Notices respecting New Boohs. 75 



was found to work very well. It should be noted that all the 

 long lines being given by the straight edge, great accuracy is 

 easily obtainable, whether with the simple paper square or 

 the more complex instrument. 



21 Norhain Road, Oxford, 

 September 28, 1895, 



VII. Notices respecting New Boohs. 



Elements of the Mathematical Theory of Electricity and Magnetism. 

 By J. J. Thomson, M.A., F.R.S. Cambridge 'University Press, 

 1895. 



STUDENTS of Electricity who desire to read the more mathe- 

 matical portions of the subject, and particularly those who wish 

 to follow the development of the aether theory of electricity and 

 the electromagnetic theory of light, usually find some difficulty in 

 the choice of a text-book. From a first-year experimental course 

 to Maxwell's treatise is too great a step, in mathematics as well as 

 in physics ; some text-book of an intermediate character is there- 

 fore required. Maxwell appears to have realized this, and he 

 attempted to remove the difficulty by his Elementary Treatise, 

 which, unfortunately, he did not live to complete. In the present 

 volume Prof. Thomson has a similar aim : he retains nearly the 

 same order of subject-matter as in Maxwell's treatise, but (with 

 few exceptions) only such problems are corsidered as can be solved 

 by the aid of the differential calculus. By this treatment the 

 mathematical difficulties are greatly diminished, while the physics 

 of the subject is satisfactorily developed and illustrated by a 

 sufficiently large number of examples. 



The author has made frequent use of Earaday tubes of force in 

 explanations of phenomena occurring in the electric field : he shows 

 very simply that such tubes will be in equilibrium if the tension 

 along their axes is accompanied by an equal pressure at right angles 

 to them. In discussing the case of an insulated sphere in a uni- 

 form field, the idea of an electric doublet is introduced, and an 

 expression is found for the moment of a doublet representing the 

 external effect of the charge on the sphere. Among other new 

 modes of treatment we may mention the use of the dissipation 

 function in determining the distribution of currents in any network 

 of conductors. Kirchhoff's laws are shown to be equivalent to the 

 statement that the currents distribute themselves so as to make the 

 total rate of development of heat- energy a minimum ; by writing 

 down the expression for this heat-energy and making it a minimum, 

 the values of the currents in each branch may be obtained. Prof. 

 Thomson has found a companion for k, the specific inductive 

 capacity, and /x, the magnetic permeability, in dimensional formulae. 

 The work done by a unit magnetic pole in threading a closed 

 circuit is 4 7r/p times the current flowing in the circuit; as the 



