162 SCIENCE PROGRESS 



The Combination of Observations. By David Brunt, M.A., B.Sc. [Pp. x + 

 220.] (Cambridge : at the University Press, 1917. Price 8s. net.) 



This volume supplies a long-felt want : there has hitherto been no book in 

 English dealing entirely with the theory of errors and the method of least squares 

 and treating the subject in a connected manner, although it has important 

 applications in several branches of science. The author has wisely kept the size 

 of the book within reasonable limits by excluding these particular applications 

 of the theory. When the student has mastered this volume he will have 

 obtained a sufficient groundwork to enable him to proceed to any special 

 applications. 



In the first seven chapters the nature of errors of observation is discussed, 

 the law of errors is explained and various proofs given, the assumptions upon which 

 the proofs rest being clearly stated ; the cases of one or several unknowns are 

 considered separately, and the principle of weighting observations explained. In 

 the next two chapters the method of adjustment of conditioned observations and 

 the guiding principles in the delicate matter of rejecting observations are briefly 

 set forth. Alternatives to the normal law of errors, the principle of correlation, 

 harmonic analysis from the standpoint of least squares and the methods of 

 periodogram analysis are dealt with in subsequent chapters as fully as possible 

 without unduly increasing the size of the book and sufficiently for the student to 

 obtain a general understanding of these portions of the subject. Each chapter is 

 followed by a few examples which have been carefully and well chosen from 

 various branches of science. 



A few misprints, such as " helmon " for " helium," have crept in, due doubtless 

 to the final proofs having been read by the author whilst on active service, and 

 which may be excused on that ground. 



H. S. J. 



PHYSICS 



Eight Lectures on Theoretical Physics. Delivered at Columbia University in 

 1909. By Max Planck. Translated by A. P. Walls. [Pp. ix + 130.] 

 (New York : Columbia University Press, 1915.) 



These lectures which Planck delivered as foreign lecturer at Columbia University 

 in the spring of 1909 have for their object the presentation of a System of 

 Theoretical Physics based on certain points of view which are explained in the 

 first lecture. Whereas, undoubtedly, the materials of Physics are the specific 

 perceptions of man as received through the channels of sense, yet all modern 

 advance in the subject has been attained by a definite elimination from all 

 physical ideas of the anthropomorphic elements, particularly those of specific 

 sense perceptions. This may be seen, for instance, by consideration of such ideas 

 as tone, colour, temperature, etc. Thus the definitions of these quantities are 

 to-day not derived from perception through the corresponding senses, but tone 

 and colour are defined through a vibration number or wave length, and tempera- 

 ture through a scale based on the second law of thermodynamics. The thesis on 

 which Planck proceeds is questionable, but the exposition based on it is interest- 

 ing, and gives an excellent idea of some of the problems now agitating the minds 

 of physicists, in particular the conditions attending irreversible phenomena, the 

 atomic theory of matter, Heat Radiation, Relativity, and the foundation of 

 Dynamics on a single principle such as the Principle of Least Action. Much of 

 the material of these lectures is to be found in the author's " Thermodynamics 



