CHAP. VI] EXCITING AMPERE-TURNS 117 



of surfaces approximately in the directions of the true equipo- 

 tential surfaces, and assuming these arbitrary surfaces to be the 

 true equipotential surfaces, the true reluctance of the path is 

 reduced. In other words, by calculating the reluctances of the 

 laminae between the " incorrect " equipotential surfaces and adding 

 these reluctances hi series, one obtains a reluctance which is lower 

 than the true reluctance of the path. This gives a lower limit for 

 the required reluctance (or an upper limit for the permeance) of 

 the path. 



Imagine now the various tubes of force of the original field 

 wrapped up in infinitely thin sheets of a material of zero permeabil- 

 ity. This does not change the reluctance of the paths, because 

 there are no paths between the tubes. But if these wrappings are 

 not exactly in the direction of the lines of force, the reluctance of 

 the field is increased, because the densities become less uniform, 

 the non-permeable wrappings forcing the lines of force from their 

 natural positions. Thus, by drawing in a given field a system of 

 surfaces approximately in the directions of the lines of force, cal- 

 culating the reluctances of the individual tubes, and adding them 

 in parallel, a reluctance is obtained which is higher than the true 

 reluctance of the path. This gives an upper limit for the reluc- 

 tance (or a lower limit for the permeance) of the path under 

 consideration. 



Therefore, the practical procedure is as follows: Divide the 

 field to the best of your judgment into cells, by equipotontial 

 surfaces and by tubes of force, and calculate the reluctance of the 

 field in two ways: first, by adding the cells in parallel and the 

 resultant laminsB in series; secondly, by adding the cells in 

 and the resultant tubes in parallel. The first result is lower than 

 the second. Readjust the position of the lines of force and of the 

 equipotential surfaces until t lie two results are sufficiently close to 

 one another; an average of the two last results gives the true 

 reluctance of the field. 



One difficulty in actually following out the foregoing method 

 is that the changes in the assumed directions of the field that will 

 give the best result are not always obvious. Dr. Th. 1 x-hmann has 

 introduced an improvement which greatly facilitates the laying out 

 of a field. 1 We shall explain this method in application to a two- 



'"Graphiaohe Methodc zur Bentimmung <l-s Knifilinicnvcrlaufcs in dcr 

 Luft "; Elcktrotochni*** ZeiUchnfl. Vol. 30 (1009), p. 996. 



