500 Profs. Ayrton and Perry on the 



The heat generated in the armature-winding per cubic 

 centim. =/oa 2 . The possible ventilation arrangements are 

 better in Gramme than in Hefner-Alteneck armatures, and it 

 is usual, therefore, to consider only the heat generated in 

 the wires on the outside convex surface of the iron of either. 

 This is %irrtha.{-p ; and as the heat emitted is found, for the 

 highest temperature 6 at which it is considered safe perma- 

 nently to work the machine, to be proportional to the convex 

 surface 27rrL, if E is the rate of loss of heat in watts per 

 square centimetre of this surface, 



or tpx? = m. 



We find that — may be taken as 83000 in the best modern 



machines ; we shall call this q 2 , so that 



W = tf (5). 



We can, therefore,, from (4), express the greatest permanent 

 output of a machine W', either in terms of a t or of t : 



W'=0-0016() — , (6) 



W'=^rNVr, (7) 



W'^rkrhfrWt, (g) 



W and /3/ being the highest allowable values of N and /?,. 

 It is on the combination of (5) and (4) that we have based 

 an important generalization regarding the magnetic circuit 

 of the dynamo, which gives the title to our paper. Members 

 of the Society are aware of the methods adopted by Mr. 

 Bosanquet, Dr. Hopkinson, and Mr. Kapp in dealing with a 

 magnetic circuit. Consider a closed tube of small cross 

 section everywhere, passing through the iron of the armature, 

 the air-spaces, the limbs of the field-magnet, and the yoke. 

 Let the section vary so that the total induction is everywhere 

 the same. Then, in a short length of the tube I, the line- 

 integral of the magnetic force required to produce this 

 induction is 



J* 



where ji, the magnetic permeability of the material at any 

 place, is 1 for air, and where its value for iron is given ir 



