this intrusive constant 4 π entering into all these physical equations and greatly adding to their difficulties in seeing the real meaning of the symbols. The true remedy for this confusion has been suggested by Mr. Oliver Heaviside to be the substitution of rational for irrational formulæ and definitions. He has restated the definition of a unit magnetic pole in such a way that the subsequently derived definitions. of important practical magnetic quantities are free from this disfiguring 47 and physically more intelligible. Mr. Heaviside's starting-point is a new definition of the unit magnetic pole as follows: A magnetic pole is said to have a strength of m units if it attracts or repels another equal pole placed at a distance of d centimetres with a force of m2 4π d2 dynes. The above definition furnishes us with a unit magnetic pole which is not the same in magnitude as the unit pole previously defined Mr. Heaviside's unit pole is called a rational pole. Hence a rational pole of strength m attracts another rational pole of strength m' placed at a distance of d centimetres in air with a force of ƒ dynes, so that f= m m' It follows from this that a rational unit magnetic pole attracts another equal and opposite rational unit pole placed at a distance of one centimetre with a force of I of a dyne, whereas the irrational, or C.G.S., unit 4π poles are of such a magnitude or strength as to attract each other with a force of I dyne under the same conditions. Hence the rational unit pole is weaker or smaller than the irrational or present unit pole in the ratio of The magnetic force due to a rational pole of strength m, or having a strength of m in rational units, at a disunits. Returning, then, tance of a centimetres, is m 4 πd 2 to our magnetic filament, let us suppose as before a small sphere of radius r described round its pole of strength m (reckoned in rational units). The magnetic force at the surface of this sphere is m 2 4πr units, and this is also, there fore, the numerical value of the magnetic flux density at that surface. Hence the total magnetic flux through the m surface of the sphere is 4πr2 x units=m units, and 2 4πr therefore the number which denotes the total magnetic flux coming out of the pole of strength m in rational units is also m. The rational system thus gives us an obvious and natural definition of a unit magnetic pole, viz, that it is a pole from which proceeds a unit of magnetic flux. It follows, therefore, that if the intensity of magnetisation of the magnet is I, the flux traversing any transverse section s of the magnet is Is units; and that if the filament is an endless or poleless iron filament, magnetised uniformly in a field by a resultant external magnetic force H, we have the equation B = I + H as a rational equation expressing the fact that the resultant magnetic flux per square centimetre of cross section along the iron is equal to the intrinsic flux I produced in the iron per se, added to the flux H produced in the same space if the iron is removed. It follows also then, that we have the equation μ = I + k as a rational equation, connecting μ and k. The meaning of this equation is, that taking the permeability of air as unity, the susceptibility k of the iron may be regarded as the amount by which the metal increases the permeability of the space which it occupies. On the rational system, since the unit pole strength has been decreased in the ratio of I to I √ATT' or 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 proceeding from a unit pole, it follows that Mr. 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. By adoping a similar rational definition of a unit of electric quantity, a complete rational system of electrical units has been framed by Mr. Heaviside, in which the magnitude of the rational units is related to those of the C.G.S., or present practical units, as follows: I Relation of the Rational to the existing Electric and Magnetic Units.* I 3 5441 present units. I 3'5441 I = 3'5441 .. I amperes. ohm. Although the rational system has obvious and immense advantages from a theoretical point of view, it * From the 'Electrician,' vol. xxxv. p. 774. may yet be some considerable time before it is introduced into practice. This latter step would involve remaking or reconstructing all the thousands of ampere-meters, voltmeters, and resistance coils in actual use, and would necessitate a practical revolution almost akin to that resulting from a proposal to change the actual lengths and weights of the standards denominated respectively a yard or a pound. 79 CHAPTER IV. ELECTRIC CURRENTS. § 1. Electric Currents and Electromotive Force. -We have already pointed out that a non-magnetic material like a copper wire can, under some conditions, exhibit magnetic qualities. If we find under any circumstances a wire of any material whatever exhibiting the two properties of being more or less hot, and having a magnetic flux taking place round it in closed loops or paths, we say that an electric current is flowing along this wire. As a matter of fact, we do not know that anything flows, or if it does, in what direction or with what velocity it flows. We use, however, the phrase electric current, sanctioned by custom, to express the sum total of all the properties possessed by the wire under these conditions, the principal ones being that the wire, or conductor as it is termed, is in some degree warm, and has a magnetic flux of greater or less strength taking place round it and within it in closed lines. The conductor is in fact the axis round which a magnetic flux takes place, the lines of which are all closed loops having their planes perpendicular to the wire. Since this flux may take place in one direction or in another, may be of any strength, and may be constant in strength or variable, we have as a principal fact about electric currents that they have direction, and magnitude or strength, and may be varying or unvarying in strength. If the embracing magnetic flux regularly changes its direction periodically, being first directed one way and then the other, |