* Valency is the atom-fixing or atom-replacing power of an element com. pared with hydrogen, whose valency is unity

+ Atomic weight is the weight of one atom of each element compared with hydrogen, whose atomic weight is unity.

Becquerel's extension of Faraday's law showed that the electro-chemical equivalent of an element is proportional to its chemical equivalent. The latter is equal to its combining weight, and not to atomic weight+valency, as defined by Thompson, Hospitalier, and others who have copied their tables. For example, the ferric salt is an exception to Thompson's rule, as are sesqui-salts in general.

Thus: Weight of silver deposited in 10 seconds by a current of 10 amperes weight of hydrogen liberated per second x number seconds X current strength 107.7 = .00001038 x 10 x 10 × 107.7.11178 gramme. Weight of copper deposited in 1 hour by a current of 10 amperes =

.00001038 3600 x 10 x 31.5 11.77 grammes.

Since 1 ampere per second liberates .00001038 gramme of hydrogen, strength of current in amperes

weight of element liberated per second
= .00001038 × chemical equivalent of element

The above table (from "Practical Electrical Engineering") is calculated apon Lord Rayleigh's determination of the electro-chemical equivalents and Roscoe's atomic weights.

ELECTRO-MAGNETS.*

Units of Electro-magnetic Measurements.

Unit magnetic pole is a pole of such strength that when placed at a distance of one centimetre from a similar pole of equal strength it repels it with a force of one dyne.

=

Gauss unit of field strength, or density, symbol H, is that intensity of field which acts on a unit pole with a force of one dyne, one line of force per square centimetre. A field of H units is one which acts with H dynes on unit pole, or H lines per square centimetre. A unit magnetic pole has

4 lines of force proceeding from it.

Maxwell unit of magnetic flux, is the amount of magnetism passing through every square centimetre of a field of unit density. Symbol, p. Gilbert unit of magneto-motive force, is the amount of M.M.F., that would be produced by a coil of 1047 or 0.7958 ampere-turns. Symbol, F. The M.M.F. of a coil is equal to 1.2566 times the ampere-turns.

If a solenoid is wound with 100 turns of insulated wire carrying a current of 5 amperes, the M.M.F. exerted will be 500 ampere-turns X 1.2566628.3 gilberts.

=

Oersted unit of magnetic reluctance; it is the reluctance of a cubic centimetre of an air-pump vacuum. Symbol, R.

Reluctance is that quantity in a magnetic circuit which limits the flux under a given M.M.F. It corresponds to the resistance in the electric circuit.

The reluctivity of any medium is its specific reluctance, and in the C.G.S. system is the reluctance offered by a cubic centimetre of the body between opposed parallel faces. The reluctivity of nearly all substances, other than the magnetic metals, is sensibly that of vacuum, is equal to unity, and is independent of the flux density.

Permeability is the reciprocal of magnetic reluctivity. It is a number, and the symbol is .

Permeance is the reciprocal of reluctance.

Lines and Loops of Force.-In discussing magnetic and electrical phenomena it is conventionally assumed that the attractions and repulsions as shown by the action of a magnet or a conductor upon iron filings are due to "lines of force" surrounding the magnet or conductor. The number of lines indicates the magnitude of the forces acting. As the iron filings arrange themselves in concentric circles, we may assume that the forces may be represented by closed curves or "loops of force." The following assumptions are made concerning the loops of force in a conductive circuit:

1. That the lines or loops of force in the conductor are parallel to the axis of the conductor.

2. That the loops of force external to the conductor are proportional in number to the current in the conductor, that is, a definite current generates a definite number of loops of force. These may be stated as the strength of field in proportion to the current.

3. That the radii of the loops of force are at right angles to the axis of the conductor.

The magnetic force proceeding from a point is equal at all points on the surface of an imaginary sphere described by a given radius about that point. A sphere of radius 1 cm. has a surface of 47 square centimetres. If

total flux, expressed as the number of lines of force emanating from a magnetic pole having a strength, M,

=4rM; M = φ+4π.

Magnetic moment of a magnet = product of strength of pole M and its length, or distance between its poles L. Magnetic moment

ᏞᏞ

Απ

*For a very full treatment of this subject see "The Electro-Magnet," published by the Varley Duplex Magnet Co., Phillipsdale, R. I.

If B = number of lines flowing through each square centimetre of crosssection of a bar-magnet, or the "specific induction," and A-cross-section, Magnetic Moment = LAB÷4π.

==

If the bar-magnet be suspended in a magnetic field of density H, and so placed that the lines of the field are all horizontal and at right angles to the axis of the bar, the north pole will be pulled forward, that is, in the direction in which the lines flow, and the south pole will be pulled in the opposite direction, the two forces producing a torsional moment or torque,

Torque = MLH = LABH÷4′′, in dyne-centimetres.

Magnetic attraction or repulsion emanating from a point varies inversely as the square of the distance from that point. The law of inverse squares, however, is not true when the magnetism proceeds from a surface of appreciable extent, and the distances are small, as in dynamo-electric machines and ordinary electromagnets.

==

The

The

Permeability.-Materials differ in regard to the resistance they offer to the passage of lines of force; thus iron is more permeable than air. permeability of a substance is expressed by a coefficient, , which denotes its relation to the permeability of air, which is taken as 1. If H = number of magnetic lines per square centimetre which will pass through an airspace between the poles of a magnet, and B the number of lines which will pass through a certain piece of iron in that space, then μ=B÷H. permeability varies with the quality of the iron and the degree of saturation, reaching a practical limit for soft wrought iron when B = about 18,000 and for cast iron when B = about 10,000 C.G.S lines per square centimetre. The permeability of a number of materials may be determined by means of the table on the following page. The Magnetic Circuit.-In the electric circuit

Reluctance is the reciprocal of permeance, and permeance is equal to permeability Xpath area ÷ path length (metric measure); hence

=3

μα

One ampere-turn produces 1.257 gilberts of magnetomotive force and one inch equals 2.54 centimetres; hence, in inch measure,

The ampere-turns required to produce a given magnetic flux in a given path will be

=

Since magnetic flux area of path magnetic density, the ampere-turns required to produce a density B, in lines of force per square inch of area of path, will be

This formula is used in practical work, as the magnetic density must be predetermined in order to ascertain the permeability of the material under its working conditions. When a magnetic circuit includes several

qualities of material, such as wrought iron, cast iron, and air, it is most direct to work in terms of ampere-turns per unit length of path. The ampere-turns for each material are determined separately, and the winding is designed to produce the sum of all the ampere-turns. The following table gives the average results from a number of tests made by Dr. Samuel Sheldon:

VALUES OF B AND H.

Cast Iron. Cast Steel. Wrought Iron Sheet Metal.

H=1.257 ampere-turns per cm,=.495 ampere-turns per inch.

EXAMPLE. A magnetic circuit consists of 12 inches of cast steel of 8 square inches cross-section; 4 inches of cast iron of 22 square inches cross-section; 3 inches of sheet iron of 8 square inches cross-section; and two air-gaps each 16 inch long and of 12 square inches area. Required, the ampere-turns to produce a flux of 768,000 maxwells, which is to be uniform throughout the magnetic circuit.

The flux density in the steel is 768,000÷8-96,000 maxwells; the ampereturns per inch of length, according to Sheldon's table, are 60.6, so that the 12 inches of steel will require 727.2 ampere-turns.

The density in the cast iron is 768,000 22 34,900; the ampere-turns 4 X 40 160.

The density in the sheet iron 768,000+8=96,000; ampere-turns per inch=30; total ampere-turns for sheet iron = 90.

The air-gap density is 768,000÷12=64,000; ampere-turns per inch 0.3133B; ampere-turns required for air-gap=0.3133 X 64,000÷8=2506.4. The entire circuit will require 727.2+160+90+2506.4-3483.6 ampereturns, assuming uniform flux throughout.

In practice there is considerable "leakage" of magnetic lines of force; that is, many of the lines stray away from the useful path, there being no material opaque to magnetism and therefore no means of restricting it to a given path. The amount of leakage is proportional to the permeance of the leakage paths available between two points in a magnetic circuit which are at different magnetic potentials, such as opposite ends of a magnet coil. It is seldom practicable to predetermine with any approach to accuracy the magnetic leakage that will occur under given conditions unless one has profuse data obtained experimentally under similar conditions. In dynamo-electric machines the leakage coefficient varies from 1.3 to 2.

Tractive or Lifting Force of a Magnet.-The lifting power or "pull" exerted by an electro-magnet upon an armature in actual contact with its pole-faces is given by the formula

a being the area of contact in square inches and B the magnetic density over this area. If the armature is very close to the pole-faces, this formula also applies with sufficient accuracy for all practical purposes, but a considerable air-gap renders it inapplicable. The accompanying table is convenient for approximating the dimensions of cores and pole-faces for tractive magnets.

Dimensions of Lifting Magnets.

Magnet Windings. Knowing the ampere-turns required to produce the desired excitation of a magnetic circuit, the winding may be approximately determined as follows:

For round cores under 1 inch in diameter make the depth or thickness of winding, t, equal to the core diameter; over 1 inch, let t=cube root of core diameter. For slab-shaped cores let the coil thickness be equal to the core thickness up to 1 inch, and to the square root of the core thickness above that.

The ampere-turns produced by any coil will be

d2

area of the wire in circular mils,

1=mean length in inches per turn of wire,

k=a coefficient depending on the temperature of the coil.