A unit of reluctance suggested by Vladimir Karapetoff¹ in 1911, henry spelled backwards (it is a reciprocal henry). The term was not taken up.

1. V. Karapetoff.
The Magnetic Circuit.
New York: McGraw-Hill Book Company, 1911.
See below.


When permittance is measured in farads, elastance is measured in darafs (see the chapter on the Electrostatic Circuit in the author's Electric Circuit).

Analogously, when two or more magnetic paths are in parallel it is convenient to use the reciprocals of the reluctances. The reciprocal of the reluctance of a magnetic path is called its permeance; eq. (1) becomes then

Φ = ℘M, (2)


℘ = 1/ℛ. (3)

A script ℘ is used for permeance in order to avoid confusing it with power. For the unit of permeance corresponding to the rel, the author proposes the name perm. A magnetic path has a permeance of one perm when one maxwell of flux is produced for each ampere-turn of magnetomotive force applied along the path. The unit “perm” has been in use among electrical designers for some time, although no name has been given to it. Notably Mr. H. M. Hobart has used it extensively in his writings, in the calculation of the inductance of windings. He speaks of “magnetic lines per ampere-turn per unit length” (of the embedded part of a coil). This is equivalent to perms per unit length.

In the ampere-ohm system the internationally accepted unit of permeance is the henry.¹ Therefore, if in eq. (2) M is measured in ampere-turns and Φ in webers, ℘ is in henrys, and no new unit for permeance is necessary. In this case the reluctance ℛ in eqs. (1) and (3) is in henrys⁻¹; or spelling the word henry backwards, as in the case of mho and daraf, the natural unit of reluctance in the ampere-ohm system gets the euphonious name of yrneh (to be pronounced earney).

Since, however, the maxwell is used almost exclusively as the unit of flux, it seems advisable to introduce the rel and the perm as units directly related to it. Should engineers gradually feel inclined to use the weber and its submultiples as the units of flux, then the henry, the yrneh, and their multiples and submultiples would naturally be used as the corresponding units of permeance and reluctance.

We have, therefore, the two following systems of units for reluctance and permeance, according to whether the maxwell or the weber is used for the unit of flux (one ampere-turn being the unit of m.m.f. in both cases):

Unit of flux Unit of permeance Unit of reluctance
maxwell perm rel
weber henry yrneh

One perm = 10⁻⁸ henry; one rel = 10⁸ yrnehs.

1 Although the henry is defined as the unit of inductance, it is shown in Art. 58 below that permeance and inductance are physically of the same dimensions and hence measureable in the same units.

V. Karapetoff.
The Magnetic Circuit.
New York: McGraw-Hill Book Company, 1911.
Pages 9-10.

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