2o6 



NA TURE 



[June 27, 1901 



Elemetits of Quaternions. By Sir W. Hamilton. 2nd 



edition. Edited by C. J. Joly. Vol. ii. Pp. liv + 502. 



(London : Longmans and Co., 1901.) Price z\s. net. 

 This being the second volume of the reprint of a book 

 that has become classical, and is known, by reputation 

 at least, to all mathematicians, it is unnecessary to review 

 it at much length. A comparison, however, seems to be 

 called for between the work of the master and that pub- 

 lished by his great disciple, Prof. Tail, since the first 

 edition of the " Elements " made its appearance. The 

 methods of treatment adopted differ radically. Prof 

 Tail's book is " essentially a working one," and for the 

 most part contains only those formuUe that are necessary 

 to a student when he commences the study of quater- 

 nions, and will afterwards be his working formulre for 

 general use. Sir \V. Hamilton's book, on the other hand, 

 aims at completeness. It gives fifty-three transformations 

 for the vector of torsion of a curve in space, and treats 

 the whole of the theory of curves and surfaces with the 

 same elaboration ! This wealth of methods and formulje, 

 which will only confuse the student who wishes to learn 

 quaternions merely in order to apply it in his investiga- 

 tions in physics, &c., makes the book indispensable to the 

 student who studies the subject for its own sake, or who 

 wishes to deepen or consolidate the knowledge of it that 

 he already possesses. Hamilton passes over statics and 

 rigid dynamics quickly, but he treats dynamics and 

 Fresnel's wave surface with his usual fulness. 



About a quarter of this volume is occupied by notes by 

 Prof. Joly. Among these are some on the invariants of 

 linear vector functions, on the tri-linear function, and on 

 the kinematical treatment of curves and surfaces. There 

 is a long note on the operator Vi «> symbol which 

 Hamilton does not use in the "Elements." These notes 

 are vety valuable, both because they bring the work up 

 to date, and because they are very suggestive of fields 

 for original investigation. We regret that mention is not 

 made of the properties of the quaternion that is the 

 sum of the vector and scalar potentials in the case of 

 irrotational fluid m.otion, iS;c., and that several useful 

 words, such as '' curl," " convergence," " vector potential " 

 are little used. No mention is made of the notation 

 {f^ g, h) for a vector. 



A difficulty under which quaternions at present suffers 

 is that, on the one hand, a worker in a branch of applied 

 mathematics does not care to publish papers in quaternion 

 notation for fear that few will understand him ; and, on 

 the other hand, that the lack of such papers discourages 

 the study of quaternions. The notation just referred to 

 seems likely to afford a convenient bridge between Carte- 

 sians and quaternions. An investigation of the electro- 

 magnetic wave surface by Prof Tait is quoted in a foot- 

 note. It might have been added that the surface was 

 first found by Heaviside. The omission is no doubt due 

 to Heaviside's use of vector algebra, but it is perhaps 

 allowable to consider the latter to be quaternions written 

 in a modified (but not improved) notation. H. C. P. 



Our Country's Shells and Hoiv to Knoi^' Them : a Guide 

 to the British Mollusea. By W. J. Gordon. Illus- 

 trated by A. Lambert. Pp. vii -I- 152. Thirty-three 

 coloured plates. (London : Simpkin, Marshall, 

 Hamilton, Kent and Co., Ltd.) Price ts. 

 Collectors of British shells will find this volume very 

 useful for reference. The plates include coloured pic- 

 tures of all our mollusea having shells, drawn life size 

 in most cases, and also representatives of each genus 

 without shells. Analytical tables are given to facilitate 

 identification, and there are chapters on the habits and 

 structures of the mollusea. If the collection of shells 

 induces students to study the characteristics of the living 

 animals, the book will be a means of education in natural 

 history as well as a convenient reference manual. 



NO. 1652, VOL. 64] 



LETTERS TO THE EDITOR. 



[ The Editor does not liold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to coj respond with the writers of, rejeaei 

 manuscripts intended for this or any other part of NaTUKE. 

 No notice is taken of anonvmous communications.^ 



Our Mountain Seclusion. 



In these days of continuous railway expansion it is only 

 natural and desirable that our mountain solitudes should be 

 made accessible to the general public. But obviously this 

 praiseworthy object should not be attained by the destruction of 

 the very seclusion which it is proposed 10 reach. A line of rail- 

 way, with its cuttings, tunneJs, embankments, stations, smoke 

 and noise, will carry us much more swiftly and conveniently 

 into a remote glen than the older and quieter modes of loco- 

 motion, but we then find that the charm of loneliness which 

 used to give the glen its special fascination has disappeared. 

 Where this transformation is absolutely necessary for the general 

 benefit of the public we must submit to it, though with a sigh. 

 But where the necessity or even the advantage may be disputed, 

 surely the beauty or grandeur or solitude of untouched and un- 

 spoiled nature ought to be allowed to have a potent influence in 

 the decision of such matters. 



I have just heard of an assault at present being waged against 

 the sanctities of Snowdon, and though it may be impracticable 

 to ward off or mitigate that assault, and possibly too late, even 

 if originally practicable, the attention of all lovers of scenery 

 and of all geologists may well be drawn to it. A bill which has 

 been introduced into Parliament for the construction of the 

 Porlmadoc, Beddgelert and South Snowdon Electric Railway, 

 or Tramway, has passed the House of Lords and the Examiners 

 in the House of Commons. If the line is ultimately sanctioned 

 it will greatly lessen the quiet beauty of one of the loveliest and 

 most secluded scenes in Britain — the easily accessible valley on 

 the south side of Snowdon. I understand that, as the result of 

 pressure, the Company has given way with reference to a pro- 

 posed embankment in the Pass of Abeiglaslyn, and will content 

 itself with a brief disappearance in a tunnel. But geologists 

 will learn with vexation that one important part of the scheme 

 consists in the embanking of that picturesque mountain tarn, 

 Llyn Llydaw, for the purpose of obtaining water-power. I need 

 not refer to the special interest and importance of this lake- 

 ba?in in questions of glacial and physiographical geology. 

 Though it has long been studied, it has not yet yielded up all 

 that it has to tell in these departments of science. But the 

 transformation proposed to be effected by the company will 

 silence it for ever by destroying the evidence which it can now 

 afford. 



Can nothing be yet done to save this geological sanctuary 

 from the vandalism of the modern company promoter? 



June 22. Arch. Geikie. 



The National Antarctic Expedition, 



There is one allusion in the article on the above subject last 

 week which calls for a few words from me. I refer to the first 

 introduction of the word " civilian." Through the kindness of 

 a friend I have recently had the opportunity of seeing a copy of 

 the agenda. The agenda correspond with the minutes, and the 

 word " civilian " is used in both. I had myself forwarded the 

 motion concerning the scientific leadership to the secretary to 

 be put on the agenda, and the word " civilian " certainly had 

 no place in my communication. 



At the meeting I moved, and Prof. Ilerdman seconded, the 

 motion in the terms of my original communication, and neither of 

 us noticed the change on the agenda paper. 



We must therefore plead guilty to some carelessness and 

 inattention ; but the argument in my letter to the Fellows of 

 the Royal Society is not seriously affected. hx\ important 

 change, exceeding the instructions drawn up for the guidance of 

 the Executive Committee, is not, on any reasonable view, 

 properly introduced by a single word which appears in the 

 agenda and is not noticed or used by the mover and seconder of 

 the motion. So important a question of principle obviously 

 demanded very special discussion. 



June 22. Edward B. Poulton. 



