Nov. 7, 1878] 



NATURE 



OUR BOOK SHELF 



Theorie der algebraischm Gleichungen. Von Dr. JuL 

 Petersen, xii. and 335 pp. (Kopenhagen, 1878.) 



The author tells us that this work owes its origin to the 

 lectures he has given on the theory of equations at the 

 Copenhagen Polytechnic School. In the preparation of 

 it he has made use of J. A. Serret's "Cours d' Algebra 

 Supdrieure," Todhunter's "Theory of Equations," and 

 Jordan' s " Traite des Substitutions." The first section 

 treats of equations in general; Cap. I. general properties 

 of algebraic equations; Cap. 11. relations between the 

 coefficients and roots; Cap. III. on elimination, de- 

 scribing the methods of Labatie, of Euler, of Sylvester, 

 of Bezout, and of Poisson ; Cap. IV. the transformation 

 of equations. The second section is devoted to the 

 algebraic solution of equations, viz., of the cubic (the 

 methods of Hudde, Lagrange, Tschimhausen, and Euler); 

 of the biquadratic (the methods of Lagrange, Descartes, 

 and others); the binomial equation, the Ouintic, the 

 breaking-up of a rational polynomial into rational 

 factors, Abelian equations (a long chapter, including the 

 division of a circumference into seventeen equal parts, 

 and the reduction of the equation x"^ =1). 



The third section is on the Numerical Solution of 

 Equations: Cap. I., on the Separation of Roots (Des- 

 cartes', Budan's, RoUe's, Sturm's, and Newton's theorems); 

 Cap. II., the Calculation of the Roots in Nimierical 

 Equations (interpolation, of Newton's Method of approxi- 

 mation, also Lagrange's and Homer's methods). The 

 fourth part, which treats of Substitution in four chapters : 

 Cap. I. Substitution in General ; Cap. II. (a long chapter, 

 including the theorems of Lagrange and Cauchy, alternate, 

 transitive, and intransitive groups, hnear substitutions, 

 &c.) ; Cap. III. Galois' Theory (this has not found its 

 way into English text-bocks ; Prof. H.J. S. Smith classes 

 Galois, for early precocity, with Pascal and Gauss); 

 Cap. IV. Applications of Galois' Theory (Abelian equa- 

 tions, the Galois and the Hessian equations). 



This bare enumeration of the principal articles will 

 show that this carefuUy-written treatise takes up some 

 ground which has not yet been opened out or even 

 ^uded to in our common text-books on equations. 



The Botany of Three Historical Records, PharaoJC s 

 Dream, The Sower, and the King^s Measure. By 

 A. Stephen Wilson. (Edinburgh : David Douglas, 

 1878.) 



This is a curious little book, the author's aim being to 

 throw what light he can," either by comparison or 

 suggestion, upon the probabihty of the plants referred to 

 in these Scripture records being this or that species of 

 cereal. Mr. Wilson seems to have given a good deal of 

 consideration to each of the above questions, which, as 

 he fsays in his preface, have only one bond of con- 

 nection between them, namely, "a common basis in the 

 botany of the cereal grasses." Notwithstanding the 

 pains the author has evidently given to each of the 

 subjects, we cannot but think that it will prove of but 

 little value, the points advanced being by no means con- 

 clusive, and even the subjects in themselves being of 

 small importance. It may be of some value to know 

 whether the cereals "stand in the same alimentary 

 relationship to mankind as they did when Joseph laid up 

 the surplus of the plenteous years in the granaries of 

 Egj-pt," because such a knowledge, if it could be proved, 

 would show the progress made in developing the pro- 

 ductive resources of these grasses, but whether the plant 

 in Pharaoh's dream was Trittcum cotnpositiim, or any 

 other species of Triticutn, is perhaps of little moment 

 to mankind at the present time. As an illustraiton of 

 what is to our mind mere speculation, we quote the 

 following from p. 6 : — " The wheats of * Minnith,' in the 



I Belka (Ezek. xxvii.) grown by the farmers of Judah and 

 Israel, seem to have been in demand in the corn- 



I market of TjTe. Probably Minnith was a remarkably 



; good locality for wheat, so that when the husbandman in 

 other districts got seed from this place they called it Min- 

 nith wheat" 



; The author's sunmiing-up of this his first " Historical 

 Record," namely, that "seven ears of corn came up 

 upon one stalk," is that it " may be wrong, and probably 

 is wrong, whereas the reading here proposed, that seven 

 ears of corn came up upon one stock, while probably 

 expressing the full meaning, can only err by defect, and 

 must necessarily be right, as embracing an essential 

 morphological fact common to all varieties of com." 



The Comtnercial Products of the Seaj or. Marine Con- 

 tributions to Food, Industry, and Art. By P. L. 

 Simmonds. With thirty-two illustrations.. (London: 

 , Griffith and Farran, 1879.) 



This is the first example this year we have had of a work 

 antedated, in this case by more than two months. We 

 cannot possibly see what is gained by this ; is it meant to 

 make readers of future years believe that a work was pub- 

 lished a year later than it really was ? If this is so, is it quite 

 honest and respectable — to put it in the mildest possible 

 form ? When one gets over Mr. Simmond's extraordinary 

 and often misleading style (for which we commit him to 

 the tender mercies of the hterarj^ Dr. Birch), it is found 

 that his work contains a great mass of useful and curious 

 information, showing great diligence in the collection of 

 facts, if not much skiU in putting them together. Mr. 

 Simmonds' work is divided into three parts, dealing with 

 food-products obtained from the sea, marine contribu- 

 tions to industr)', and marine contributions to art. 

 Detailed accoimts and statistics are given of the various 

 fisheries of the world, under the first head ; imder the 

 second head the sponge fisheries are dealt with, oils, 

 isinglass, shells, seaweed, marine salt, and other products ; 

 and under part iii. tortoise-shell, mother-of-pearl, coral, 

 i and amber. It will thus be seen that the work has a wide 

 range ; it shows how much has been done, and how 

 , much yet remains to be done by science, to make the 

 i most of the products with which the waters swarm. Alto- 

 gether the work contains much useful and interesting 

 information in a handy form. 



LETTERS TO THE EDITOR 



[T7te Editor does not hold himself responsible for opinions expressed 

 by his correspondents, Neither can he undertake to return, or 

 to correspond with the writers of, rejected manuscripts. No 

 notice is taken of anonymous communications. 



[The Editor urgently requests correspondents to keep their letters as 

 short as possible. The pressure on his space is so great that it 

 is impossible otherwise to ensure the appearatue even of com- 

 munications containing interesting and novd facts ^ 



A Question raised by the observed Absence of an 

 Atmosphere in the Moon 



It is known that there is physical evidence of an absence of 

 atmosphere in the moon. It would appear reasonable to con- 

 clude that the moon at one time l^d an atmosphere; for, 

 according to the generally-accepted principles of Laplace, whidi 

 make the sun and members of the solar system to have a common 

 nebulous origin, it would seem very extraordinary if the par- 

 ticulai offshoot of the conunon nebula which formed the moon 

 had no gaseous constituent in it. If we admit, therefore, as 

 probable that the moon at one time had an atmosphere, the 

 question naturally su^ests itself as to what has become of it. 

 Various surmises have been hazarded in reply to this. I would 

 venture to submit the following as a possible explanauon, which, 

 as far as it goes, is based on accepted principles : — It is kuown 

 to be a demonstrated fact in connection with the estabUshed 

 kinetic theory of gases that thfi velocities of the molecules of a 

 gas vary among themselves from zero to an indefinitely great 



