pressed in one system into the other, it being remembered that in each case the units of length, mass, and time employed in the two systems must be the same. When these units are the centimetre, the second and the gram v is equal to 3 x 100 cm./sec. As an example of the application of this method of converting from one system of units into the other, we may take the following problem. A conducting sphere is placed on an insulating stand at a great distance from all other conductors, and has a radius of 10 cm., what is its capacity expressed in electro-magnetic units? In § 464 it was shown that the capacity of such a sphere in electro-static units was numerically equal to the radius. Hence the capacity of the sphere in electro-static units is 10[cm. K]. If n is the value of the capacity in electro-magnetic units, then, since the dimensions of capacity in this system are [L-1Tμ-1], we have the following relation :—

Hence the capacity of the sphere is 1.11 × 10-20 electro-magnetic units of capacity. Since a microfarad is equal to 10-15 electro-magnetic units of capacity, the capacity of the sphere is equal to 1.11 X 10-5 microfarads.

538. The Practical System of Electro-magnetic Units.-It will be convenient for the sake of reference to gather together the relations between the c.g.s. electro-magnetic units and those on the practical system, and the following table exhibits these relations :—

These practical units, with the exception of the microfarad, are those which would be obtained if 109 cm. were taken as the unit of length and 10 gram as the unit of mass, the unit of time remaining the second. Thus the dimensions of resistance being [LT-1μ], if we increase the unit

-11

of length 10 times, keeping the unit of time the same, we shall increase the unit of resistance 10° times; that is, the ohm is 109 c.g.s. units. The dimensions of current being [Z1111], the increase of the unit of length to 10 cm. will increase the unit of current 10 times, while the change in the unit of mass to 10-11 grams will reduce the unit of current 10 times, so that the net result is that the unit of current on the practical system is 10-) times, or 1/10 of the c.g.s. unit.

When considering the thermal effects of currents, it is often convenient to express the results in terms of calories. Since one joule is 107 ergs and one calorie is equal to 4.189 × 107 ergs, we get that a joule is equal to 107 / 4.189 × 107 calories or 0.2387 calories. The calorie employed in this reduction is the quantity of heat required to raise the temperature of one gram of water through one degree Centigrade at a temperature of 15° C. Since a watt is equal to one joule per second, it is equal to 0.2387 calories per second.

In order to obviate the use of very large or very small numbers, units are sometimes used which are a million times (10) as great or one millionth (106) of the practical units. These units are indicated by the prefixes mega- and micro- respectively. Thus a megohm is equal to a million ohms or to 1015 c.g.s. units of resistance. A microfarad is equal to one-millionth of a farad; that is, 10-6 farad or 10-15 c.g.s. units of capacity.

The term milliampere is sometimes used to indicate a current of a thousandth (10-3) of an ampere.

In electrical engineering it is usual to measure activity or power in kilowatts, a kilowatt being 1000 watts, or 101o ergs per second. Since a horse-power is equal to 7.46 × 10o ergs per second, it follows that a kilowatt is equal to 1.341 horse-power.

PART VIII

ELECTROLYSIS, ELECTROMOTIVE FORCE OF CELLS, AND PASSAGE OF ELECTRICITY THROUGH GASES

CHAPTER XV

ELECTROLYSIS

539. Faraday's Law.--We have in the preceding pages seen that when an electric current passes through a metallic conductor a certain quantity of heat will be developed in the conductor; but after the passage of the current, except for changes caused by the rise of temperature produced by the heat developed in this way, there will be no change either in its chemical composition or physical state. In addition to metals, some liquids conduct electricity, and are called electrolytes, and we now proceed to consider what phenomena accompany the passage of a current through these bodies. The magnetic properties of a circuit which consists wholly or in part of electrolytes differ in no way from those of a circuit composed of metals only, and hence do not require any further consideration. The passage of a current through an electrolyte is accompanied, however, not only by the production of heat as in a metallic conductor, but also by certain chemical changes which take place in the electrolyte, and we now proceed to consider these in detail.

When a current is passed through an electrolyte, such as a solution of sulphuric acid in water, by dipping two platinum plates into the solution, and connecting one of these, called the anode, with the positive pole of a battery, and the other, called the kathode, with the negative pole, decomposition of the electrolyte will accompany the passage of the current. The two products of the decomposition of the electrolyte, whether they are either or both elements or compounds, will be liberated one at the cathode and the other at the anode, and not at all at any point of the liquid between. That part of the electrolyte which is liberated at the anode is called the anion, and that part liberated at the kathode the kation. It does not necessarily follow that the anion and kation are actually given off as such at the anode and kathode respectively, for secondary chemical changes often take place between the ions and the electrodes, as the plates used to form the anode and kathode

are called, or with the undecomposed portion of the electrolyte. Thus in the case of the electrolysis of a solution of sulphuric acid (H2SO), the kation is H, while the anion is SO4. But while hydrogen is given off at the kathode, at the anode a secondary reaction takes place, the SO reacting with the water of the solution so as to produce sulphuric acid and free oxygen according to the equation

SO4 + H2O=H2SO1+O.

The laws which govern electrolysis were discovered by Faraday, and are hence known as Faraday's laws. These are:

1. The quantity of an electrolyte decomposed is proportional to the quantity of electricity which passes.

2. The mass of any ion liberated by a given quantity of electricity is proportional to the chemical equivalent weight of the ion.

In the case of elementary ions the chemical equivalent weight is the atomic weight divided by the valency, while in that of a compound ion it is the molecular weight divided by the valency. If the weight of an ion liberated by the passage of the unit quantity of electricity is called the electro-chemical equivalent of the ion, then Faraday's laws can be put into the form :

The mass of an ion liberated is equal to the product of the quantity of electricity which passes into the electro-chemical equivalent of the ion; the electro-chemical equivalents of the ions being to one another as the chemical combining weights of these ions.

Since, if the electro-chemical equivalent of any one ion is known, that of any other can be calculated from the chemical equivalent weights, it is of importance to determine the value of the electro-chemical equivalent in the case of one ion. Accurate experiments have shown that when one coulomb of electricity passes, that is, when a current of one ampere passes for one second, the weight of silver deposited from a solution of a silver salt is 0.001118 grams. Since the atomic weight of silver is 107.94, and the valency is 1, while the atomic weight of hydrogen is 1, and its valency is also I, the electro-chemical equivalent of hydrogen is equal to 0.001118/107.94, or .000010357. Hence a current of A amperes flowing for seconds will liberate 1.0357 × 10 ̃3At grams of hydrogen, or, if q is the chemical equivalent weight of any ion, will liberate m grams of this ion where m is given by

m=1.0357 × 10 ̃3qAt.

As an example, in the case of copper as a cupric salt, the atomic weight is 63, while the valency is 2; hence the chemical equivalent is 63/2, and the electro-chemical equivalent of copper is 1.0357 × 10 × 31.5.

Since the passage of t coulomb will deposit .001118 grams of silver, it will require the passage of 107.94/.001118 coulombs, or 96,550 coulombs, to deposit 1 gram equivalent, that is, the chemical equivalent in grams, of

silver. By Faraday's second law it follows that the passage of 96,550 coulombs will cause the separation of one gram equivalent of any kind of ion. In the case of ions which can have more than one chemical valency there will be more than one chemical equivalent. Thus iron can exist in a compound either in the ferric condition, when it has a valency 3, and consequently a chemical equivalent of 56/3 or 18.7, or as a ferrous salt, when it has a valency of 2, and hence the chemical equivalent is 56/2, or 28. Thus when a ferric salt is electrolysed the electro-chemical equivalent of iron is 1.0357 × 10 × 18.7; while when a ferrous salt is electrolysed the electro-chemical equivalent is 1.0357 × 10 5 × 28.

Since the passage of 96,550 coulombs of electricity through an electrolyte always liberates one gram equivalent of each ion, if we suppose the electricity to pass by a kind of convection, being carried by the ions, a positive charge being carried by the kations in the direction of the current, and a negative charge by the anions in the opposite direction, it follows that the charge carried by the chemical equivalent of each ion must be the same. In the case of univalent ions the electro-chemical equivalents are proportional to the atomic or molecular weights according as the ion is an element or a compound. Hence, if we extend the term ion to mean the smallest portion of the substance producing the ion which can take part in a chemical reaction, the charge carried by each ion must, in the case of all univalent ions, be the same. Let be the charge carried by a univalent ion, then if w is the weight of the ion of hydrogen, one gram of hydrogen will correspond to 1/w ions, and since the quantity of electricity transported by one gram of hydrogen ions is 96,550 coulombs, the quantity transported by each ion is given by

e=96550×w,

or, if we suppose that an ion of hydrogen is the same as the atom, and that an atom of hydrogen weighs 8.3 × 10-25 grams,

e=96550 × 8.3 x 10-25-8 x 10-20 coulomb.

Thus the quantity of electricity transported by a univalent ion is 8 × 10-20 coulomb. If the ion is a kation is positive, that is, each ion carries a positive charge. If, however, the ion is an anion, the charge is negative, and is transported in the opposite direction to that in which the current flows.

In the case of a divalent ion, such as copper or SO, the charge carried by each ion must be equal to ±26, for each atom of copper weighs 63 times as much as an atom of hydrogen, while the weight of copper deposited by the passage of a given quantity of electricity is only 63/2 times as much as the weight of hydrogen liberated by the same quantity of electricity. Thus the number of ions of copper deposited by one coulomb is half the number of hydrogen ions liberated by the same quantity of electricity, and hence each copper ion must carry twice as