238 Notices respecting JSfew Books. 



The mass of the Earth is given, and also of an estimate of the 

 ocean ; the mass of the atmosphere may be stated as the mass 

 of an ocean of mercury covering the Earth, of mean depth the 

 average height of the barometer. 



The chief value of these tables is in giving the latest measured 

 value of a physical quantity to the number of figures warranted 

 by experiment, and not to wander off into the region of the 

 dishonest decimal. 



These accurate statements appear more eloquent and convincing 

 as a small correction on a large round number representing the 

 accepted average value : and risk of error is diminished in the 

 large leading figures of a result in this enormous mass of data. 



Stated in logical order, the length I of the seconds' pendulum 

 is the measured quantity, and g is derived from it by the relation 



Introduction to the Theory of Fourier 's Series and Integrals. By 

 H. S. Cakslaw, Professor of Mathematics in the University of 

 Sydney. (Macmillan, 1921, 320 pages ; price 30 shillings.) 



Although classing itself modestly as a mere Introduction to the 

 subject, the work extends to over 300 pages, and costs 30 shillings; 

 and a sequel seems promised in the future to a complete treatise. 



This is very complete at present in a rigorous examination of 

 the nature of the convergency and continuity of the Fourier 

 series, a succession of fluctuating harmonic terms, equivalent of 

 the harmonics of the monochord, with frequency in the ratio of 

 the integer 1, 2, 3, .... , or wave-length in the harmonic pro- 

 gression of the reciprocal. 



These are the commensurable, periods in the terms of a Eourier 

 series. But in the Lunar and Planetary theory the various 

 anomalies are resolved into terms of different incommensurable 

 period, such as evection and variation. 



The Eourier series is a summation of the harmonics of commen- 

 surable period such as those produced on the monochord, and the 

 theory was born of the representation of any arbitrary musical 

 vibration of the chord by a resolution into the pure harmonics. 



The legitimacy was disputed by the originators of the idea, 

 d'Alembert. Euler, Bernoulli; but Lagrange settled the question 

 on the modern point of view, although the difficulties and 

 objections raised by Euler still exist, and form the bulk of the 

 discussion in this treatise. 



The new mathematician is interested chiefly in what may be 

 called the morbid pathology of the series, in its behaviour at 

 points of discontinuity where a differentiation may be expected to 

 break down, and the convergence requires examination, whether 

 regular, uniform, or not. 



But the man who employs the series in an application to an 

 electrical alternating current, or to the balance of quick running 



