Page:EB1911 - Volume 27.djvu/769

 measurement. Professor Giorgi proposes that the four fundamental quantities shall be the units of length, mass, time and electrical resistance, and takes as the concrete units or standards the metre, kilogramme, second and ohm. Now this proposal not only has the advantage that the theoretical units are identical with the actual practical concrete units, but it is also a rational system. Moreover, the present practical units are unaltered; the ampere, volt, coulomb, weber, joule and watt remain the actual as well as theoretical units of current, electromotive force, quantity, magnetic flux, work and power. But the unit of magnetic force becomes the ampere-turn per metre, and the unit of electric force the volt per metre; thus the magnetic units are measured in terms of electric units. The numerical value of the permeability of ether or air becomes 4 × 10−7 and the dielectric constant of the ether or air becomes 1/4 × 9 × 109 their product is therefore 1/(3 × 108)2, which is the reciprocal of the square of the velocity of light in metres per second.

For a discussion of the Giorgi proposals, see a paper by Professor M. Ascoli, read before the International Electrical Congress at St Louis, 1904 (Journ. Inst. Elect. Eng. Lond., 1904, 34, 176).

It can hardly be said that the present system of electrical units is entirely satisfactory in all respects. Great difficulty would of course be experienced in again altering the accepted practical concrete units, but if at any future time a reformation should be possible, it would be desirable to bear in mind the recommendations made by Oliver Heaviside with regard to their rationalization. The British Association Committee defined the strength of a magnetic pole by reference to the mechanical stress between it and another equal pole: hence the British Association unit magnetic pole is a pole which at a distance of one centimetre attracts or repels another equal pole with a force of one dyne. This, we have seen, is an imperfect definition, because it omits all reference to the permeability of the medium in which the experiment takes place; but it is also unsatisfactory as a starting-point for a system of units for another reason. The important quantity in connexion with polar magnets is not a mechanical stress between the free poles of different magnets, but the magnetic flux emanating from, or associating with, them. From a technical point of view this latter quality is far more important than the mechanical stress between the magnetic poles, because we mostly employ magnets to create induced electromotive force, and the quantity we are then mostly concerned with is the magnetic flux proceeding from the poles. Hence the most natural definition of a unit magnet pole is that pole from which proceeds a total magnetic flux of one unit. The definition of one unit of magnetic flux must then be that flux which, when inserted into or withdrawn from a conducting circuit of one turn having unit area and unit conductivity, creates in it a flow or circulation of one unit of electric quantity. T he definition of a unit magnetic pole ought, therefore, to have been approached from the definition of a unit of electric quantity.

On the C.G.S. or British Association system, if a magnetic filament has a pole strength 𝑚—that is to say, if it has a magnetization , and a section 𝑠, such that 𝑠 equals 𝑚—then it can be shown that the total flux emanating from the pole is $$4\pi m$$. The factor $$4\pi$$, in consequence of this definition, makes its appearance in many practically important expressions. For instance, in the well-known magnetic equation connecting the vector values of magnetization $$\text{I}$$, magnetic force $$\text{H}$$ and magnetic flux density $$\text{B}$$, where we have the equation

$$\text{B} = \text{H} + 4\pi \text{I}$$,

the appearance of the quantity $$4\pi$$ disguises the real physical meaning of the equation.

The true remedy for this difficulty has been suggested by Heaviside to be the substitution of rational for irrational formulae and definitions. He proposes to restate the definition of a unit magnetic pole in such a manner as to remove this constant $$4\pi$$ rational from the most frequently employed equations. His start system mg-point IS a new definition according to which a unit

magnetic pole is said to have a strength of in units if it attracts or repels another equal pole placed at a distance of 𝑑 centimetres with a force of 𝑚24𝑑2 dynes. It follows from this definition that a rational unit magnetic pole is weaker or smaller than the irrational or British Association unit pole in the ratio of 1/√$\overline$ to 1, or 0·28205 to 1. The magnetic force due to a rational pole of strength 𝑚 at a distance of 𝑑 centimetres being 𝑚/4𝑑2 units, if we suppose a magnetic filament having a pole of strength 𝑚 in rational units to have a smaller sphere of radius 𝑟 described round its pole, the magnetic force on the surface of this sphere is 𝑚/4𝑟2 units, and this is therefore also the numerical value of the flux density. Hence the total magnetic flux through the surface of the sphere is

4𝑟2 × 𝑚/4𝑟2 units＝𝑚 units;

and therefore the number which denotes the total magnetic flux coming out of the pole of strength in in rational units is also 𝑚.

The Heaviside system thus gives us an obvious and natural definition of a unit magnetic pole, namely, that it is a pole through which proceeds the unit of magnetic flux. It follows, therefore, that if the intensity of magnetization of the magnetic filament is and the section is 𝑠, the total flux traversing the centre of the magnet is 𝑠 units; and that if the filament is an endless or poleless iron filament magnetized uniformly by a resultant external magnetic force H, the flux density will be expressed in rational units by the equation B＝ + H. The physical meaning of this equation is that the flux per square centimetre in the iron is simply obtained by adding together the flux per square centimetre, if the iron is supposed to be removed, and the magnetization of the iron at that place. On the rational system, since the unit pole strength has been decreased in the ratio of to 1/√$\overline$, or of 3·5441 to 1, when compared with the magnitude of the present irrational unit pole, and since the unit of magnetic flux is the total flux proceed in from a magnetic pole, it follows that Heaviside’s unit of magnetic flux is larger than the C.G.S. unit of magnetic flux in the ratio of 3·5441 to 1.

It will be seen, therefore, that the Heaviside rational units are all incommensurable with the practical units. This is a great barrier to their adoption in practice, because it is impossible to discard all the existing resistance coils, ammeters, voltmeters, &c., and equally impossible to recalibrate or readjust them to read in Heaviside units. A suggestion has been made, in modification of the Heaviside system, which would provide a system of rational practical units not impossible of adoption. It has been pointed out by J. A. Fleming that if in place of the ampere, ohm, watt, joule, farad and coulomb, we employ the dekampere, dekohm, the dekawatt, the dekajoule, the dekafarad and the dekacoulomb, we have a system of practical units such that measurements made in these units are equal to measurements made in Heaviside rational units when multiplied by some power of 4. Moreover, he has shown that this power of 4, in the case of most units, varies inversely as the power under which, appears in the complete dimensional expression for the quantity in electromagnetic measurement. Thus a current measured in Heaviside rational units is numerically equal to (4)undefined times the same current measured in dekamperes, and in the electromagnetic dimensional expression for current, namely, LundefinedMundefinedT−1−, appears as −. If, then, we consider the permeability of the ether to be numerically 4 instead of unity, the measurement of a current in dekamperes will be a number which is the same as that given by reckoning in Heaviside rational units. In this way a system of Rational Practical Units (R.P. Units) might be constructed as follows:—

All except the unit of magnetic force and magnetic polarity are commensurable with the corresponding C.G.S. units, and in multiples which form a convenient practical system.

Even the rational systems already mentioned do not entirely fulfil the ideal of a system of physical units. There are certain constants of nature which are fundamental, invariable, and, as far as we know, of the same magnitude in all parts of the universe. One of these is the mass of the atom, say of hydrogen. Another is the length of a wave of light of particular refrangibility emitted by some atom, say one of the two yellow lines in the spectrum of sodium or one of the hydrogen lines. Also a time is fixed by the velocity of light in space which is according to the best measurement very close to 3 × 1010 cms. per sec. Another natural unit is the so-called constant of gravitation, or the force in dynes due to the attraction of two spherical masses each of 1 gramme with centres at a distance of 1 cm. Very approximately this is equal to 648 × 1010 dynes. Another natural electrical