discharges it n times per second, is arranged in one branch of a Wheatstone's Bridge, it can be treated and measured as if it were a resistance, and its equivalent resistance calculated in terms of the resistance of all the other branches of the bridge (see Phil. Mag., 1885, 20, 258).
| Quantity. | Symbol. | Dimensions on the Electro- static System E.S. |
Dimensions on the Electro- magnetic System E.M. |
Ratio of E.S. to E.M. | ||
| Magnetic permeability | (μ) | L−2 T2 K−1 | μ | L−2 T2 K−1 μ−1 | ||
| Magnetic force of field | (H) | L12 M12 T−2 K12 | L−12 M12 T−1 μ− 12 | L T−1 K12 μ12 | ||
| Magnetic flux density or induction | (B) | L32 M12 K−12 | L−12 M12 T−1 μ12 | L−1T K−12 μ−12 | ||
| Total magnetic flux | (Z) | L12 M12 K−12 | L32 M12 T−1 μ12 | L−1T K−12 μ−12 | ||
| Magnetization | (I) | L−32 M12 K−12 | L−12 M12 T−1 μ12 | L−1T K−12 μ12 | ||
| Magnetic pole strength | (m) | L12 M12 K−12 | L32 M12 T−1 μ12 | L−1T K−12 μ−12 | ||
| Magnetic moment | (M) | L32 M12 K−12 | L52 M12 T−1 μ12 | L−1T K−12 μ−12 | ||
| Magnetic potential or magnetomotive force |
(M.M.F.) | L32 M12 T−2 K12 | L12 M12 T−1 μ−12 | LT−1 K12 μ12 | ||
| Specific inductive capacity | (K) | K | L−2 T2 μ−1 | L2 T−2 K μ | ||
| Electric force | (e) | L−12 M12 T−1 K−12 | L12 M12 T−2 μ12 | L−1 T K− 12 μ− 12 | ||
| Electric displacement | (D) | L−12 M12 T−1 K12 | L−32 M12 μ−12 | L T−1 K12 μ12 | ||
| Electric quantity | (Q) | L32 M12 T−1 K12 | L12 M12 μ−12 | LT−1 K12 μ12 | ||
| Electric current | (A) | L32 M12 T−2 K12 | L12 M12 T−1 μ−12 | LT−1 K12 μ12 | ||
| Electric potential | (V) | L12 M12 T−1 K−12 | L32 M12 T−2 μ12 | L−1 T K−12 μ−12 | ||
| Electromotive force | (E.M.F.) | |||||
| Electric resistance | (R) | L−1 T K−1 | L T−1 μ | L−2 T2 K−1 μ−1 | ||
| Electric capacity | (C) | LK | L−1 T2 μ−1 | L2 T−2 Kμ | ||
| Self inductance | (L) | L−1 T2 K−1 | L μ | L−2 T2 K−1 μ−1 | ||
| Mutual inductance | (M) | |||||
Accordingly, we have two methods of measuring the capacity of a conductor. One, the electrostatic method, depends only on the measurement of a length, which in the case of a sphere in free space is its radius; the other, the electromagnetic method, determines the capacity in terms of the quotient of a time by a resistance. The ratio of the electrostatic to the electromagnetic value of the same capacity is therefore of the dimensions of a velocity multiplied by a resistance in electromagnetic value, or of the dimensions of a velocity squared. This particular experimental measurement has been carried out carefully by many observers, and the result has been always to show that the velocity v which expresses the ratio is very nearly equal to 30 thousand million centimetres per second; v=nearly 3× 1010. The value of this important constant can be determined by experiments made to measure electric quantity, potential, resistance or capacity, both in electrostatic and in electromagnetic measure. For details of the various methods employed, the reader must be referred to standard treatises on Electricity and Magnetism, where full particulars will be found (see Maxwell, Treatise on Electricity and Magnetism, vol. ii. ch. xix. 2nd ed.; also Mascart and Joubert, Treatise on Electricity and Magnetism, vol. ii. ch. viii., Eng. trans. by Atkinson).
Table II. gives a list of some of these determinations of v, with references to the original papers.
It will be seen that all the most recent values, especially those in which a comparison of capacity has been made, approximate to 3 × 1010 centimetres per second, a value which is closely in accord with the latest and best determinations of the velocity of light.
We have in the next place to consider the question of practical electric units and the determination and construction of concrete standards. The committee of the British Association charged with the duty of arrangingPractical units a system of absolute and magnetic units settled also on a system of practical units of convenient magnitude, and gave names to them as follows:—
| 109 absolute electromagnetic | units of resistance | ＝1 ohm |
| 108 〃 〃 | units of electromotive force | ＝1 volt |
| 110th of an 〃 〃 | unit of current | ＝1 ampere |
| 110th of an 〃 〃 | unit of quantity | ＝1 coulomb |
| 10−9 〃 〃 | units of capacity | ＝1 farad |
| 10−15 〃 〃 | units of capacity | ＝1 microfarad |
Since the date when the preceding terms were adopted, other multiples of absolute C.G.S. units have received practical names, thus:—
| 107 ergs or absolute C. G. S. units of energy | ＝1 joule |
| 107 ergs per second or C.G.S. units of power | ＝1 watt |
| 109 absolute units of inductance | ＝1 henry |
| 108 absolute units of magnetic flux | ＝1 weber[1] |
| 1 absolute unit of magnetomotive force | ＝1 gauss[1] |
An Electrical Congress was held in Chicago, U.S.A. in August 1893, to consider the subject of international practical electrical units, and the result of a conference between scientific representatives of Great Britain, the United States, France, Germany, Italy, Mexico, Austria, Switzerland, Sweden and British North America, after deliberation for six days, was a unanimous agreement to recommend the following resolutions as the definition of practical international units. These resolutions and definitions were confirmed at other conferences, and at the last one held in London in October 1908 were finally adopted. It was agreed to take:—
“As a unit of resistance, the International Ohm, which is based upon the ohm equal to 109 units of resistance of the C.G.S. system of electromagnetic units, and is represented by the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice 14·4521 grammes in mass, of a constant cross-sectional area and of the length of 106·3 cm.
“As a unit of current, the International Ampere, which is one-tenth of the unit of current of the C.G.S. system of electromagnetic units, and which is represented sufficiently well for practical use by the unvarying current which, when passed through a solution of nitrate of silver in water, deposits silver at the rate of 0·00111800 of a gramme per second.
“As a unit of electromotive force, the International Volt, which is the electromotive force that, steadily applied to a conductor whose resistance is one international ohm, will produce a current of one international ampere. It is represented sufficiently well for practical purposes by 1000010184 of the E.M.F. of a normal or saturated cadmium Weston cell at 20° C., prepared in the manner described in a certain specification.
“As a unit of quantity, the International Coulomb, which is the quantity of electricity transferred by a current of one international ampere in one second.
“As the unit of capacity, the International Farad, which is the capacity of a condenser charged to a potential of one international volt by one international coulomb of electricity.
“As a unit of work, the Joule, which is equal to 107 units of work in the C.G.S. System, and which is represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm.
“As a unit of power, the Watt, which is equal to 107 units of power in the C.G.S. System, and which is represented sufficiently well for practical use by the work done at the rate of second.
“As the unit of inductance, the Henry, which is the induction in a circuit when an electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampere per second.”
- ↑ 1.0 1.1 Neither the weber nor the gauss has received very general adoption, although recommended by the Committee of the British Association on Electrical Units. Many different suggestions have been made as to the meaning to be applied to the word “gauss.” The practical electrical engineer, up to the present, prefers to use one ampere-turn as his unit of magnetomotive force, and one line of force as the unit of magnetic flux, equal respectively to 10/4π times and 1 times the C.G.S. absolute units. Very frequently the “kiloline,” equal to 1000 lines of force, is now used as a unit of magnetic flux.
