(1) The Combination of Observations (2) Fundamental Conceptions of Modern Mathematics Variables and Quantities With a Discussion of the General Conception of Functional Relation (3) Revision Papers in Arithmetic (4) Differential Calculus

Abstract

(1) MR. BRUNT gives an account of the method of least squares, without entering into elaborate descriptions of instruments or experimental methods. 1 he book is not easy reading, but this is principally because the material is chosen from a rather difficult branch of applied mathematics, and modern work is discussed very thoroughly. The proof of the law of error is based on Hagen's hypothesis regarding errors of observation, and a generalised form of it, due to Prof. Eddington, is given on p. 15. Other chap ters deal with the case of one unknown, observa tions of different weight, observations involving several unknowns, conditioned observations, the rejection of observations, and alternatives to the normal law of errors. The three last chapters deal with correlation, harmonic analysis from the point of view of least squares, and the periodografn. This last part is of great interest in connection with the modern work of Sir Ronald Ross and Dr. Brownlee, and a recent paper by Sir Joseph Larmor on what may be called “practical harmonic analysis.” There are a great number of valuable references in the book, which is much to be com mended.

(1) The Combination of Observations.

By D. Brunt. Pp. x + 219. (Cambridge: At the University Press, 1917.) Price 8s. net.

(2) Fundamental Conceptions of Modern Mathematics. Variables and Quantities. With a Discussion of the General Conception of Functional Relation.

By R. P. Richardson E. H. Landis. Pp. xxii + 216. (Chicago and London: The Open Court Publishing Company, 1916.) Price 1.25 dollars or 5s. net.

(3) Revision Papers in Arithmetic.

By W. G. Borchardt. Pp. viii + 156 + answers xxxii. (London: Rivingtons, 1917.) Price 2s.

(4) Differential Calculus.

By Dr. H. B. Phillips. Pp. vi + 162. (New York: John Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1916.) Price 5s. 6d. net.