364 



NATURE 



[August 20, 1908 



Tin account of recent research in Western Asia, and 

 are important as giving a summary of all the latest 

 results achieved by explorers in the valleys of the 

 Tigris and Euphrates. The authors repeat the view 

 recently brought forward by Mr. King that the first 

 Babylonian dynasty was in part contemporaneous with 

 the second, and that the latter consisted of Sumerian 

 kings who had established themselves in the Sea 

 Country. This contemporaneity of the first and 

 second Babylonian dynasty, of course, brings down 

 the chronology of Babylonian history, and this fact 

 i-.iust henceforward be borne in mind by Egyptolo- 

 gists, for there are several synchronisms between 

 Babylonian and Egyptian history which have been 

 well established. The authors deal in the sixth 

 chapter with early Babylonian life and customs, and 

 this is certainly the most interesting part of the book. 

 Since Prof. Maspero wrote his history, two new 

 sources of information have been made available 

 which have greatly increased our knowledge of the 

 constitution of the early Babylonian State, and of the 

 conditions of life of the various classes of the popu- 

 lation. The most important new source is the great 

 Code of Laws drawn up by Hammurabi for the guid- 

 ance of his people, and defining the duties and privi- 

 leges of all classes of his subjects. This was dis- 

 covered by M. de Morgan at Susa, and is one of 

 the most remarkable documents that has ever fallen 

 to the lot of an excavator to unearth. The other new 

 source of information consists of a series of royal 

 letters written by kings of the First Dynasty to the 

 governors and officials of various great cities in Baby- 

 lonia. These tablets are now preserved in the British 

 Museum, and the range of subjects with which they 

 deal is enormous, and, as the authors say, " there is 

 scarcely one of them which does not add to our 

 knowledge of the period." 



The three last chapters are devoted to the most 

 recent discoveries in connection with the history of 

 the later periods of the Egyptian and Assyrian 

 Empires. A good summary is to be found here of 

 all the latest finds at Thebes, including those in the 

 Valley of the Tombs of the Kings, which have so 

 enriched the National Museum at Cairo. 



POTENTIAL ENERCrY AND THE FIGURE OF 



THE EARTH. 

 Das tnechanischc Potcniial nach Vorlcsungen, von L. 



Boltzmann hcarhcitct, und Die Theorie der Figur 



der Erdc, zur Ei\ifu)irung in die holiere Geoddsie. 



By Dr. H. Buchholtz. Erster Teil. Pp. xvi + 470. 



(Leipzig : J. A. Barth, 1908.) Price 15 marks. 

 A N intimate knowledge of the theory of potential 

 ■^*- energy is of undoubted value to the student of 

 theoretical geodesy, and it is with this object that Dr. 

 Buchholtz has given us in this book a complete and 

 exhaustive treatise on the subject since its inception 

 by Newton down to the present day. But it is not 

 alone to those interested in the complex study of the 

 figure of the earth that this portion of the book will 

 appeal; for in the application of the potential theory, 

 not only is gained a knowledge of some of the most 

 elegant mathematical theorems, but at the same time 

 a deep insight into nature is obtained. 

 NO. 2025, VOL. 78] 



It would be difficult to over-estimate the excellent 

 treatment of the subject by Dr. Buchholtz, who in 

 his preface acknowledges his debt of gratitude and 

 inspiration to his former teacher, the late Prof. Boltz- 

 mann, to whom is due a great number of the explana- 

 tions and theorems met with in the book. 



The author takes his reader through the whole 

 history of the subject, and the demonstrations and 

 mathematical proofs are very clearly put. Indeed, it 

 is the clearness and fulness of the several mathe- 

 matical steps, which are so often omitted in treatises 

 of this nature to the consequent disappointment and 

 discouragement of the majority of students, that 

 make the book so generally attractive. 



After giving the necessary definitions and explana- 

 tions of the various terms and formulae due to all 

 the learned philosophers who have made this subject 

 their particular study, Dr. Buchholtz completes thei 

 first portion of the book with two very able chapters 

 on the theory of the attraction of the ellipsoid and 

 the potential of the La Place spheroid. In both 

 chapters nothing has been omitted w-hich could help 

 the student fully to understand the complexity of this 

 difficult question. 



In the second portion of the book, which deals with 

 higher geodesy. Dr. Buchholtz has been content to 

 follow closely on the lines adopted by Col. Clarke in 

 his " Geodesy." Nothing, indeed, could be more 

 flattering to the famous English geodesist than the full 

 use he has made of his work, from which nearly all 

 the numerical examples dealing with the subject have 

 been taken in their complete form. 



Dr. Buchholtz, however, does not give an historical 

 account of the various geodetic enterprises which have 

 supplied the data for the solution of the many problems 

 introduced, and which form by no means the least 

 attractive portion of the English work. 



The two chapters which make up this second por- 

 tion of the book are confined to pure theory, but let 

 it be said at once that the treatment is most thorough 

 and complete, and the mathematical proofs extremely 

 clear and easy to follow. In this respect the book 

 is much more one for the beginner than Clarke's. 



The first chapter gives a sketch of the classical 

 theories of the form of the earth ; and the various 

 proofs by Clairant and La Place, which are of great 

 historical interest and on which are based their re- 

 spective important theorems, are fully treated. This 

 is especially the case in the sections dealing with the 

 well-known formula for the value of gravity at any 

 latitude, with La Place's law of density and the 

 deduction from it, and the observed constant of pre- 

 cession of the earth's ellipticity. The determination 

 of the figure of the earth as a form of equilibrium is 

 also fully dealt with in this chapter. 



The second chapter is devoted to the calculation of 1 

 distances, azimuths, and triangles on the spheroid € 

 and to " geodetic lines." It is chiefly taken from 

 Clarke, and indeed a large portion of it is a literal 

 translation of this work. In the matter of dealing with i 

 " geodetic lines," Dr. Buchholtz has given a far more I 

 exhaustive discussion than is to be found in most 

 books on geodesy, the section dealing with the geo- 

 metrical properties of the geodetic being excellent. 



