33^ 



NATURE 



[August 4, 1892 



be fairly covered ; though a smaller weber would have been 

 better if it had been equally convenient as regards the volt. 

 The pull between two parallel surfaces joined by a weber 



is — — dynes, or four hundred thousand tons. A milli-weber 



gives less than half a ton pull ; and a micro-weber less than half 

 a gramme. 



Because of the property that the voltage excited in a circuit is 

 equal to the webers cut by it per second, a weber might be 

 called a sec-volt. It is equal to a secohm-ampere-turn ; that is to 

 say, if a single turn of wire can have a self-induction coefficient 

 of one secohm, it will excite a weber of induction for every 

 ampere passing through it. 



[Such a circuit in the form of an anchor ring would be enormous, 

 something like a mile across ; but it could be made in the form 

 of a solid cylinder of best iron (yu = 2500), with an axial per- 

 foration for the wire, and 80 metres long. 



If a secohm coil has n turns, then an ampere passing through it 



excites only -th of a weber ; for, since every turn encloses the 



n 

 induction, the latter is effective n times over, and so the in- 

 duction coefficient is n times the induction per ampere, or w^ 

 times the induction per ampere turn.] 



No name is needed for intensity (or density) of induction (B), 

 for that can always be expressed in webers per unit area. 



[For instance, strongly magnetized iron, with say 10,000 lines 

 to the square centimetre, has one-tenth of a weber per square 

 foot, or 07 milli-webers per square inch.] 



And there is a practical gain in thus leaving the specification 

 of area open, for it enables British units of length to be employed 

 in measuring air-gaps, yokes, cores, and polepieces. 



So long as dynamo dimensions are commonly expressed in 

 inches, there is no serious objection to specifying induction in 

 fractions of a weber per square inch or per square foot. 



Magnetomotive Force. 



Now consider the magnetic analogue of the volt ; the unit of 

 magnetic potential or magnetomotive force. By this is under- 

 stood the line integral of the magnetizing force H, the quantity 

 4ir«C, the step of potential once through and all round the 

 circuit of a coil. It is a quantity most important in practice, 

 and requires a name. 



Mr. Heaviside has suggested the name "gaussage," as analogous 

 to voltage ; and, if this were adopted, the unit of magnetomotive 

 force would be the gauss. The intensity of magnetizing force 

 would be the gauss-gradient, or drop of gaussage per centimetre ; 

 no special name is needed for the unit of this quantity H. 



The common practical unit of gaussage at present is the 

 ampere-turn, and this has several advantages. It may, how- 

 ever, be found better to make some convenient number of 

 ampere-turns into a gauss ; for instance, the c.g.s. unit of 



gaussage would be --or 1*2566 ampere- turns. If that were 



adopted as the gauss, the horizontal component of the earth's 

 magnetic intensity about here would be, say "iS gauss per linear 

 centimetre. 



But this unit, whether the c.g.s. unit or the ampere-turn, is 

 very small. The step of potential all round a single ampere- 

 turn is only equivalent to a vertical step of about 2 centimetres 

 in the earth's field. 



Nevertheless, in spite of its smallness, the ampere-turn as 

 practical unit of gaussage will probably commend itself by 

 reason of its simplicity. Let us see how it works out. 



Reluctance. 

 The ratio of gaussage to the induction excited by it, is a 

 quantity characteristic of the magnetic circuit, and called its 



reluctance or magnetic resistance. This is the quantity — for 



Am 



simple circuits, or 2 .— for complex ones ; it is unfortunately not 



A^ 

 constant for any but air circuits. This constitutes one difficulty of 

 naming its unit satisfactorily, else it might be expressed as so 

 many "gilberts" or "sturgeons" (analogous to ohms). It is, 

 however, fairly constant under many common conditions of 

 practice, and it can always be expressed as gausses per weber ; 

 and perhaps this way is sufficient. 



A magnetic circuit with unit reluctance is one that requires 

 ■one gauss to induce in it one weber. 



NO. II 88, VOL. 46] 



Permeability. 

 Permeability (/u), analogous to electric conductivity, would be 

 measured by the webers induced through unit cube of the 

 material between whose faces there is unit fall of gaussage. It has 

 been suggested (by Prof. Perry) that the permeability of air had 

 better be called 4ir x ro"^. But the whole electromagnetic 

 system of units is based on the ;u for air being called i ; so it 

 would be rather confusing to change that. Moreover, it would 

 be a retrograde step to affix another incorrect value to the con- 

 stant /u, instead of waiting and trying to find out what its value 

 really is. It is better to adhere for the present to the existing 

 table of permeabilities, and to use whatever constant factor may 



be needed in order to turn —- into practical units of reluctance. 



mA 



Permeance. 

 But the reciprocal of reluctance, or the webers induced per 

 gauss, may be the more instructive thing to attend to and name ; 

 just as conductivity is often more directly interesting than resist- 



uA 

 ance. This reciprocal ratio, ^, has been called "permeance," 



and that is not a bad name for it ; it is proportional to the 

 inductance of a single-looped circuit. Permeability is the per- 

 meance of unit cube of the material. Permeance is the webers 

 induced per unit drop of gaussage. Permeability is the webers 

 per unit area induced by unit gauss gradient. 



The permeance of the magnetic circuit enclosed by a solenoid of 

 wire is the same as its appropriate self- induction- coefficient 

 divided by o^-k times the square of its number of turns. 



The cg.s. unit of permeance (or of reluctance) is that of a 

 centimetre cube of air, and is not a bad-sized unit. But it is 

 inconsistent with the weber as 10* and the gauss as a single 

 ampere turn. 



One of the three must give way. 



On the whole I have no hesitation in suggesting that the 

 derived unit (that of permeance) must give way, and be taken as 

 47r X 10^ c.g.s. units, in order to harmonize with the other two as 

 already defined. 



The fact is that the great size of the weber renders a small 

 gauss desirable, in order that their product may not represent 

 too large a quantity of energy. For instance, if i c.g.s. unit were 

 taken as[the unit of permeance, the weber being fixed at 10*, then 

 the gauss would also be 10^, and the gauss-weber would be 10^ 

 joules, or nearly 300 Board of Trade units ; which is far too 

 much. 



Whereas if the unit of permeance is fixed high, and the gauss 

 kept small, then the energy corresponding to a gauss-weber may 

 be moderate. Thus with 10* c.g.s. as weber, and an ampere-turn 



as gauss, their product is only — ergs, or — or about 8 



47r 4^ 



joules ; which will be useful in energy considerations connected 

 with the heating of transformers. 



I therefore propose, in order to retain the ampere-turn as 

 unit of gaussage, that the permeance of a cylinder of material of 



length / and area A be reckoned as ^ multiplied by \-k x 10^, 



if dimensions of the cylinder are measured in centimetres ; ju being 

 its ordinarily tabulated value with air = i. If dimensions are 

 measured in inches, then the permeance of a cylinder will be 



^ multiplied by 4— x 10^. that is by about \ lo^ 



The unit of permeance thus suggested is immensely big, and 

 it requires a name of which easy sub-multiples could be formed. 



A slab of iron l centimetre thick, and with its ^ = 2500, 

 would need an area of 5 square metres in order to have unit 

 permeance ; but a micro-unit would be possessed by an air-gap 

 a millimetre thick and less than a decimetre square. 



Proposed Resolutions. 



(1) That the unnecessary prefix "micro" be dropped before the 

 word farad, and that the farad be defined afresh as lo"^^ c.g.s. 

 electromagnetic units of capacity. 



(2) That the name "mo" for the unit of conductance or the 

 ampere per volt, be recognized and adopted. (Every mo in a 

 cable enables it to carry an ampere with a drop of i volt.) 



(3) That the ampere-hour be recognized as a convenient 

 practical unit of electrical quantity. 



(4) That the volt-ampere-hour be recognized as a convenient 



