Magnetic Circuit of Dynamo Machines. 497 



We shall speak indifferently of the drum or Hefner-Alteneck 

 and the cylindric Gramme armature — that is, the Gramme 

 armature which receives its induction through its cylindric 

 surface from two pole-pieces. It is easy to make the slight 

 changes in the formulae required for flat gramme ring- 

 armatures like those of the Victoria, Gulcher, and Schiickert 

 machines, which receive induction through their flat sides, 

 and for all machines with more than two pole-pieces. 

 r, outside radius of armature. 

 L, length of armature parallel to the axis. 

 k, a constant such that krh = a 1 ; k is as much as 1*25 in 

 drum or Hefner-Alteneck armatures, and as little as 05 

 in short cylindric or other Gramme armatures. 

 t, the thickness of the winding of the armature. 

 d, the clearance between wire and pole-piece, 

 8=d + t, the total distance from iron of armature to pole- 

 piece. 

 n, the revolutions per second of the armature. 

 v, the circumferential velocity of the armature in centi- 

 metres per second v = 2irrn. 

 S, wires counting all round the outside of the armature. 

 A, amperes in each wire. 

 SA will be called the " ampere-wires V on the armature, 

 being the ampere-turns if it is a Gramme, and being 

 twice the ampere-turns if it is a Hefner-Alteneck. 

 a, amperes per sq. centim. flowing in the section of the 

 armature-winding made by a plane at right angles to 

 the axis. 

 a L , the highest permanent value of a. allowable. 

 p, the electric resistance of the armature-winding per cubic 

 centimetre. That is, per centimetre of its length per 

 sq. cm. of cross section. Of course p is greater than 

 the specific resistance of copper, as the space is partly 

 occupied by insulating material, p is greater with finer 

 wire ; but for some practical purposes it is advisable to 

 assume p constant for all kinds of winding. 

 pa?, watts developed as heat per cubic centimetre of the 

 winding, so that total rate of development of heat 

 = 27rrtLpa?. 

 a x , cross section of iron of armature by a diametral plane. 

 a 2 , area of pole-piece exposed to the armature, increased by 



a fringe of 0*8 8 in breadth all round, 

 a, the cross section of any other portion of the magnetic 



circuit which may be considered. 

 /3, the induction in C.G.S. units, given in lines per square 

 centimetre anywhere in the magnetic circuit. 



