202 Notices respecting New Books. 



the same axis. The entirely different method of taking up the 

 subjects of chapters iv. and v., namely by Spherical Harmonics, or 

 rather by Zonal Harmonics only, is now entered upon, and we could 

 have wished that the whole treatment of the subject had been on this 

 method. We know of no mathematical subject, capable of being 

 of great value to the practical electrician, which has received so 

 little attention as this of Spherical Harmonics. We know of no 

 publication, for example, of the general development in Spherical 

 Harmonics of the magnetic potential due to a current flowing in a 

 cylindric coil such as these authors are considering ; and it is not 

 at all easy at first sight to obtain it. When it is obtained the 

 practical man will find it quite useless, as, near the end of the coil, 

 he will require to make his calculation from about twenty terms. 

 When some practical mathematician takes up this subject seriously, 

 he will approximately give the potential by means of a series of a 

 few terms only, and show the working electrician that the subject 

 of Spherical Harmonics is not merely a beautiful mathematical 

 conception, but that it can really be made of use ; and when that 

 time arrives, men will have as definite notions concerning the 

 attractions of coils for one another, and the values of the coeffi- 

 cients of self and mutual induction of coils as they have of resist- 

 ance. At the present time few electricians would be surprised to 

 hear that their notions of the values of these magnitudes for par- 

 ticular coils were 100 times too great or too little. Although, 

 however, we might wish a fuller treatment of the subjects of these 

 two chapters by Spherical Harmonics, readers will find that these 

 subjects are here entered into much more fully than in any other 

 treatise. The potential on the axis due to a current in a circular 

 spire ; the external potential of a long coil ; the mutual induction 

 of two long coils ; the potential of coils wound spherically ; mutual 

 induction of circular currents ; these are investigations taken up 

 by the Spherical Harmonic method. Maxwell's method of obtain- 

 ing the Coefficient of Self-induction of a coil is carefully worked 

 out, and the chapter finishes with the study of some particular 

 cases. At the beginning of chapter v. we find taken up the case of 

 parallel currents when the size of the wires cannot be neglected. 



It would be quite easy from our notes to describe in the same 

 sort of way the rest of this volume, but readers will find that our 

 description of Part I. applies fairly well to the whole volume. 

 There is everywhere else the same careful development of details 

 which Maxwell and others have left somewhat obscure; and it is 

 evident that, in assisting students so carefully as they have done, 

 the authors were engaged in a labour which delighted them. 



We are sorry to say that it will be necessary to make a number 

 of corrections of printers' errors in a second edition. These errors 

 put great difficulties in the way of students ; for it has to be borne 

 in mind that many of the letters in use by French mathematicians 

 are such as would not be used in English books, a; represents an 

 angle, for example, where we should use fJ ; T is the time of only 

 half what we call a complete oscillation. A weight in grammes is 



