118 THE MAGNETIC CIRCUIT [ART. 41 



dimensional field, though theoretically it is applicable to three- 

 dimensional problems also. According to Lehmann, lines of force 

 and level surfaces are drawn at such distances that they enclose 

 cells of equal reluctance. Consider a slice, or a cell, in a two- 

 dimensional field, v centimeters thick in the third dimension 

 (where v=l///), and of such a form that the average length I of 

 the cell in the direction of the lines of force is equal to its average 

 width w in the perpendicular direction. The reluctance of such a 

 cell is always equal to one rel, no matter whether the cell itself is 

 large or small. This follows from the fundamental formula for 

 the reluctance, which in this case becomes (R = vl/(vXw) = l. 



The judgment of the eye helps to arrange cells of a width equal 

 to the length; in the proper position with respect to each other and 

 to the adjoining iron; the next approximation is apparent from 

 the diagram, by inspecting the lack of equality in the average 

 width and length of the cells. Lord Rayleigh's condition is 

 secured by this means, since the combination of cells of equal 

 reluctance leads to but one result, whether they are combined 

 first in parallel or first in series. After a few trials the space is 

 properly ruled, and it simply remains to count the number of cells 

 in series and in parallel. Dr. Lehmann shows a few applications 

 of his method to practical cases of electrical machinery, and the 

 reader is referred to the original article for further details. 



The foregoing methods apply only to the regions outside the 

 exciting current, because only in such parts of the field the maxi- 

 mum permeance corresponds to the maximum stored electromag- 

 netic energy. Within the space occupied by the exciting windings 

 the condition for the maximum of energy is different (see Art. 57), 

 and is of a form which hardly permits of the convenient application 

 of a graphical method. However, in most practical cases the 

 directions of the lines of force within the exciting windings are 

 approximately known a priori: or else, the windings themselves 

 can be assumed, for the purposes of computation, to be concentrated 

 within a very small space. For instance, the field winding can be 

 assumed to consist of an infinitely thin layer close to the pole-waist. 

 Then the condition that the permeance is a maximum is fulfilled in 

 practically the whole field, and the field is mapped out on this basis. 



Prob. 18. Sketch the field between the armature and a pole-piece 

 or some proportion of tooth, slot, and air-gap and determine the lower 

 and upper limits of the reluctance by Lord Rayleigh's method. 



