July 20, 1876] 



NATURE 



247 



sea, a question which now seems to us out of date. We 

 think, considering the object of his work, the author has 

 made a mistake in filling up so much space with a com- 

 parison of opinions on these questions ; he has done the 

 same with the Gulf Stream and Ocean Current question, 

 introducing large quotations from the well-known authors 

 who have discussed it. We do not see that all this matter 

 is quite relevant to the object for which the book has been 

 published. The English readers, for whom the work must 

 be meant, are already familiar with all that Mr. van 

 Campen has brought forward, and so, we should think, 

 are the Dutch readers who are likely to take an interest 

 in the work. For both English and Dutch readers great 

 compression would here have been advisable ; and, in- 

 deed, we think the whole work might have been con- 

 tained in one volume. All these conjectures as to the 

 nature of the Polar region and the extent of the Gulf 

 Stream seem to us waste of energy, as the only method 

 of solution is to go and see. And this is what Mr. van 

 Campen wants the Dutch to do. He also discusses the — 

 to English readers, at least — somewhat threadbare ques- 

 tion of routes, and with justice shows that the route for 

 the Dutch is their old one by Spitzbergen or Novaya 

 Zemlya. He thinks they might try either a route to the 

 north-east by Novaya Zemlya somewhat on the traces of 

 the Payer- Weyprecht expedition ; or — and he seems to 

 prefer this — they might make Spitzbergen a basis of ope- 

 rations, and with two ships establish a depot, and by 

 taking plenty of time, might in this way, partly by ship 

 partly by sledge-boat, reach the Pole. Happily, however, 

 Mr. van Campen does not hold up the Pole as the only 

 and chief goal of Arctic exploration ; he shows forcibly 

 and fully the many great gains to science and humanity 

 which are to be obtained by a perfectly equipped Arctic 

 expedition. It would, we think, be fortunate both for the 

 Dutch and for science if they could be persuaded again 

 to occupy the field on which of old they reaped so much 

 glory ; and now that there is every likelihood of an inter- 

 national system of stations being established around the 

 Polar regions, we cannot see that so important, though 

 so small a nation, can any longer withhold itself 

 from doing its share of the wodd's work in this matter. 

 No doubt the Dutch have for long had much to do in 

 looking after the affairs of their own household, but now 

 there are signs that they have leisure and wealth enough 

 to take a substantial part in cosmopolitan work. Mr, van 

 Campen's arguments have already been brought under 

 the notice of several prominent Dutchmen, and we think 

 his object would be better served by the publication of 

 a compressed Dutch edition, than it seems likely to be by 

 this lecture read to the nation in the hearing of the 

 English. "As certainly as the North Pole exists is it 

 necessary to our command of the forces of nature, in the 

 interests of mankind, that we should know in what way 

 the ice and snow, the long nights and day, the tides and 

 the geological formation of lands and islands about that 

 mysterious summit of the Polar axis, react upon more 

 favourable and fully inhabited climes. The Alert and 

 Discovery have gone forth, then, at the call of England 

 only, not to serve England only, but the entire world. 

 And not less important, we may add, would prove a Dutch 

 Arctic expedition for the service of science and man- 

 kind." 



For English readers who want, in short space, to get 

 a knowledge of the arguments in favour of Arctic explora- 

 tion, of the discussion on the subject of the various routes, 

 of an " open Polar sea," and the configuration of the un- 

 known region, and on the question of ocean currents and 

 the Gulf Stream, Mr. van Campen's first volume will prove 

 useful. The second volume will, however, possess for us 

 more of novelty and interest, as it will contain a history of 

 Dutch Arctic enterprise. As there are no cuts in this 

 volume, we presume Volume II. will be well supplied 

 with illustrations and maps. We hope soon to have it 

 before us. 



OUR BOOK SHELF 



Proceedings of the London Mathematical Society. Vol. VI. 

 (London : Messrs. Hodgson, 1876.) 



Prof. Cayley contributes to this volume several memoirs 

 bearing on the theory of attraction. References to some 

 of his earlier papers on the subject are given in Tod- 

 hunter's " Histoiy." The titles of the present papers are 

 " On the Potentials of Polygons and Polyhedra," " On 

 the Potentials of the Ellipse and the Circle," " Determina- 

 tion of the Attraction of an Ellipsoidal Shell on an 

 Exterior Point," " Note on a Point in the Theory of 

 Attraction." The order of the papers will indicate' the 

 direction of growth the subject took in the author's hands. 

 Mehler has treated of the attraction of polyhedra, but 

 Prof. Cayle/s results " are exhibited under forms which 

 are very different from his, and which give rise to further 

 developments of the theory." He finds general formulae 

 for the potentials of a cone and a shell, he then takes the 

 case of a polyhedron or a polygon, obtains results for 

 rectangular pyramid, rectangle, and cuboid, and verifies 

 some of these results. The attraction of an indefinitely 

 thin ellipsoidal shell was shown by Poisson to be in the 

 direction of the axis of the circumscribed cone, this pro- 

 perty was also demonstrated geometrically by Steiner. 

 The geometrical investigation was subsequently com- 

 pleted by Prof. Adams so as to obtain from it the finite 

 expression for the attraction of the shell, a result which 

 had also been obtained analytically by Poisson. Prof. 

 Cayley states the geometrical theorems, proves them, and 

 obtains analytical expressions for the attraction of the 

 shell and for the resolved attractions. The law of attrac- 

 tion throughout is that of the inverse square. The same 

 writer also contributes a paper " On the Expression of 

 the Co-ordinates of a Point of a Quartic Curve as Func- 

 tions of a Parameter." This last is the development of a 

 process of Prof. Sylvester's. Dr. Hirst's remarks on 

 " Correlation in Space" are a mere abstract of results, a 

 fuller statement of which is reserved for a future commu- 

 nication. Prof. Wolstenholme contributes a neat piece of 

 analysis called "A New View of the Porism of the In- 

 and circum-scribed Triangle." Prof. Sylvester contributes 

 two interesting notes from M. Mannheim with reference to 

 Peaucellier's cells and their application. The Rev. W. H. 

 Laverty supplies an " Extension of Peaucellier's Theorem." 

 Mr. Routh has a paper " On Laplace's Three Particles, 

 with a Supplement on the Stability of Steady Motion ; " 

 Mr. Samuel Roberts contributes a paper " On a Simplified 

 Method of obtaining the Order of Algebraical Conditions." 

 This method is illustrated by various geometrical applica- 

 tions. Further papers of an analytical character are 

 " On the Solution of Linear Differential Equations in 

 Series," Mr. J. Hammond ; " Note on some Relations 

 between Certain Elliptic and Hyperbolic Functions," Mr. 

 J. Griffiths ; " Notes on Laplace's Coefficients," Mr. J. 

 W. L. Glaisher. In mixed mathematics we have papers 

 " On the Application of Hamilton's Characteristic Func- 

 tion to the Theory of an Optical Instalment symmetrical 



