572 Sot ice 6 respecting Sen: Boohs. 



of vibration. The small difference between (23) and (27) 

 shows the success of the method and indicates that (27) is but 

 very little in excess of the troth. 



If the result were of special importance it would be quite 

 practicable to take another step in the approximation, deter- 

 mining p 2 as the lowest root of a cubic equation. 



A question naturally suo-o-ests itself as to the significance of 

 the value of p 2 in (27). r lhe general theory of constraints* 

 shows that it may be regarded as a first, but probably a 

 rather rough, approximation to the frequency of the second 

 low est mode of the complete system. Just as for the oravest 

 mode of all. the second lowest roots of the series of deter- 

 minants (of the 2nd. 3rd. and following orders) form 

 successive approximations to the true value, each value being 

 lower and truer than its predecessor. The second approxi- 

 mation would be the middie root of the cubic above mentioned. 

 But for this purpose it is doubtful whether the method is 

 practical. 



LY. Notices respectino Sew Books. 



An Introduction to tlie Mathematical Theory of Attraction. By 

 P. A. Takletox. Sc.D. (Longmans, 1899, pp. xiv+21 



T^E. TAPLETOX remarks that it is a matter of much ini- 

 •*-* portance that the acquisition of a competent knowledge of 

 the Theory or Attractions should be made as easy as possible. 



His object in the present work is to assist in doing this, and so 

 he writes for Students and not for Professors. Thojgh there is 

 much of new presentment of the details of the work, he naturally, 

 nay necessarily, draws extensively upon previous authorities, more 

 especially upon Maxwell's ' Electricity and Magnetism/ Thomson 

 and Tait's ' Xatural Philosophy/ and Dr. Eouth's recent treatise 

 on the subject in vol. ii. of his ' Analytical Statics. 3 The main 

 problems are. as he points out, to find the resultant force between 

 two bodies, and to determine the distributions of electricity and 

 magnetism which take place under given conditions. 



Prof. J. D. Forbes, in his Dissertation on Physical Science (Enct/c. 

 Brit. p. 5*89) describes the doctrine of Attractions as being a 

 complex and difficult one even when the distribution of the attract- 

 ing matter as well as the fundamental law of attraction is known. 

 And our author points out that the recent progress of the sciences 

 of Electricity and Magnetism has increased the direct value of the 

 theory. He discusses the 'Resultant Force' at some length, and then 

 considers ; Lines of Force ': next he devotes nearly one third of his 

 Treatise to the consideration of the Potential. This branch is very 

 thoroughly treated. The remaiuing chapters are devoted to Sur- 



* ' Theorv of Sound.' 2nd ed. § 92 a. 



