inch thick. The knobs of both are placed at the same time in contact with the prime conductor of an electrical machine, so that on working the machine they are both charged. Show what are the relative charges of the jars, and the relative amounts of heat produced by discharging them.

The capacity of a Leyden jar is

ks

Απα

Q charge = W per Q repelled.

When two jars of the same substance are at the same potential, we derive

Again, the amount of energy in a jar is v W; hence the relative amounts of energy and therefore of heat developed in discharging is

2 W in former = 3 W in latter.

EXERCISE XLVII,

1. Find in terms of the C.G.S. unit the quantity of electricity which will attract an equal quantity at the distance of a metre with a force of 100 dynes. 2. Two insulated spheres, whose diameters are 5 and 8 centimetres, are charged with equal quantities of positive electricity; determine their relative potentials. 3. Two spheres of 5 cm. and 10 cm. diameter are charged with 25 and 30 units of electricity respectively; they are then connected by a long thin wire, and separated. What will now be the respective charges on the spheres?

4. If a globe one metre in diameter be insulated and charged to a potential of 7 electrostatic units; what is the amount of the charge?

5. One pole of a powerful battery is connected to earth, and a long insulated wire projects from the other end. Two insulated metal balls, of 1 inch and 5 inch diameter respectively, are put one after the other in contact with the end of the insulated projecting wire. What are the comparative quantities and densities of the electricities on the two balls?

6. A spherical conductor of 5 cm. diameter has a charge of 6 electrostatic units; what is the density of the distribution?

7. Equal quantities of electricity are placed on spheres of 1 centimetre and 1 decimetre diameter; compare the densities of the distributions.

8. The charge on a sphere of 4 inches diameter is allowed by means of a long thin wire to distribute itself over another sphere of 6 inches diameter. Compare the energy of the final with that of the original distribution.

9. The areas of the armatures of three condensers, exactly alike in all other respects, are as the numbers 3, 4, 5. Find their relative charges when at the same potential.

10. Five units of electricity are conducted into the interior of a Leyden jar of 200 sq. cm. surface, and 6 units of electricity are conducted into the interior of a similar jar of 300 sq. cm. surface. Compare the heat developed by discharging each.

11. A Leyden jar is charged from an electric machine, an unit jar being interposed, and ten discharges of the unit jar occur. Compare the energy expended by the person working the machine in each successive time of charging the unit jar.

12. A condenser is formed of two concentric spheres, one of which is 100 mm. and the other 101 mm. in radius. The specific inductive capacity of the dielectric is 2. The condenser is charged with 1,000,000 electrostatic units. Calculate in calories the amount of heat developed by the discharge.

SECTION XLVIII.—ELECTROMAGNETIC.

ART. 219. Electromagnetic Unit of Quantity. As before, let Q denote any unit of quantity of electricity; then the strength of a uniform current of electricity flowing round a wire will be expressed in terms of Q per T. When a uniform current flows round a circular arc, the intensity of the magnetic field produced at the centre of the arc is directly proportional to the strength of the current, and to the length of the circular arc, and inversely proportional to the square of the radius of the arc. Thus we have

the law

kF/P = (Q/T) × L arc/(L radius)2;

a reciprocal form of which is

1/k Q/T =(F/P) × (L radius)2/L arc.

It has been already shown that the units F and P can be defined systematically in terms of L, M, T. Hence Q is defined syste

matically by making k=1. It is implied that the medium is air.

ART. 220.-Ratio of the two Units of Quantity. Since both are units for the same thing, there is an equivalence

n electrostatic Q = electromagnetic Q,

in which n denotes a numerical quantity.

It is evident that there may be a particular set of fundamental units, for which n is 1; let them be L, M, T. The multiplier for changing the electrostatic Q is limit1, and that for changing the electromagnetic Q is lim. Hence when we change from the units L, M, T to the units L', M', T' the equivalence changes to

limat-electrostatic Q'm electromagnetic Q',

i.e., lt electrostatic Q'electromagnetic Q'.

Now It is the value of a velocity; and according to the theory of Clerk Maxwell,* it is the value of the velocity of light. It has been found as the result of a large number of experiments that the value ranges about that of the velocity of light in air, which is 3 x 1010 cm. per sec.

ART. 221.-Coulomb; Ampere. The C.G.S. systematic unit is defined by a special case of the above, namely

1 Qe.gs. per sec. = dyne per Pe.gs. by (cm. radius) per cm. arc. At the International Congress of Electricians, which met at Paris in 1881, one-tenth of this electromagnetic unit of quantity was adopted as a convenient practical unit, and denominated a coulomb.

As it is not the unit of electricity but the unit of current which is directly measured, it is important to have a single word for denoting coulomb per second. At the Congress referred to, the term ampere was chosen for the purpose.

The practical units form a system in which L is 107 metres, M is 10-11 gramme, and T is the sound.

ART. 222.—Unit of Electromotive Force; Volt. The electromotive force of a circuit is the amount of work done on a unit of positive electricity in passing once round the circuit. It is expressed in terms of W per Q moved round; hence in the C.G.S. system, by erg per Q. The Congress adopted as a practical unit the unit which had been defined and adopted by the British Association, namely, 10 erg per Q..., denominated the rolt.

c.g.s.)

Hence 1 volt = 103 erg per Qegs,

= 109 erg per coulomb.

The volt, as will be seen from the following short table, is nearly equal to the electromotive force of a Daniell's cell.

A customary abbreviation for the term electromotive force is e.m.f.

ELECTROMOTIVE Force of Voltaic Cells.

Name of Cell. Daniell. Grove. Bunsen. Latimer-Clark.

Leclanché.

ART. 223.-Unit of Capacity; Farad. We have seen that the idea of capacity is expressed in terms of Q per (W per Q). The ordinary C.G.S. unit is Qe.gs. per (erg per Qe.g.).

The Congress adopted the practical unit of the British Association, namely, the farad. It is defined by

or

1 farad = coulomb per volt,

= 10-9 Qe.g.s. per (erg per Qc.g.s.). The microfarad, which is the one millionth part of the farad, is the most convenient unit for actual work.

A cable is an infinitely long cylindrical condenser. For a cable having a metallic core of a L radius, an insulating sheath of b L radius, and a specific inductive capacity k, the capacity per unit of length is

ART. 224.-Unit of Resistance; Ohm. When a steady current

of electricity flows round a circuit, the amount of the current is the same at every cross-section of the circuit. When the electromotive force is varied, the circuit being kept the same and at the same temperature, the amount of the current is found to be proportional to the electromotive force. Hence we have the law,

discovered by Ohm,

kW per Q = Q per T.

This gives us the idea of electric resistance.

The C.G.S. unit is erg per Qe.gs. per (Qc.g.s. per sec.).

The practical unit, originated by the British Association and adopted by the Electrical Congress, is

volt per ampere.

The single equivalent term is ohm; so that

1 ohm = volt per ampere,

= 109 C.G.S. unit of resistance.

=

ART. 225.-The Standard Ohm.

The British Association after defining the ohm appointed a committee to construct a standard which should realize the definition. The result of their measurements was that the ohm is represented by the resistance of a column of pure mercury at 0° C., one square millimetre in section and 105 centimetres long. In accordance with this result, standard coils were constructed of an alloy of two parts of silver to one of platinum, and issued to experimenters.

Subsequent measurements, made by various experimenters, agreed in showing that the standard ohm was slightly less than the ohm of the definition. The Paris Congress appointed a committee of electricians to make a fresh determination; and on their report the standard ohm has been authoritatively defined as the resistance of a column of mercury at 0° C., having a section of one square millimetre and a length of 106 centimetres.

The Siemens unit of resistance was defined as the resistance of a column of mercury at 0° C., having one sq. mm. in section, and 1 metre long.

S