ELECTROMAGNETS. MAGNETISM OF IRON. 



373 



around the field coils so as to surround the whole (or half) of the 

 total flux + </>, and another winding of the same number (or 

 half the number) of turns is arranged on the stationary armature 

 so as to surround the useful flux <l>. These windings are con- 

 nected to a ballistic galvanometer, one at a time, and the throw 

 of the galvanometer is observed when the field current is re- 

 versed. The ratio of these two throws is the leakage coefficient. 



Calculation of magnetic leakage. Since magnetic leakage flux passes through the 

 air, it is evident that the calculation of leakage flux must be based upon the calcula- 

 tion of the magnetic reluctances of air gaps. The magnetic reluctance of a short air 

 gap between plane iron faces, parallel to each other or inclined, may be calculated 



Fie. 13. 



with considerable accuracy. The reluctance of a long air gap, that is a gap which is 

 long in comparison with the length and width of the iron faces which bound it, cannot 

 be accurately calculated by any simple formula. 



(a) Magnetic reluctance of a short air gap betiueen parallel iron faces. In this 

 case the sectional area of the gap is equal to, or but very little larger than, the area of 

 the smaller face, and the reluctance of the gap may be accurately calculated by the 

 formula : 



in which / is the length of the gap in centimeters, and s is its sectional area in square 

 centimeters. 



() Magnetic reluctance of a long air gap between parallel faces. In this case 

 one may use equation (12) with sufficient accuracy for most purposes, using for s the 

 value (s' -f- s // )J2, where s' and s" are the areas of the respective faces as shown in 



Fig- 13- 



(c) Magnetic reluctance of a short air gap between similar, rectangular, plane 

 iron faces inclined at an angle 6 as shown in Fig. 14. Let C be the line of the inter- 

 section of the two faces, and let p v and p 2 be the radial distances from C to the edges 

 of the faces as shown in Fig. 14. Then 



