242 



NA TURE 



[July 13, 1905 



relating to stellar temperatures and stellar change, 

 and the problems of the sun's heat, the mechanical 

 pressure of light, and the re-construction of a universe 

 are the concluding chapters. The last chapter of all, 

 the validity of the new knowledge, deals with the 

 question, Is all this true? And here there is a touch 

 of philosophy. For " A system is ' true ' if it is 

 entirely consistent and coherent, if it is completely 

 self-explanatory. ' ' 



" There is no criterion of absolute truth, there is 

 no way of attaining to absolute truth, and we may 

 as well acknowledge it. Should we therefore abandon 

 the world-riddle? Assuredly not. If we may never 

 'know a system to be true, we may believe it to be 

 true. We may not have a knowledge of truth, but 

 we mav have a recognition of it." " Meanwhile this 

 system of the new knowledge ... is simply the 

 outermost circle covering the greatest area of know- 

 ledge, and while its diameter is by no means infinite, 

 it is the truest expression of the truth attainable at 

 this time, and as such is vastly useful. Its utility in 

 the evolution of knowledge is its sole apology for 

 existence." 



This work is the first attempt which I have seen 

 to bring into suitable compass, in an intelligible 

 manner, the various problems which are occupying the 

 attention of many physicists and chemists. There are 

 few errors, and these are unimportant. Whether the 

 author might not have omitted much fine writing is 

 a question of taste. But even if it be regarded as 

 ill-placed, it does not destroy the intrinsic value of 

 his work. W. R. 



THEORETICAL GEODESY. 



Trattato di Geodesia Teoretica. By Paolo Pizzetti. 

 Pp. ix + 467. (Bologna: Zanichelli, 1905.) 



SIGNOR PIZZETTI has treated the subject of 

 geodesy in a thoroughly exhaustive manner. 

 The theoretical portion of the book, dealing with the 

 formulae used in geodesy, is very ably demonstrated, 

 and the mathematical proofs of the various problems 

 are sufficiently clear to be easily followed by those 

 practically uninitiated in the subject. The same, how- 

 ever, cannot be said of the descriptive narrative of 

 geodetical operations in general. The book, in fact, 

 impresses one far more from the theoretical than from 

 the practical point of view. The absence of practical 

 demonstrations of the use of the various formulae 

 must be a great loss in a work of this nature, and 

 for this reason it compares unfavourably with such 

 standard treatises as Puissant's " Traite de Geodesic " 

 and Clarke's " Geodesy," where ample practical 

 illustrations of the application of geodetical formula 

 are given to help the student in this complicated sub- 

 ject. Even a few examples taken from any modern 

 geodetic triangulation would have been of the greatest 

 assistance. Theory alone is almost bound to have a 

 deterrent effect. 



The book contains a short and concise history of the 

 several hypotheses as to the form and constitution of 

 the earth prior to any actual geodetical operations, but 

 the account of the several measurements of " arcs of 

 meridian " is very meagre, and confines itself prac- 

 NO. 1863, VOL. 72] 



tically to mentioning those measured in Peru and 

 Lapland in the eighteenth century. 



Doubtless these " arcs " played a most important 

 part in geodesy, but subsequent measurements have 

 been of equal importance, and have been carried out 

 with the advantage of superior knowledge and more 

 perfect instruments. 



Like most Continental geodesists, the author 

 adheres to the data for the figure of the earth deduced 

 by Bessel in 1840, and it is only in an appendix that 

 any reference is made to Clarke's determination. 

 This, I think, is scarcely fair to English geodesy, 

 considering that Clarke had the advantage of a far 

 larger number of arcs whence to deduce his values, 

 as given in his excellent treatise in 18S0. A reference 

 to these values should find a place in every standard 

 work on geodesy, and it is noteworthy that the 

 American Geodetic Survey, which previously employed 

 Bessel's values, has, within recent years, discarded 

 them in favour of Clarke. This was in great part 

 due to the close agreement between Clarke's values 

 and those deduced by the Americans themselves in 

 their various arc measurements. 



Several chapters are devoted to the mathematical 

 proof of the various functions of a spheroid of revolu- 

 tion. On the whole, they are easily followed, and 

 differ but slightly from those used by Puissant in his 

 great work. The formula in chapter iv. for the deter- 

 mination of the geographical coordinates are similar 

 to those used in the Indian auxiliary tables. Here, 

 particularly, the want of definite examples is greatly 

 felt, and I cannot but think that Signor Pizzetti would 

 greatly enhance the value of his work by adding a 

 few taken at hazard from any survey. The actual 

 illustration given in this chapter is one but rarely 

 used in geodesy. 



Three chapters are given up to the description of 

 base measurements and the practical observation of 

 geodetic angles. It may at once be said that the 

 account is far from thorough, and the practical 

 student desirous of studying the methods to be 

 employed in the field would glean but a scanty know- 

 ledge. Mention is made of some of the more im- 

 portant instruments used in base measurement, such 

 as Borda's rods, Ibenaz's apparatus, and the American 

 contact duplex bars, but no word is given of Colby's 

 compensation bars, and only the slightest reference is 

 made to measurements by means of steel or invar 

 tapes or wires. There is little doubt that in future 

 all geodetic bases will be measured by the latter 

 means. Only quite recently in South Africa bases 

 have been measured with an extraordinary degree of 

 precision with invar wires. 



As regards the measurements of the angles, there 

 is but little information as to the practical work to 

 be done, but a very exhaustive treatise is given of 

 the causes of the various instrumental errors. It is 

 mainlv in agreement with those chapters in Chau- 

 venet's " Astronomy " dealing with this subject. 



Reference is made to the various instruments used 

 for astronomical work, such as transit — altazimuth — 

 and zenith telescopes. The various errors to which 

 such instruments are liable is very carefully gone 

 into. 



