 their generality and precision as well as the facility with 

 which they are effected. There are six articles and two 

 notes. In the preliminarj' observations, the writer's aim is 

 concisely stated to be the turning of an expression com- 

 posed of incommensurable numbers (incommensurables 

 avec I'unitd) into a decimal to any given degree of exact- 

 ness. He here treats of absolute and relative error, and 

 then proceeds to summation. In the third article, in 

 applying his methods to multiplication and involution, 

 he sketches out the contracted process of multiplication 

 employed by Oughtred ; then follow contracted division 

 (reference made to Serret's " Arithmdtique "), evolution, 

 and functions of a single variable. Amongst the im- 

 portant additions in this edition, is a complete solution 

 of the problem " Combien de chiffres exacts faut-il cal- 

 culer d'un nombre pour pouvoir en extraire la racine 

 micme avec n chiffres exacts ? " 



Many illustrative selections might be made, but as 

 these would not be of general interest, we content our- 

 selves with recommending those who take an interest in 

 either of the subjects discussed by M. Ruchonnet to 

 taste and judge for themselves. 



LETTERS TO THE EDITOR 



[The Editor does not hold himself responsible for opinions expressed 

 by his correspondents. No notice is taken of anonymous 

 communications i\ 



Flight of Birds 

 In Nature, vol. x. p. 147, I observe a letter signed "J 

 Guthrie," and dated from the Cape, on the subject of the Flight 

 of Birds, and particularly on the "hovering" of birds. It 

 appears that one of your correspondents had referred to my chap- 

 ter on this subject in the " Reign of Law " as giving a satis- 

 factory explanation oi this phenomenon. Mr. Guthrie thinks, 

 on the contrary, that what I have there said " requires no 

 refutation ;" which is not wonderful considering the entire 

 misconception which he evinces of the explanation I have 

 given. He quotes me as affirming that " by a proper arrange- 

 ment of its wings and tail and the position of its body, a bird 

 can, wilhout mtisciilar exertion, remain suspended in a hori- 

 zontal ail-current, provided the latter be of sufficient velocity." 

 If I had said this I should have talked nonsense. But I have 

 not said it, as your readers may see by referring to the page 

 (170, first edition) to which Mr. Guthrie himself refers. What I 

 have said is, that under certain conditions of strength of air- 

 current a kestrel can maintain the hovering position " with 

 no viiible muscular motion wliatever." Mr. Guthrie omits 

 the word " visible," and probably has no idea of its force 

 and meaning in the sentence referred to. Tlie maintenance of 

 the wings and tail in the proper position, and of the body at 

 the proper angle, does in itself, of course, involve continuous 

 and difficult muscular action, although it is not visible, just as a 

 rope-dancer standing still in some tiptoe attitude may require 

 immense muscular effort although no motion be visible, and 

 although the whole aim, object, and effect of that exertion be to 

 produce stillness, and not motion. 



