88 PROCEEDINGS OF SECTION A. 



section 22, it is shown that the value ot" p the field resistance has 

 practically no effect on the r operators forfalteruators as ordinarily 

 constructed. 



Hence we see that i' is the alternating field current i£ the 

 dampers are absent, $ its value when the dampers are attached, and 

 these currents are connected by the relation — 



e =(! + /<) $. 



In addition as 2zC' = xp^' 



2 1 . , 



pt- = -zC- = ,,~-| - t; pi'* . 



Hence, if H' be the copper loss in the field coils due to induced 

 alternating currents when the generator is without the dampers, H 

 the same when the dampers are attached, and Ji the loss in the dampers 

 themselves — 



(I+k)'' (1 + «)=' ^ 1 + k' 



If we assume that the mean length of a field turn is equal to the 

 length of a damper turn, it is easy to show that k is the ratio of the 

 volume of copper in the dampers to the volume of copper in the field 

 windings when there is no resistance external to the windings in the 

 field circuit, and greater than this ratio if there is external resistance ; 

 so the action of the dampers in reducing the heating in the field 

 windings, due to induced current in them, has been determined. 



The magnetic flux in the field cores being ff {v$' + nee cos wt} is 

 practically unaffected by the presence of the dampers, so that the iron 

 losses in the field magnets remain the same. 



24. If a source of alternating e.m.f. E where — 



E=E, sin (W + AJ+E3 sin (3 wt+h;)'i-'E. sin (5oj^+A,)+ &c. 



=e^-{-e^-{-e.-{- &c. (vectors) 



be included in the armature circuit, and, if the armature rotate in 

 synchronism with this e.m.f., we have the case of the synchronous 

 motor. 



The armature and field currents x and $ are now connected by 

 the equations (see section 1) — 



r^+ - ] ^•^'+ '"t cos wf [ = 2 ^q sin {g^wt-\-hq ) 



p^ -{- - \ X^-\-mx cos wf \ -=7] . 

 at L ) 



Assuming, as in section 2, that — 



^ = a^ + ^3 + ^5 + &c. 



