47' 



NATURE 



[March 22, i<S94 



points, the expansions which represent it in the neigh- 

 bourhood of ordinary and singular points, its cycles, &c. 

 Chapter v., on integration, introduces the fundamental 

 theorems of Cauchy, with their applications to the 

 establishment of the theorems of Weierstrass and Mittag- 

 Leffler regarding the general expressions for functions 

 with assigned singularities. In chapters vi. and ix. we 

 have the substance of Riemann's theory, both direct and 

 inverse. The account of the inverse theory consists 

 largelyof an exposition of Schwarz's solution of Dirichlet's 

 problem, on which depends the proof of the existence of 

 " functions of position '' on a given Riemannian surface. 

 The applications of the theory are amply illustrated in 

 chapter vii., which contains an admirable sketch, already 

 alluded to, of the Weierstrassian theory of doubly periodic 

 functions ; and in chapters viii. and x. on double theta- 

 functions and Abelian integrals. 



From this enumeration our mathematical readers 

 will see that Messrs. Harkness and Morley have provided 

 for them an ample and varied bill of fare ; and we have 

 no hesitation in saying that the feast is worthy of the 

 bill. We would merely express, in conclusion, our desire 

 to see this pair of authors soon abroad again in another 

 of the many fields that still await the conscientious writer 

 of English mathematical text-books. G. Ch. 



THE CONSTRUCTION OF DRUM ARM A TURES 



AND COMMUTATORS. 

 Drum Armatu7-es and Co/iunutalors. By F. M. Wey- 

 mouth. (London : The Electrician Printing and Pub- 

 lishing Co., 1893.) 



IN the preface to this book we are told that it is in- 

 tended as " a useful guide or introduction to those 

 who may ultimately wish to proceed with the mathe- 

 matical treatment of the subjects," and further, that " the 

 beginner will read these pages during the early period 

 of his training, while he is studying his mathematics, 

 and so may combine the two together at a later and more 

 advanced stage." To such this work can be recommended, 

 for the author has collected a good deal of information, 

 which is well illustrated by woodcuts, showing how 

 different makers have built up their armatures and com- 

 mutators, thus giving the student a variety of experience 

 in this direction. 



In the first three chapters the drum armature is dis- 

 cussed from a general point of view. It is contrasted 

 with that of Gramme, and the generation of electromotive 

 force explained. The distinctive difference between 

 " electromotive force " and " potential difference " might 

 have been at this stage (p. 9) pointed out with greater 

 clearness. For instance, in a direct current dynamo when 

 working on open circuit the "electromotive force " of the 

 machine and the "potential difference " at the brushes 

 are the same in magnitude if no current flows through 

 the armature. But when giving current to the external 

 circuit between the brushes, a difference at once steps in, 

 the " electromotive force " being greater than the 

 " potential difference " by an amount represented by the 

 current into the ohmic resistance of the armature. 



In chapter iii. the winding of armatures for heavy 

 currents is discussed generally ; then follow some notes 

 on balancing armatures properly. 

 NO. 1 273, VOL. 49] 



With regard to an effect of current in the armature, it 

 is stated on p. 30 that when " the field is bored con- 

 centric with the axis of the armature, Foucault currents 

 arise principally, if not entirely, when the bars pass under 

 the trailing horns of the pole-pieces, where the induction 

 lines are particularly dense. By 'trailing' horn is meant 

 the last horn of a pole-piece which the bars leave or 

 recede from as they revolve.' This statement is not 

 sufficient. Take the case of a shunt-wound motor (of the 

 ordinary type) when loaded and working with a negative 

 lead. Here it is at the "trailing' horn that the induc- 

 tion per unit area of the polar-surface is less dense than 

 at any other part of the surface. ^ It should also be 

 impressed upon the beginner that it is the " loading" of 

 generator or motor which brings about this disturbance. 



Six chapters (iv.-ix.) on the details of drum arma- 

 tures for heavy currents, specially with reference to the 

 end-connections, follow. These have been carefully 

 compiled, and it must be said that they give a good 

 insight into the construction of drum armatures. In the 

 first of this series of chapters the prevention of Fou- 

 cault currents is dealt with. With regard to making the 

 air-space longer near the horns in order to remove the 

 cat(se of Foucault currents, a word could be added. In 

 what is generally termed the "inverted horse-shoe" 

 type of machine, so largely used at the present time, the 

 pull upon the armature due to magnetism is in an upward 

 direction, and with concentric fields outbalances the 

 weight of the armature, thus causing a considerable 

 pressure on the upper brasses of the bearings. When 

 such a dynamo is direct-coupled to a steam-engine which 

 works with a constant downward thrust, serious stresses 

 are brought mto play by these opposite forces acting at 

 different points on the shaft. In such cases the widen- 

 ing of the air spaces near the two top horn pieces is 

 usually resorted to, to relieve the pull on armature due to 

 magnetism. 



After describing the Edison " plate " end connection 

 in detail, we come, in chapter vi., to the " evolute " end 

 connection, which is described firstly in connection with 

 bars cranked radially towards the shaft. Then follows a 

 description of " evolutes," in which the cranked bar is 

 dispensed with entirely. With regard to this latter, it is 

 unfortunate that the author has not given details of the 

 "Siemens" bar armature, which would have added to 

 the value of the work. He of course recognises Von 

 Hefner Alteneck as the inventor of evolute end- 

 connections. 



Eickemeyer's evolute wire-winding, Kapp's helical 

 end-connection, and Swinburne's chord-winding are 

 described in great detail. Chapter ix. treats of the 

 Parson's helical outside end-winding, which is specially 

 interesting on account of the enormous speed at which 

 these armatures rotate. A description of Fritsche's 

 winding is also given. 



The subject of commutators claims chapters x.-xiii. 

 In the introductory chapter (x.) "end play" in the 

 bearings is mentioned as tending to more even wear of 

 the surface of commutators. In this connection the 

 author does not mention the " Halpin" gear, which has 

 been introduced for the purpose of automatically moving j 

 the brushes longitudinally backward and forward on thej 



1 See Proceedings of the Royal Society, vol. li. p. 49. 



