322. Electromagnetic Units.-The preceding magnetic units give rise to the following set of electrical units, in which the strength of currents, etc., are expressed in magnetic measure. The relation of this "electromagnetic" set of units to the "electrostatic" set of units of Art. 257 is explained in Art. 365. Unit Strength of Current.-A current has unit strength when one centimetre length of its circuit bent into an arc of one centimetre radius (so as to be always one centim. away from the magnet-pole) exerts a force of one dyne on a unit magnet-pole placed at the centre (Art. 196). Unit of Quantity of Electricity is that quantity which is conveyed by unit current in one second. Unit of Difference of Potential (or of Electromotive-force). Potential is work done on a unit of electricity; hence unit difference of potential exists between two points when it requires the expenditure of one erg of work to bring a unit of electricity from one point to the other against the electric force. Unit of Resistance.—A conductor possesses unit resistance when unit difference of potential between its ends causes a current of unit strength (i.e. one unit of quantity per second) to flow through it. 323. Practical Units.-Several of the above "absolute " units would be inconveniently large and others inconveniently small for practical use. The following are therefore chosen instead, as electromagnetic units :— Electromotive-force.-The Volt, 1 = 108 absolute units (being a little less than the E.M.F. of one Daniell's cell). Resistance.-The Ohm, = 109 absolute units of resistance (and theoretically the resistance represented by the velocity of one earth-quadrant per second). (See Art. 364.) Current.-As a practical unit of current, that furnished by a potential of one volt though one ohm is taken, being IO of an absolute (electro-magnetic) unit of current, and is known as one Ampère (formerly one "weber "). Quantity.-The Coulomb, = 10-1absolute units of quantity of the electromagnetic system. Capacity.-The Farad, = ΙΟ (or one one-thousandmillionth) of absolute unit of capacity. 9 Seeing, however, that quantities a million times as great as 1 1.000.000 This system of "practical" units was devised by a committee 324. Dimensions of Magnetic and Electromagnetic Units. UNITS. DIMENSIONS. (Magnetic.) Strength {Quantity of magnetism} = √/force × (distance)? Magnetic Potential (Electro-magnetic.) Electromotive-Force Resistance Capacity = work = force strength of pole M LT-1 = strength of pole = ML-T-1 } NOTE ON MEASUREMENT OF EARTH'S MAGNETIC FORCE IN ABSOLUTE UNITS. 325a. The intensity of the earth's magnetic force at any place is the force with which a magnet-pole of unit strength is attracted. As explained in Art. 138, it is usual to measure the horizontal component H of this force, and from this and the cosine of the angle of dip to calculate the total force I, as the direct determination of the total force is surrounded with difficulties. To determine H in absolute (or C.G.S.) units, it is necessary to make two observations with a magnet of magnetic moment M; (the magnetic moment being, as mentioned in Art. 313, the product of its length into the strength of one of its poles). In one of these observations the product MH is determined by a M method of oscillations; in the second the quotient is deterH mined by a particular method of deflection. The square root of the quantity obtained by dividing the latter by the former will, of course, give H. (i.) Determination of MH.-The time t of a complete oscillation to-and-fro of a magnetic bar is where K is the "moment of inertia of the magnet. This formula is, however, only true for very small arcs of vibration. By simple algebra it follows that 4π2K HM = 12. Of these quantities is ascertained by a direct observation of the time of oscillation of the magnet hung by a torsionless fibre ; and K can be either determined experimentally or by one of the following formulæ :— where w is the mass of the bar in grammes, its length, a its radius (if round), b its breadth, measured horizontally (if rectangular). M (ii.) Determination of -The magnet is next caused to deflect a small magnetic needle in the following manner, "broadside on." The magnet is laid horizontally at right angles to the magnetic meridian, and so that its middle point is (magnetically) due south or due north of the small needle, and at a distance from its centre. Lying thus broadside to the small needle its N.-pole will repel, and its S.-pole attract, the N.-pole of the needle, and will exercise contrary actions on the S.-pole of the needle. The total action of the magnet upon the needle will be to deflect the latter through an angle d, whose tangent is directly proportional to and inversely proportional to the cube of the distance r; or M M H' Dividing the former equation by this, and taking the square root, we get, √ NOTE ON INDEX NOTATION. 325b. Seeing that electricians have to deal with quantities requiring in some cases very large numbers, and in other cases very small numbers, to express them, a system of index notation is adopted, in order to obviate the use of long rows of cyphers. In this system the significant figures only of a quantity are put down, the cyphers at the end, or (in the case of a long decimal) at the beginning, being indicated by an index written above. Accordingly, we may write a thousand (= 10 × 10 × 10) as 103, and the quantity 42,000 may be written 42 x 103. The British National Debt of £770,000,000 may be written £77 × 107. Fractional quantities will have negative indices when written as exponents. Thus (= 0.01), = I 10 ÷ 10 = 10-2. And so the decimal o'00028 will be written 28 × 10-5 (being = 28 × '00001). The convenience of this method will be seen by an example or two on electricity. The electrostatic capacity of the earth is 630,000,000 times that of a sphere of one centimetre radius, 63 × 107 (electro static) units. The magnetic moment of the earth is, according to Gauss, no less than 85,000,000,000,000,000,000,000,000 times that of a magnet of unit strength and centim. length, i.e. its magnetic moment is 85 × 1024 units. The resistance of selenium is about 40,000,000,000, or 4 × 1010 times as great as that of copper; that of air is about 1026, or 100,000,000,000,000,000,000,000,000 times as great. The velocity of light is about 30,000,000,000 centimetres per second, or 3 x 1010. As a final example we may state that the number of atoms in the universe, as far as the nearest fixed star, can be shown to be certainly fewer than 7 × 1091 LESSON XXVI.—Electromagnets. 326. Electromagnets.—In 1820, almost immediately after Oerstedt's discovery of the action of the electric current on a magnet needle, Arago and Davy independently discovered how to magnetise iron and steel by causing currents of electricity to circulate round them in spiral coils of wire. The method is shown in the simple diagram of Fig. 114, where a current from a single cell is passed through a spiral coil of wire, in the |