pivoted about a verticaxis, as in Fig. 177, was made to rotate very rapidly and uniformly. Such a ring in rotating cuts the lines of force of the earth's magnetism. The northern half of the ring, in moving from west toward east, will have (see Rule, Art. 225) an upward current induced in it, while the southern half, in crossing from east toward west, will have a downward current induced in it. Hence the rotating ring will, as it spins, act as its own galvanometer if a small magnet be hung at its middle; the magnetic effect due to the rotating coil being proportional directly to the horizontal component of the earth's magnetism, to the velocity of Fig. 177. E -N rotation, and to the number of turns of wire in the coil, and inversely proportional to the resistance of the wire of the coils. Hence, all the other data being known, the resistance can be calculated and measured as a velocity. The earliest ohms or B.A. units were constructed by comparison with this rotating coil; but there being some doubt as to whether the B.A. unit really represented 10o centims. per second, a redete. mination of the ohm was suggested in 1880 by the British Association Committee. At the first International Congress of Electricians in Paris 1881, the project for a redetermination of the ohm was endorsed, and it was also agreed that the practical standards should no longer be constructed in German silver wire, but that they should be made upon the plan originally suggested by Siemens, by defining the practical ohm as the resistance of a column of pure mercury of a certain length, and of one millimetre of cross-section. The original "Siemens' unit" was a column of mercury one metre in length, and one square millimetre in section, and was rather less than an ohm (0′9540 B.A. unit). Acting on measurements made by leading physicists of Europe, the Paris Congress of 1884 decided that the mercury column representing the "legal" ohm should be 106 centimetres in length. This was, however, never legalized in this country or in America, as it was known to be incorrect. Lord Rayleigh's determination gave 106:21 centimetres of mercury, as representing the true theoretical ohm (= 109 absolute units); and Rowland's determinations at Baltimore came slightly higher. The British Association Committee in 1892 agreed to lengthen it to 106 3 centims., and to define by mass instead of section. This was decided finally as the international ohm by the Congress of Chicago in 1893. These international units are now legalized in England and the United States. The bulletin issued by the U. S. Superintendent of Standard Weights and Measures, and endorsed by the Secretary of the U. S. Treasury, is given in abstract in Appendix B. The old B.A. unit is only 0.9863 of the true ohm; the Siemens' unit is only 0-9408. 359. Ratio of the Electrostatic to the Electromagnetic Units. If the student will compare the Table of Dimensions of Electrostatic Units of Art. 283 with that of the Dimensions of Electromagnetic Units of Art. 356, he will observe that the dimensions assigned to similar units are different in the two systems. Thus, the dimensions of " Quantity" in electrostatic measure are M L T1, and in electromagnetic measure they are Ma L. Dividing the former by the latter we get LT-1, a quantity which we at once see is of the nature of a velocity. This velocity occurs in every case in the ratio of the electrostatic to the electromagnetic measure of every unit. It is a definite concrete velocity, and represents that velocity at which two electrified particles must travel along side by side in order that their mutual electromagnetic attraction (considered as equivalent in so moving (Art. 397) to two parallel currents) shall just equal their mutual electrostatic repulsion (see Art. 260). This velocity, "v," which is of enormous importance in the electromagnetic theory of light (Art. 518), has been measured in several ways. (a) Weber and Kohlrausch measured the electrostatic unit of quantity and compared it with the electromagnetic unit of quantity, and found the ratio v to be=3·1074 × 1010 centims. per second. (b) Lord Kelvin compared the two units of potential and found (c) Professor Clerk Maxwell balanced a force of electrostatic attraction against one of electromagnetic repulsion, and found = 2.88 X 1010. (d) Professors Ayrton and Perry measured the capacity of a condenser electromagnetically by discharging it into a ballistic galvanometer, and electrostatically by calculations from its size, and found so we take v as 3 x 1010, or thirty thousand million centimetres per second. 360. Rationalization of Dimensions of Units. It seems absurd that there should be two different units of electricity; still more absurd that one unit should be thirty thousand million centimetres per second greater than the other. It also seems absurd that the dimensions of a unit of electricity should have fractional powers, since such quantities as M and L are meaningless. These irrational things arise from the neglect to take account of the properties of the medium in applying the law of inverse squares to form definitions of the unit of electricity in the electrostatic system, and of the unit-pole in the magnetic system. If we were to insert the dielectric constant k in the former, and the permeability in the latter, we might, if we knew the dimensions of these quantities, be able to rationalize the dimensional formulæ. But we do not know their dimensions. Rücker has, however, shown that they can be rationalized, and the two sets of units brought into agreement,* by assuming that the product kμ has the dimensions of the reciprocal of the square of a velocity: or v = 1/√k. If k were the reciprocal of the rigidity of the ether, and its density, would represent the velocity of propagation of waves in it. Compare Art. 518 on electromagnetic theory of light. 361. Earth's Magnetic Force in Absolute Units. In making absolute determinations of current by the tangent galvanometer, or of electromotive-force by the spinning coil, it is needful to know the absolute value of the earth's magnetic field, or of its horizontal component. The intensity of the earth's magnetic force at any place is the force with which a magnet-pole of * See Everett's Units and Physical Constants, 4th edition (1893), p. 208. unit strength is attracted. As explained in Art. 153, 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, as the direct determination of the latter 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 (Art. 135). In one of these observations the product MH is determined by a method of oscillations (Art. 133); in the second the quotient is determined by a particular method of deflexion (Art. 138). The square root of the quantity obtained by dividing the former by the latter will, of course, give H. M 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 Of these quantities T 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 formula: where 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 r 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 8, whose tangent is directly propor Dividing the former equation by this, and taking the square Foot, we get LESSON XXVIII. — Properties of Iron and Steel 362. Magnetization of Iron. - When a piece of magnetizable metal is placed in a magnetic field, some of the lines of magnetic force run through it and magnetize it. The intensity of its magnetization will depend upon the intensity of the field into which it is put and upon the metal itself. There are two ways of looking at the matter, each of which has its advantages. We may think about the internal condition of the piece of metal, and of the number of magnetic lines that are running through it and emerging from it into the surrounding space. This is the modern way. Or we may think of the magnetism of the iron or other metal as something resident on the polar surfaces, and expressed therefore in units of magnetism. This is the old way. The fact that soft iron placed in the magnetic field becomes highly magnetic may then be expressed in the following two ways: (1) when iron is placed in the magnetic field, the magnetic lines run in greater quantities through the space now occupied by iron, for iron is very permeable to the lines of magnetic induction, being a good conductor of the magnetic lines; (2) iron when placed in the magnetic field develops strong poles on its end-surfaces, being highly susceptible to magnetization. Each of these ideas may be rendered exact by the introduction of appropriate coefficients. 363. Permeability. — The precise notion now attached to this word is that of a numerical coefficient. Suppose a magnetic force — due, let us say, to the circulation of an electric current in a surrounding coil were to |