Notices respecting New Books. 201 



the end part is particularly important in magnetic work ; although 

 we must confess that here, as in the rest of the book, if the trans- 

 lation were less literal, and were slightly altered in places by the 

 introduction of English technical terms instead of the literal trans- 

 lations of French terms, it would be more useful to students. 



The third chapter, on the Measurement of Couples, is rightly 

 very elaborate, but in our opinion the authors are a little weak in 

 regard to the properties of materials ; they do not sufficiently 

 understand the importance of " Fatigue " in materials subjected to 

 strains. In § 712 they neglect the expansion of the vibrating 

 body. In § 713 they do not seem to be aware that, if silver wire 

 were drawn out very fine, its tenacity per square centimetre and 

 its coefficient of rigidity might be very greatly altered. 



Chapter iv. treats of the properties of Circular Currents. Twenty 

 pages are devoted to the magnetic moment of a cyhndric coil and 

 the field at the middle of its axis, leading to well-known theorems 

 concerning the most suitable dimensions of the coil for a given 

 length of wire ; or to give greatest field when the source of the 

 current is given ; or the best radial section of coil of a galvano- 

 meter ; in these various cases the section of the wire may be 

 constant or varying. In places (§ 734 for example) the temptation 

 to pursue a mathematical investigation to the end, although the 

 result may be of but little practical importance, has not been per- 

 haps sufficiently resisted. The twenty-four remaining pages of the 

 chapter are devoted to finding useful expressions for the field at 

 other points than the central one, and these naturally lead to the 

 expressions in chapter v. for tlie coefficients of induction of coils. 

 The field at any point due to a circular current is obtained in a 

 series involving the powers of the coordinates x and y of the point, 

 and the series are integrated to obtain the field for a cylindrical 

 coil ; it being shown that only certain terms of the series need be 

 taken in particular cases, the Quadrature method and Maxwell's 

 " mean-value " method being given for a long coil. The results 

 are applied to find the action of the coil on a magnetic needle ; to 

 show the value of Gaugain's method of placing the needle; the 

 value of Hehnholtz's arrangement of two parallel coils ; the three 

 parallel coils ; the four parallel coils ; and also two parallel coils with 

 currents in opposite directions. Knowing the field at a point, 

 there is a general rule for finding the average field [the mean action 

 it is called in this treatise] at points on any circular area whose 

 plane is at right angles to the axis. Finding this average field in 

 the case of an annular coil (like the winding on a G-ramme ring) 

 for portions of the cross section is evidently given by tie authors 

 as a mathematical exercise ; of course the results are of no prac- 

 tical importance. 



In chapter v., on coefficients of induction, the results of chap. iv. 

 are at once applicable in any case where the size of the wire is 

 negligible. But the method of expressing the coefficient of mutual 

 induction of two spires near one another by elliptic integrals with 

 Maxwell's useful table is also given, and its extension to coils with 



