For dry air at o° and a megadyne per square centim., we have 145. Expansions of Volumes per degree Cent. (abridged from Watts's 'Dictionary of Chemistry, Article Heat, pp. These results are partly from direct observation, and partly calculated from observed linear expansion. 120 CHAPTER X. MAGNETISM. 146. 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 L2' the dimensional equations P2L-2 = force = MLT-2, P2= ML3T-”, P= M*L*T ̃1; that is, the dimensions of a pole (or the dimensions of strength of pole) are ML T-1. 147. The intensity of a magnetic field is the force which a unit pole will experience when placed in it. Denoting this intensity by I, the force on a pole P will be IP. Hence IP = force = MLT-2, I = MLT-2. MLT=MLT1; that is, the dimensions of field-intensity are M3⁄4L ̄*T ̃2. 148. 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, MLT-1. 5 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 -1 ; a couple ML2T-2 by a field-intensity MLT1; that is, it is MLT1 as before. 149. If different portions be cut from a uniformly magnetized substance, their moments will be simply as their volumes. Hence the intensity of magnetization of a uniformly magnetized body is defined as the quotient of its moment by its volume. But we have 5 moment – MLT-1. L−3 = ML ̄T1. volume = Hence intensity of magnetization has the same dimensions as intensity of field. When a magnetic substance (whether paramagnetic or diamagnetic) is placed in a magnetic field, it is magnetized by induction; and each substance has its own specific coefficient of magnetic induction (constant, or nearly so, when the field is not excessively intense), which expresses the ratio of the intensity of the induced magnetization to the intensity of the field. For paramagnetic substances (such as iron) this coefficient is positive; for diamagnetic substances (such as bismuth) it is negative; that is to say, the induced polarity is reversed end for end as compared with that of a paramagnetic substance placed in the same field. ル 150. 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 1. To find the multiplier for reducing magnetic intensities from the foot-grain-second system to the C.G.S. system. The dimensions of the unit of intensity are ML-T-1. In the present case we have M = '0648, L⇒ 30°48, T=1, since a grain is 0648 gramme, and a foot is 30:48 centim. Hence MLT-1 = 0648 30.48 = 04611; that is, the foot grain-second unit of intensity is denoted by the number *04611 in the C.G.S. system. This number is accordingly the required multiplier. 2. To find the multiplier for reducing intensities from the millimetre-milligramme-second system to the C.G.S. system, we have 3. Gauss states (Taylor's 'Scientific Memoirs,' vol. ii., p. 225) that the magnetic moment of a steel bar-magnet, of one pound weight, was found by him to be 100877000 millimetre-milligramme-second units. Find its moment in C.G.S. units. |