descent with the Germans, and all our well-founded appreciation of their excellence, we weary of their very virtues. One turns from their copious Gründlichkeit, as from the indispensable labour of life, and one finds in the reading of a good French text-book a never-failing pleasure.

Only the first volume of the Leçons is as yet before us, and some of our criticisms may have, on that account, to be taken with allowance; for the head, however important, is not the whole body. We see at once that there is little in common between them and the "Électricité Statique;" the plan of the work, so far as it has gone, is quite different. It originated, so the preface tells us, in the lectures of one of the authors at the Collège de France. The first volume is general and theoretical; the second is to be special and practical. As to the propriety of such an arrangement, much depends on the class of students to which it is addressed. If it is meant for such as have already a considerable knowledge of electrical phenomena, and some practice in accurately conceiving and describing them, then the plan is good. If, on the other hand, the reader is supposed to be a beginner in electrical science, knowing nothing of the phenomena, but furnished merely with the requisite mathematical knowledge, then we do not think well of it. We prefer in that case, the arrangement of the "Electricité Statique," that is, a fuller account of the phenomena upon which the fundamental principles rest, with a mathematical treatment sufficient to prevent vagueness of impression, and thereafter a detailed deductive account of the consequences of the fundamental principles, and a full description of the phenomena irrespective of their agreement or disagreement with theory. Assuming that we have to deal with a student, who has the first element of a physi cist, viz. a tolerable mathematical education, perhaps the greatest danger to be avoided is formalism, or blind swearing, in verba magistri. Nothing is more likely to encourage this, than hurried and hasty discussion of fundamental facts. Nothing in reality is gained by driving the learner express to the law of the inverse square, and then leisurely expounding its consequences. Far better, that we should first secure for him a thorough qualitative understanding of the natural phenomena; and then teach him how they can be built together upon an abstract frame-work, whose lines they will follow, not necessarily with absolute coincidence. The learner must be taught at the very outset that analysis is the servant and not the master of the physicist; and that a physical idea is not always simplified by clothing it in an analytical suit of buckram. This much as a warning to possible

students of this volume.

With one feature of the plan of these Leçons we must express unqualified satisfaction; that is the adoption of the methods of Thomson and Maxwell. At times these are so closely followed that the paragraphs are little more than translation; at other times considerable changes, chiefly in the way of simplification, are introduced. At the same time, the authors have not scrupled to borrow from other sources, where good material was to be had. They have gone on the principle of Molière, "je prends mon bien où je le trouve"; and rightly, for scientific light (unlike political or theological), is not supposed to be the property of one sect or one country. The English reader

will not find much that is new, or perhaps we should say not accessible to him in his own language, however much he may learn as to arrangement and demonstration. Originality apparently is not aimed at; the authors put before their readers such of the modern development of electrical theory as they deem most impor tant in themselves, or most likely to be useful to the physicist. We are of opinion that their selection on the whole has been judicious; and therein lies the chief merit of the book. It will, therefore, fill a great gap in French scientific literature. Possibly the second volume may help to fill the corresponding gap in the experimental part of the subject, which exists, unfortunately, in English as much as in French literature.1 How urgently such treatises are wanted, and how ignorant one nation may be of what is common-place to another, is well exemplified by the fact that a distinguished savant like Prof. Clausius lately published, both in Wiedemann's Annalen and in the Philosophical Magazine, as something new and noteworthy, the theorem of mutual potential energy and certain consequences therefrom, that have been familiar to us ever since we knew anything of electrical theory, i.e. some ten years or more.2

We are thus led to notice the one serious defect of this treatise the entire want of all references to original sources of information. These Leçons can have been meant only for those that contemplate a special study of electricity or original work of some kind bearing upon it; for such learners knowledge at first hand in some degree is essential; and who is to lead the scientific sheep to the water-springs if their responsible shepherds do not? We are well aware, from bitter experience, of the drudgery involved in this part of book-making, and of the difficulty, with all care, of being absolutely accurate and just; but utter neglect of the duty is inexcusable. Here is a provoking instance. The reader is aware that there are two different ways of representing the action of a mass of polarised molecules :-First, by a volume and a surfacedistribution of attracting centres; second, by a surface distribution alone. The first of these is undoubtedly due to Poisson. The second is continually used in German books, and attributed to Gauss (the first method, and Poisson with it, they mostly ignore). Now MM. Mascart and Joubert add to the diversity by quoting the second method as Poisson's. It is certainly news to be told that Poisson knew of any such general theorem, and a cursory re-examination of his memoirs failed to find it. Until the exact reference is given, we must hold our previous conviction that the theorem in question was virtually first given by Green in his essay on "Electricity and Magnetism" (Nottingham, 1828). It was discovered independently by Gauss, whose statement of it (the first explicit one) is given in Art. 2, “Intensitas Vis Magnetica, &c.," read December, 1832, to the Royal Society of Göttingen. His demonstration is given in Art. 36 of the "Allgemeine Lehrsätze, &c." Again, the corollaries from Gauss' Theorem of Mutual Potential Energy in Art. 1 The Germans have the admirable treatise of Wiedemann, which, in its forthcoming shape, with electrostatics added, will be the greatest expen mental treatise on electricity in existence.

2 The theorem is simply a particular discrete form of Green's theorem and in this shape was originally given by Gauss in his "Allgemeine Lehr

sätze, &c." In one point of view it is simply a property of homogeneous functions of the second degree, and plays a part in many branches of mathematics, eg. curves and surfaces of the second degree, theoretical dynamics, strains and stresses, &c.

63 may have been originally drawn by M. Bertrand; but, as no reference is given, we cannot meantime be sure whether his claim is any better than that of Clausius.

Detailed analysis being clearly out of place here, we conclude with a few running comments on the different parts of the work. The first part deals with Electrostatical Phenomena. Except that we think the introductory chapter somewhat hurried and meagre, we commend the general simplicity of the arrangement. A quasiphysical proof of most of the general propositions concerning electrified systems is given, and, we think, in the interest of the physical reader, that this is right. The seventh chapter of this part is especially recommended to the notice of our readers; there, so far as we know for the first time, Sir W. Thomson's theory of dielectrics finds its place in a text-book on Electrostatics; both here and in the corresponding chapters on Magnetism the authors show a complete appreciation and mastery of this important step in mathematical physics. Until Maxwell's treatise was written, this piece of Thomson's work had been apparently forgotten. It has lately been taken up in Germany, more especially by Helmholtz more suo. This neglect is no doubt to be explained by the equal neglect of the ideas of Faraday, of which Thomson's theory is the mathematical embodiment. The errors one occasionally finds on this subject in continental textbooks of authority are very surprising, eg. it will be found stated that a small sphere of magnetic or diamagnetic substance tends to move along the lines of force; the better diffusion of the true theory will surely tend to prevent such fundamental mistakes as this. The application of Thomson's theory to dielectrics is most interesting and important theoretically; but great difficulty has been found in verifying it experimentally, owing to the scarcity of bodies that will insulate sufficiently well. Its application to magnetics has been most successful, as our readers doubtless know.

The second part treats of electric currents, stationary and variable, and will probabiy be found well suited for the higher class of practical electricians; the account of the theory of telegraphic signalling deserves special mention. In Chapter II. of this part the authors are more cautious as to Volta's law of contact than they are at the end of the former part, knowing doubtless, as sound practicians, that they are on delicate ground.

netic action of the heavenly bodies as something fresh in a text-book.

The last part of the work deals with Electro-magnetism. The connection between a current and the equivalent magnetic shell is deduced in a very ingenious (although we scarcely think simple) way from the law of Biot and Savart. The other method, which we prefer, is also given, in which the elementary proposition is that a plane circuit, whose linear dimensions are infinitely small compared with the distance of the point at which its action is considered may be replaced by a small magnet. A separate chapter is very properly given to the Methods of Ampère, and the authors have shown their judgment in refraining from loading their pages with the various solutions of the indeterminate problem to find the elementary law of electrodynamic action of which we have lately had a superfluity. An excellent account is given of the general theory of Maxwell. The only thing we would take objection to is yet another meaning given to that overburdened word Electromotive Force; the authors use Force Electromotrice Totale in place of Maxwell's Vector Potential. The deduction of the rotation of the plane of polarisation from Hall's phenomenon is given; but Prof. Rowland's name is not mentioned in connection with it; although we are under the impression that it was first given by him in the American Journal of Mathematics.

In a supplementary chapter some examples are given of the application to electrical phenomena of the principles of Carnot. Certain of these, due to M. Lippmann, are ranged under the somewhat high-sounding title of the Conservation of Electricity. We are a little inclined to question the propriety of this phrase; but we are certainly obliged to MM. Mascart and Joubert for a succinct account of what we are to understand by it.

We shall look with much interest for the second volume of this work, in which, among other things of interest to practical electricians, we are promised a discussion of the efficiency of electric generators and electromotors, a subject on which the recent experience of the authors at the Paris Exhibition must have well qualified them to give an opinion. G. C.

OUR BOOK SHELF

Die Gasteropoden der Meeres-ablagerungen der ersten und zweiten miocänen mediterran-stufe in der Oesterreichisch -Ungarischen Monarchie. Von R. Hörnes und M. Auinger. Lieferung 1, 2, 3. (Vienna: Hölder, 18791882.)

descent with the Germans, and all our well-founded appreciation of their excellence, we weary of their very virtues. One turns from their copious Gründlichkeit, as from the indispensable labour of life, and one finds in the reading of a good French text-book a never-failing pleasure.

Only the first volume of the Leçons is as yet before us, and some of our criticisms may have, on that account, to be taken with allowance; for the head, however important, is not the whole body. We see at once that there is little in common between them and the "Électricité Statique;" the plan of the work, so far as it has gone, is quite different. It originated, so the preface tells us, in the lectures of one of the authors at the Collège de France. The first volume is general and theoretical; the second is to be special and practical. As to the propriety of such an arrangement, much depends on the class of students to which it is addressed. If it is meant for such as have already a considerable knowledge of electrical phenomena, and some practice in accurately conceiving and describing them, then the plan is good. If, on the other hand, the reader is supposed to be a beginner in electrical science, knowing nothing of the phenomena, but furnished merely with the requisite mathematical knowledge, then we do not think well of it. We prefer in that case, the arrangement of the "Electricité Statique," that is, a fuller account of the phenomena upon which the fundamental principles rest, with a mathematical treatment sufficient to prevent vagueness of impression, and thereafter a detailed deductive account of the consequences of the fundamental principles, and a full description of the phenomena irrespective of their agreement or disagreement with theory. Assuming that we have to deal with a student, who has the first element of a physicist, viz. a tolerable mathematical education, perhaps the greatest danger to be avoided is formalism, or blind swearing, in verba magistri. Nothing is more likely to encourage this, than hurried and hasty discussion of fundamental facts. Nothing in reality is gained by driving the learner express to the law of the inverse square, and then leisurely expounding its consequences. Far better, that we should first secure for him a thorough qualitative understanding of the natural phenomena; and then teach him how they can be built together upon an abstract frame-work, whose lines they will follow, not necessarily with absolute coincidence. The learner must be taught at the very outset that analysis is the servant and not the master of the physicist; and that a physical idea is not always simplified by clothing it in an analytical suit of buckram. This much as a warning to possible

students of this volume.

With one feature of the plan of these Leçons we must express unqualified satisfaction; that is the adoption of the methods of Thomson and Maxwell. At times these are so closely followed that the paragraphs are little more than translation; at other times considerable changes, chiefly in the way of simplification, are introduced. At the same time, the authors have not scrupled to borrow from other sources, where good material was to be had. They have gone on the principle of Molière, "je prends mon bien où je le trouve"; and rightly, for scientific light (unlike political or theological), is not supposed to be the property of one sect or one country. The English reader

will not find much that is new, or perhaps we should say not accessible to him in his own language, however much he may learn as to arrangement and demonstration. Originality apparently is not aimed at; the authors put before their readers such of the modern development of electrical theory as they deem most important in themselves, or most likely to be useful to the physicist. We are of opinion that their selection on the whole has been judicious; and therein lies the chief merit of the book. It will, therefore, fill a great gap in French scientific literature. Possibly the second volume may help to fill the corresponding gap in the experimental part of the subject, which exists, unfortunately, in English as much as in French literature.1 How urgently such treatises are wanted, and how ignorant one nation may be of what is common-place to another, is well exemplified by the fact that a distinguished savant like Prof. Clausius lately published, both in Wiedemann's Annalen and in the Philosophical Magazine, as something new and noteworthy, the theorem of mutual potential energy and certain consequences therefrom, that have been familiar to us ever since we knew anything of electrical theory, ¿e. some ten years or more.2

We are thus led to notice the one serious defect of this treatise-the entire want of all references to original sources of information. These Leçons can have been meant only for those that contemplate a special study of electricity or original work of some kind bearing upon it; for such learners knowledge at first hand in some degree is essential; and who is to lead the scientific sheep to the water-springs if their responsible shepherds do not? We are well aware, from bitter experience, of the drudgery involved in this part of book-making, and of the difficulty, with all care, of being absolutely accurate and just; but utter neglect of the duty is inexcusable. Here is a provoking instance. The reader is aware that there are two different ways of representing the action of a mass of polarised molecules :-First, by a volume and a surfacedistribution of attracting centres; second, by a surface distribution alone. The first of these is undoubtedly due to Poisson. The second is continually used in German books, and attributed to Gauss (the first method, and Poisson with it, they mostly ignore). Now MM. Mascart and Joubert add to the diversity by quoting the second method as Poisson's. It is certainly news to be told that Poisson knew of any such general theorem, and a cursory re-examination of his memoirs failed to find it. Until the exact reference is given, we must hold our previous conviction that the theorem in question was virtually first given by Green in his essay on "Electricity and Magnetism" (Nottingham, 1828). It was discovered independently by Gauss, whose statement of it (the first explicit one) is given in Art. 2, "Intensitas Vis Magneticæ, &c.," read December, 1832, to the Royal Society of Göttingen. His demonstration is given in Art. 36 of the "Allgemeine Lehrsätze, &c." Again, the corollaries from Gauss' Theorem of Mutual Potential Energy in Art.

The Germans have the admirable treatise of Wiedemann, which, in its forthcoming shape, with electrostatics added, will be the greatest experi mental treatise on electricity in existence.

2 The theorem is simply a particular discrete form of Green's theorem; and in this shape was originally given by Gauss in his "Allgemeine Lehr

sätze, &c." In one point of view it is simply a property of homogeneous

functions of the second degree, and plays a part in many branches ol mathematics, eg. curves and surfaces of the second degree, theoreticaf

dynamics, strains and stresses, &c.