Ex. 2. Calculate the conductivity in the following instance. A square metre of a substance, one centimetre thick, has one side kept at 100° C., and the other by means of ice at 0° C.; and in the course of 30 minutes one kilogramme of ice is melted by this operation. We shall express conductivity in terms of Hence 79 Calories 79 79 = 1 kgm. of ice melted 30 minutes; calories per min. per 1002 sq. cm. = 100 deg. Cent. per cm., calories per min. per sq. cm. = deg. Cent. per cm. 30 × 1003 i.e., 2.6 × 10-6 calories per min. per sq. cm. = deg. Cent. per cm. EXERCISE XLV. 1. How many gramme-degrees of heat will be conducted in an hour through an iron bar two square centimetres in section and four centimetres long, its two extremities being kept at the respective temperatures of 100° C., and 178° C., the mean conductivity of iron being '12. The units are a gramme, a centimetre, a second, and a degree centigrade? 2. Calculate the quantity of heat lost per hour from each square metre of the surface of an iron steam-boiler 0·8 centimetres in thickness, when the temperature of the inner surface of the boiler is 120°, and that of the outer surface 11910, the coefficient of conductivity of iron being 115, referred to the centimetre as the unit of length, the minute as the unit of time, and the quantity of heat required to raise the temperature of a gramme of water from 0° C. to 1o C. as the unit of heat. 3. Find how much heat is conducted in an hour across a plate of copper, one square metre in area, 16 centimetres thick, one side of the plate being kept 25 degs. Cent. hotter than the other. The conductivity of copper for heat is 1.108 in centimetre-gramme-second units. 4. The thermal conductivity of iron is about 0·0133, the units being the foot, minute, and degree Centigrade. Find how much heat per hour is lost by a boiler of inch plate, whose surface is 10 square yards, and whichat the dimenat 110° C., the external surface of the boiler being kept at 100° C. 5. Find how much heat is conducted in half an hour through an iron centimetres thick and 1000 square centimetres in area, the temperature o two sides being kept at 0° C. and 20° C. 6. The inside of the wall of a house is kept at 16° C., while the outside is at 0° C.; the wall is of solid stone, and two feet thick. How much heat is lost across it per square foot per hour? Take the conductivity at 0·001 lb. of water by deg. Cent. per sec. per sq. ft. deg. per ft. thick. = 7. The conductivity of silver in terms of the millimetre, second, deg. Cent., and water is 109; express it in terms of the C.G.S. thermal unit. 8. From the table deduce the thermal resistance relatively to silver, of lead, copper, mercury, German silver. SECTION XLVI.-MAGNETIC. ART. 203.-Unit Magnetic Pole. A quantity of magnetism concentrated at a point is called a magnetic pole. The repulsive or attractive force exerted by one magnetic pole on another is proportional to the amount of magnetism of the one pole and to the amount of magnetism of the other pole, and is inversely proportional to the square of the distance between the poles. The law is the same as that of gravitation (Art. 168), with the exception that there may be repulsion as well as attraction. Let P denote any unit of magnetism, concentrated at a point; then the law is expressed by FP repelled by P repelling per (L distance)2; or, using the symbols for "by" and "per" (Art. 79), k F = P repelled × P repelling / (L distance)2. By means of this law we are enabled to define P in terms of L, M, T; for F is already so defined (Art. 79). when the poles are of equal strength, then k FP2 / (L distance)2; Take the case Thus P can be defined in magnitude by assigning a special value to k, and the most convenient value is 1. Hence 1 P2 = F × L2, = M × L/T/T × L2. It is evident from the expression for the unit that the dimensions of P are for M, & for L, and −1 for T. It is assumed that the medium is air. ART. 204. Special Units. In the C.G.S. system F becomes the dyne, and L the centimetre. Hence Before the establishment of the C.G.S. system, it was customary in Britain to use for a unit pole that obtained by taking F as the grain by ft. per sec. per sec., and L as the foot. In that case Pigs. 1/7000 poundal by ft.2. f.g.s. = It was proposed by Clausius at the Paris Congress of Electricians (Art. 221) to give the name of weber to the unit magnetic pole of the practical system of units. The denomination was not adopted on account of its having been used to denote a unit of current. It would be defined by 1 weber = 108 √dyne by centimetre. ART. 205.-Intensity of Magnetic Field. We have then the law, 1 F = P repelled × P repelling /(L distance)2. If the strength of the repelling pole is m P, then m F = P repelled / (L distance)2; (1) and this expresses the intensity at unit distance of the magnetic field round the attracting pole. If, further, the distance is constant, say d L, then the intensity at this distance is Suppose that the repulsion is due not to one pole, but, as is always the case, to a distribution of magnetism. In the neighbourhood of any distribution of magnetism, or of a current flowing in a conductor, there is a field of magnetic force, just as in R the neighbourhood of the earth there is a field of gravitational force. At each point of the magnetic field there is a certain value of which is the resultant of the intensity at that point of all the elements of which the distribution is made up. Sir W. Thomson has suggested the denomination of gauss for the practical unit of intensity of field. ART. 206.--Magnetic Potential. To move a magnetic pole from one position to another in a magnetic field involves an amount of work which is independent of the path taken, and which is proportional to the amount of magnetism in the pole moved, provided that the amount of magnetism of the pole is not large enough to change sensibly the intensity of the field. It must be a particle of magnetism compared with the magnetism producing the field. This gives us the idea of magnetic potential, which is expressed in terms of W per P repelled. In the C.G.S. system it is expressed by erg per Pe... repelled. As the idea involves two points, or rather two surfaces, we consider either difference of magnetic potential; or, if we consider magnetic potential simply, we imply that the zero surface is at an infinite distance; that is, a surface at every point of which the intensity of the field is inappreciable. ART. 207.-Magnetic Moment. When a magnet has the form of a long thin bar, there are two equal and opposite poles situated near the extremities. Such a magnet, when placed in a field of magnetic force, with its axis transverse to the direction of the force at the place, experiences a couple. Let the strength of a |