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The adjustment of errors in practical science
Nov., I93o.]
681
BOOK REVIEWS.
the other opposite, and that these finally broke off, producing the raw material for the planets. But, he argues, the material that heaped up in these bulges had to come from somewhere else on the sun, so at the same time there was a low tide belt at right angles to them. With surface material removed, deeper, hotter, and presumably more explosive matter was exposed. This would then be violently erupted all around this low tide zone. The material thrown out would be pulled by the gravitational attraction of the other star, but masses ejected on opposite sides of the low tide belt would be given motions in exactly opposite directions. Some would mingle with material torn from the other sun. All this ejected material, suggests Dr. Olivier, formed the comets and meteors as well as many asteroids and perhaps some of the satellites. Such a theory easily explains the retrograde motions of many of these bodies and their varying, and in some eases high, inclinations to the ecliptic. This book, therefore, is to be recommended both to the scientist who wants a complete summary of the essentials of cometary astronomy and to the layman who wants a very interesting and readable account of some of the most fascinating objects that come within reach of the astronomer's telescope and, occasionally, the naked eye. Though non-mathematical in the main text, an appendix gives a brief account of the elementary facts about orbits. Physically, the printing, the paper, and the binding all combine to make it a work of which the publishers may well be proud, and, except for a few unimportant and obvious typographical errors, it realizes their motto of "Sans Tache." JAMES STOKLE¥. THE MARITIME PROVINCES, CANADA;being a short description of the developments in New Brunswick, Nova Scotia, and Prince Edward Island. 79 pages, illustrations, map, I2mo. Ottawa, National Development Bureau, Department of the Interior, n. d. From this booklet the reader can in a few moments acquire much authoritative information about the progress and potentialities of New Brunswick, Nova Scotia and Prince Edward Island, their principal resources and development. The wealth of these provinces has been overlooked during the growth of western Canada and the industrial expansion of Ontario and Quebec, and it is only now that they are receiving the recognition to which their resources in agricultural lands, forests and fur-bearing animals, minerals, fisheries and waterpowers rightly entitle them. Eight pages are devoted to Recreational Resources. The work is illustrated by half-tone illustrations from original photographs. R. THE ADJUSTMENTOF ERRORS IN PRACTICALSCIENCE. By R. W. M. Gibbs, B.A. (Camb.), B.Sc. (Lond.). 112 pages, 43 figures, I2mo. New York, Oxford University Press; London, Humphrey Milford, 1929. This little volume represents an attempt to simplify and condense into a readable form the gist of the Theory of Errors. Primarily it is intended for the use of research students in practical science but various portions no doubt will be found to be of value to students of sociology, psychology and education. In these
682
BOOK REVIEWS.
[J. F. I.
three studies, all data must be subjected to a correlation process before worthy, deductions can be drawn. Following the introduction, the author discusses in turns, Probability Normal Curve of Errors, Area and Volume, Distribution, Line of Closest Fit, the Correlation Coefficient, Partial Correlation and Weighted Observations, Correlation Ratios and Errors. The appendix contains a list of twenty-six formulas. T. K. CLEVELAND. LA GAMME, INTRODUCTION A L'ETUDE DE LA MUSIQUE. Par P.-J. Richard, Anciene eleve de l'Ecole Polytechnique. Preface de M. Marius Casadesus. viii-23I pages, I2mo, paper. Paris, Librairie Scientifique Herman et Cie. Price 28 francs.
It is generally recognized that all art is susceptible of analysis in accordance with the principles of physical science provided all the component causes which enter into an effect pleasing to the senses are capable of classification for the purpose of formulation. In modern times, the purely physical features of tone have been the subject of a great amount of brilliant development, only to mention the classic investigations of Von Hemholtz, Lord Rayleigh and Koenig. More recently architectural acoustics and acoustical apparatus have also made important strides. The particular theme of the present work is an examination of that graduated series of tones, known as the musical scale, on a purely physical basis, what rules govern the intervals between these tones and a consideration of the methods which have been adopted in actual practice in constructing such scales in accord with the artistic requirements of musical composition. The work is intended primarily for the young students of the Conservatoire and schools of music that they may be provided with an arithmetical and physical explanation of the musical scale independently of artistic considerations and instrumental technique. Dealing wholly with arithmetical relationships in the analysis, the author in the first chapter wisely provides a review of the arithmetic of fractional numbers, certain theorems of inequalities, and logarithms which are employed in the discourse. The author's procedure is first a presentation of the historic evolution of scales from early times and the numerical relations between their component tones, a consideration of their relation to musical acoustics and an analysis of scales which have received common adoption. All of these receive searching numerical comparison. Regarding the physico-mathematical derivation of a rational scale, the author says: " T h e scale is not a mathematical production. It is not expressed in rigorous figures which may not be varied without offending the ear. The ear, fortunately, though very sensitive, permits approximations; and these approximations, between which a choice may be made, are represented by numerical series which it is convenient to employ in the resolution of certain elementary problems of musical acoustics, and in arriving at an explanation of certain musical facts." The work is a thoroughgoing study of the musical scale to which the historical notes interspersed throughout its rather formidable collection of numerical data, and the concise account of the physics of the subject supply a needful zest for the perusal of the volume. L. E. PICOLET.
681
BOOK REVIEWS.
the other opposite, and that these finally broke off, producing the raw material for the planets. But, he argues, the material that heaped up in these bulges had to come from somewhere else on the sun, so at the same time there was a low tide belt at right angles to them. With surface material removed, deeper, hotter, and presumably more explosive matter was exposed. This would then be violently erupted all around this low tide zone. The material thrown out would be pulled by the gravitational attraction of the other star, but masses ejected on opposite sides of the low tide belt would be given motions in exactly opposite directions. Some would mingle with material torn from the other sun. All this ejected material, suggests Dr. Olivier, formed the comets and meteors as well as many asteroids and perhaps some of the satellites. Such a theory easily explains the retrograde motions of many of these bodies and their varying, and in some eases high, inclinations to the ecliptic. This book, therefore, is to be recommended both to the scientist who wants a complete summary of the essentials of cometary astronomy and to the layman who wants a very interesting and readable account of some of the most fascinating objects that come within reach of the astronomer's telescope and, occasionally, the naked eye. Though non-mathematical in the main text, an appendix gives a brief account of the elementary facts about orbits. Physically, the printing, the paper, and the binding all combine to make it a work of which the publishers may well be proud, and, except for a few unimportant and obvious typographical errors, it realizes their motto of "Sans Tache." JAMES STOKLE¥. THE MARITIME PROVINCES, CANADA;being a short description of the developments in New Brunswick, Nova Scotia, and Prince Edward Island. 79 pages, illustrations, map, I2mo. Ottawa, National Development Bureau, Department of the Interior, n. d. From this booklet the reader can in a few moments acquire much authoritative information about the progress and potentialities of New Brunswick, Nova Scotia and Prince Edward Island, their principal resources and development. The wealth of these provinces has been overlooked during the growth of western Canada and the industrial expansion of Ontario and Quebec, and it is only now that they are receiving the recognition to which their resources in agricultural lands, forests and fur-bearing animals, minerals, fisheries and waterpowers rightly entitle them. Eight pages are devoted to Recreational Resources. The work is illustrated by half-tone illustrations from original photographs. R. THE ADJUSTMENTOF ERRORS IN PRACTICALSCIENCE. By R. W. M. Gibbs, B.A. (Camb.), B.Sc. (Lond.). 112 pages, 43 figures, I2mo. New York, Oxford University Press; London, Humphrey Milford, 1929. This little volume represents an attempt to simplify and condense into a readable form the gist of the Theory of Errors. Primarily it is intended for the use of research students in practical science but various portions no doubt will be found to be of value to students of sociology, psychology and education. In these
682
BOOK REVIEWS.
[J. F. I.
three studies, all data must be subjected to a correlation process before worthy, deductions can be drawn. Following the introduction, the author discusses in turns, Probability Normal Curve of Errors, Area and Volume, Distribution, Line of Closest Fit, the Correlation Coefficient, Partial Correlation and Weighted Observations, Correlation Ratios and Errors. The appendix contains a list of twenty-six formulas. T. K. CLEVELAND. LA GAMME, INTRODUCTION A L'ETUDE DE LA MUSIQUE. Par P.-J. Richard, Anciene eleve de l'Ecole Polytechnique. Preface de M. Marius Casadesus. viii-23I pages, I2mo, paper. Paris, Librairie Scientifique Herman et Cie. Price 28 francs.
It is generally recognized that all art is susceptible of analysis in accordance with the principles of physical science provided all the component causes which enter into an effect pleasing to the senses are capable of classification for the purpose of formulation. In modern times, the purely physical features of tone have been the subject of a great amount of brilliant development, only to mention the classic investigations of Von Hemholtz, Lord Rayleigh and Koenig. More recently architectural acoustics and acoustical apparatus have also made important strides. The particular theme of the present work is an examination of that graduated series of tones, known as the musical scale, on a purely physical basis, what rules govern the intervals between these tones and a consideration of the methods which have been adopted in actual practice in constructing such scales in accord with the artistic requirements of musical composition. The work is intended primarily for the young students of the Conservatoire and schools of music that they may be provided with an arithmetical and physical explanation of the musical scale independently of artistic considerations and instrumental technique. Dealing wholly with arithmetical relationships in the analysis, the author in the first chapter wisely provides a review of the arithmetic of fractional numbers, certain theorems of inequalities, and logarithms which are employed in the discourse. The author's procedure is first a presentation of the historic evolution of scales from early times and the numerical relations between their component tones, a consideration of their relation to musical acoustics and an analysis of scales which have received common adoption. All of these receive searching numerical comparison. Regarding the physico-mathematical derivation of a rational scale, the author says: " T h e scale is not a mathematical production. It is not expressed in rigorous figures which may not be varied without offending the ear. The ear, fortunately, though very sensitive, permits approximations; and these approximations, between which a choice may be made, are represented by numerical series which it is convenient to employ in the resolution of certain elementary problems of musical acoustics, and in arriving at an explanation of certain musical facts." The work is a thoroughgoing study of the musical scale to which the historical notes interspersed throughout its rather formidable collection of numerical data, and the concise account of the physics of the subject supply a needful zest for the perusal of the volume. L. E. PICOLET.