as 1 to 1.367 Expansion from 0° to 100° at const. pressure, Pressure-height at 0° C., about 7.99 × 105 cm., Standard barometric column,. or as 273 to 373 •2375 •1691 or about 26210 ft. 76 cm. 29.922 inches. 1033 3 gm. per sq. cm. or 14.7 lbs. per sq. inch. or 2117 lbs. foot. or 1 0136 × 106 dynes per sq. cm. 001293 gm. per cub. cm. or '0807 lbs. per cub. foot. Standard density, at 0° C.,......... Standard bulkiness,. وو 773.3 cub. cm. per gm. or 12:39 cub. ft. per lb. If A denote the density of dry air and W that of vapour at saturation, the density of saturated air is A-W, or more exactly A 608 W. 144 CHAPTER X. MAGNETISM. 179. THE unit magnetic pole, or the pole of unit strength is that which repels an equal pole at unit distance with unit force. In the C.G.S. system it is the pole which repels an equal pole, at the distance of 1 centimetre, with a force of 1 dyne. If P denote the strength of a pole, it will repel an equal P2 pole at the distance L with the force Hence we have the dimensional equations P2L- -2 force = MLT-2, P2 = L2 ML3T-2, P = MLT1; that is, the dimensions of a pole (or the dimensions of strength of pole) are MLT1. 180. The work required to move a pole P from one point to another is the product of P by the difference of the magnetic potentials of the two points. Hence the dimensions of magnetic potential are work ML2T-2. M ̃3L ̄*T = MaL1T ̄1. Р = 181. The intensity or strength of a magnetic field is the force which a unit pole will experience when placed in it. 1 Denoting this intensity by H, the force on a pole P will be HP. Hence HP = force = MLT-2, H = MLT-2. M ̄3L ̄*T = M3L ̄ ̄1T1; that is, the dimensions of field intensity are M3L_3T ̃1. 182. The moment of a magnet is the product of the strength of either of its poles by the distance between them. Its dimensions are therefore LP; that is, M L T1. Or, more rigorously, the moment of a magnet is a quantity which, when multiplied by the intensity of a uniform field, gives the couple which the magnet experiences when held with its axis perpendicular to the lines of force in this field. It is therefore the quotient of a couple ML2T-2 by a field-intensity MLT; that is, it is ML T1as before. 183. If different portions be cut from a uniformly magnetised substance, their moments will be simply as their volumes. Hence the intensity of magnetisation of a uniformly magnetised body is defined as the quotient of its moment by its volume. But we have moment MLT-1. L-3 = ML-T-1. volume = Hence intensity of magnetisation (often called simply magnetisation) has the same dimensions as intensity of field. When a magnetic substance (whether paramagnetic or diamagnetic) is placed in a magnetic field, it is magnetised by induction. From this point of view the intensity of the field to which the magnetisation is due is called the magnetising force. 184. If we suppose a narrow crevasse to be excavated in the magnetised substance, there will be no free mag K netism on its sides if their direction be longitudinal, that is, parallel to the direction of magnetisation; and when we speak of the magnetising force at a point in a body we mean the field which would exist in such a crevasse excavated about the point. Magnetising force is now usually denoted by H. It is called, indifferently, magnetising force, magnetic force, or strength of field. On the other hand, if the narrow crevasse be transverse, that is, if it cut the lines of magnetisation at right angles, there will be free magnetism of opposite signs on the two faces of the crevasse, the surface-density of this magnetism on either face being numerically equal to the intensity of magnetisation, which is denoted by I. These two surface-layers produce a field of intensity 41 in the narrow space between them, and this field must be compounded with the field H in order to obtain the resultant field within the transverse crevasse. This resultant is called the intensity of induction, or more briefly the induction, at the point in question, and is denoted by B. Accordingly, whether the body is isotropic or not, B is the resultant of H and 47 1. 185. If the substance is isotropic, and has no magnetism except what is called out by the existing field, H and I have parallel directions, which are the same or opposite according as the substance is paramagnetic (like iron) or diamagnetic (like bismuth). In the former case H and I must be regarded as having the same sign, and in the latter case opposite signs. In both cases we K μ denoting the ratio of B to H, and κ the ratio of I to H. μ is called the permeability and κ the susceptibility of the substance. These ratios are by no means constant for a given substance, but largely depend on the value of H. As H increases from zero, their values (in most cases at least) first increase to a maximum and then decrease. The value of κ when negative is always small so that μ is always positive, being greater than unity for paramagnetic and less than unity for diamagnetic substances. -1 The dimensions of B, H, and I are M L3 T−1; μ and are mere numerical quantities independent of the units of mass, length, and time. 186. In air is sensibly zero even in strong fields, and B is therefore sensibly equal to H. It can be shown that the component of B normal to the surface of a magnetised body (whether the magnetisation be temporary or permanent) has the same value just outside as just inside the body; whence it can be deduced that if tubes be drawn following the direction of B, the value of the product Bx section of tube will be the same at all parts of one and the same tube. Every such tube returns into itself. One portion of it may be within a magnetised body, and the other portion in the external air. It is convenient to make the tubes of such sizes that the value of the constant product B x section is unity for each. Then the number of these "tubes of induction" that cut any area is called the "flux of induction across the area. If the area is bounded by a conducting |