117 maining errors are also due to the height-differences in the terrain and the result is necessarily that the correspondence between adjacent rectifications is worse than in the former case. The practical value of the maps will therefore be deminished, although the overall absolute precision of the situation of points may be practically the same in both cases. For these reasons the idea of Dr. Arnold will probably not find a wide field of application. A. J. van der Weele Grossmann, W. : Grundzifge der Ausgleichungsreehnung nach der Methode der kleinsten Quadrate nebst Anwendungen in der Geodd.~ie. 15 X 23 cm, 269 pages. Springer- Verlag, Berlin, 1954. DM 19.80. This book originates from lecture notes which were already published in a more simple form in 1952. This new edition is well got up and clearly written. Its contents might be characterized as an excellent version of the first part of the well-known manual by Jordan (-Eggert). Many well-chosen examples such as applications in the domain of triangulation and traverse measurements, ~lotogrammetry and altimetry explain the theory. If a text-book is desired on the classical theory of errors then this one can be recommended in every respect. Yet, personally, I very much regret that the author has restricted himself in the choice of his theme. The development of the theory of Gauss has not only been continued for geodesy but, as may be remarked, since 1920 this development has especially been fruitful for the mathematical statistics and calculus of probability. The question could be asked whether the author's reference to German litterature only, means that modern vieus regarding the essence of adjustment have escaped the author's attention like for instance J. M. Tienstra's articles published in the Bulletin G~od~sique 1947 and 1948 which are not mentioned at all. Knowing the author personally I cannot believe this. More likely it is a matter of personal taste as this is also expressed by his neglecting the application of the calculus of matrices which has also been published in Germany. As there is no accounting for taste, I could leave things as they are, were it not that on the one hand many theoretical problems can be posited more regorously by statistics and matrix calculus and that on the other hand the numerical problems can be solved more comprehensively. Thus it seems to me that by using the modern theory of mathematical statistics and calculus of matrices questions such as definition of systematic errors, true errors and residuals, rejection of observations, limitedness of Taylor development of functions, influence of rounding-off errors, co-operation of systematic and rand- om errors, direct and deduced observations, estimation of mean square or standard errors, accuracy and precision~ heterogeneous observations of for instance angles and lengths, significance of the law of errors of Gauss, nature of aajustment, significance and nature of error ellipses (to mention only a few of the questions dealt with in this book) can be treated more efficiently and will be more comprehensible to the student. May the above remarks be taken as a positive criticism for the very reason that there is so much to be appreciated in the book reviewed here, like the treatment of the error ellipses, the symbolic method of writing of Tienstra for the application of the law of propagation of errors, the Boltz's method of solving a system of linear equations and many other problems. The clearness of style has been praised before. We wish the authoL" that soon a second edition of his book will be necessary in which case the above remarks may perhaps lead to a broadening of the basis. W. Baarda

Gorssman, W.: Grundzüge der Ausgleichungsrechnung nach der Methode der kleinsten Quadrate nebst Anwendungen in der geodäsie. 15 X 23 cm, 269 pages. Springer Verlag, Berlin, 1954

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Page 1: Gorssman, W.: Grundzüge der Ausgleichungsrechnung nach der Methode der kleinsten Quadrate nebst Anwendungen in der geodäsie. 15 X 23 cm, 269 pages. Springer Verlag, Berlin, 1954

117

maining errors are also due to the height-differences in the terra in and the result is necessarily that the correspondence between adjacent rectifications is worse than in the former case. The practical value of the maps will therefore be deminished, although the overall absolute precision of the situation of points may be practically the same in both cases.

For these reasons the idea of Dr. Arnold will probably not find a wide field of application.

A. J. van der Weele

Grossmann, W. : Grundzifge der Ausgleichungsreehnung nach der Methode der kleinsten Quadrate nebst Anwendungen in der Geodd.~ie. 15 X 23 cm, 269 pages. Springer- Verlag, Berlin, 1954. DM 19.80.

This book originates from lecture notes which were already published in a more simple form in 1952. This new edition is well got up and clearly written. Its contents might be characterized as an excellent version of the f i rs t pa r t of the well-known manual by Jordan (-Eggert) . Many well-chosen examples such as applications in the domain of triangulation and traverse measurements, ~ lo togrammetry and al t imetry explain the theory. I f a text-book is desired on the classical theory of errors then this one can be recommended in every respect.

Yet, personally, I very much regret that the author has restricted himself in the choice of his theme. The development of the theory of Gauss has not only been continued for geodesy but, as may be remarked, since 1920 this development has especially been f ru i t fu l for the mathematical statistics and calculus of probability. The question could be asked whether the author 's reference to German l i t terature only, means that modern vieus regarding the essence of adjustment have escaped the author 's attention like for instance J. M. Tienstra 's articles published in the Bulletin G~od~sique 1947 and 1948 which are not mentioned at all. Knowing the author personally I cannot believe this. More likely it is a mat te r of personal taste as this is also expressed by his neglecting the application of the calculus of matrices which has also been published in Germany.

As there is no accounting for taste, I could leave things as they are, were it not tha t on the one hand many theoretical problems can be posited more regorously by statistics and matr ix calculus and that on the other hand the numerical problems can be solved more comprehensively. Thus it seems to me tha t by using the modern theory of mathematical statistics and calculus of matrices questions such as definition of systematic errors, true errors and residuals, rejection of observations, limitedness of Taylor development of functions, influence of rounding-off errors, co-operation of systematic and rand- om errors, direct and deduced observations, estimation of mean square or s tandard errors, accuracy and precision~ heterogeneous observations of for instance angles and lengths, significance of the law of errors of Gauss, nature of aajustment, significance and nature of error ellipses (to mention only a few of the questions dealt with in this book) can be treated more efficiently and will be more comprehensible to the student.

May the above remarks be taken as a positive criticism for the very reason tha t there is so much to be appreciated in the book reviewed here, like the t rea tment of the error ellipses, the symbolic method of wri t ing of Tienstra for the application of the law of propagation of errors, the Boltz's method of solving a system of l inear equations and many other problems. The clearness of style has been praised before. We wish the authoL" tha t soon a second edition of his book will be necessary in which case the above remarks may perhaps lead to a broadening of the basis.

W. Baarda