We have now to consider one of the most important laws of electrical science. It is known as Ohm's Law, being first formulated in 1827 by Dr. G. S. Ohm, a German mathematician, and is as follows : "The strength of a current is directly proportional to the electro-motive force and inversely proportional to the resistance."

In the first chapter of these studies the flow of water through pipes was used to illustrate the flow of the electric current. This comparison will again be utilized in studying that property of materials by virtue of which they obstruct the flow of electricity through them, and which is termed " resistance." In the water or gas pipes this obstructing force is known as friction. The reservoirs and standpipes of a water-supply system serve the purpose of giving a pressure adequate to overcoming the friction of long lines of pipe and forcing the water to distant places. A large short pipe will deliver water much faster than a long, small pipe. The higher the reservoir, the greater the pressure on the water-pipes and the faster the flow of the water.

The greater the initial pressure, the stronger is the current of electricity; and also, the greater the resistance, the less the current.

The ohm is the term used to measure and express in definite numbers the comparative resistance of different materials. As adopted by the International Congress of Electricians which met at the Columbian Exposition in 1893, the ohm 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 centimeters." A little easier to remember is the fact that 100 yards of ordinary iron telegraph wire has approximately a resistance of 1 ohm.

The resistance of a conductor depends upon several conditions :

1. Its length.

2. Its cross-section.

3. The material of which it is composed, including the purity and density of such material.

4. The temperature.

To this may be added the resistance due to imperfect contact, but this is more properly a matter of construction than a property of the materials. It is made valuable use of, however, in telephone transmitters and coherers of wireless telegraphy apparatus.

Considering the first of these conditions, we find that the resistance of a conductor is proportional to its length. If the resistance of a certain length of wire is 5 ohms, then the resistance of a wire ten times as long, would be ten times as great, or 50 ohms.

The resistance of conducting wires is inversely proportional to the square of their diameters, or to the area of their cross-sections. A wire 1/4" in diameter would conduct four times as well as a wire 1/8" in diameter; if of the same length, the larger wire would have only one-quarter the resistance of the smaller one. The necessity of a careful calculation of the capacity and requirements of the wiring for electric plants is evident.

Some materials offer greater resistance to the electric current than others. Silver, copper, aluminum, platinum, iron and lead are the metals most commonly used in electrical work, and are given in the order of relative resistances, the lowest first. Iron offers about six times the resistance of copper. Annealed wire gives less resistance than hard-drawn. An alloy of two metals will have a higher resistance than either alone has. Nearly all pure metals increase their resistance with an increase in temperature at the rate of about .4 per cent for each degree Cent. Carbon is an exception to this rule, the resistance diminishing on heating.

Some materials, having such a high resistance as to be practically nonconductors, are called insulators. Glass, porcelain, marble, slate, mica, shellac, wax, paraffin, hard and soft rubber, various oils and fats are those most commonly used. With these materials the resistance decreases rapidly with the increase in temperature. The property of resistance is utilized in electrical measurements and in rheostats to regulate the flow of currents to motors. In a rheostat a number of coils of wire are so arranged that, by moving a switch, the resistance as gradually reduced, allowing more of the current to flow till all the resistance is cut out and the full current passes directly to the motor.

The energy of the current in overcoming this resistance is converted into heat. Those who have witnessed a break in a wire carrying an electric current of high potential, such as trolley wire, have seen that, when the broken wire comes in contact with the ground, it soon becomes red hot. This heat is developed by the resistance of the wire. Fires in buildings have been caused by a wire carrying a heavy current becoming "crossed " or in contact with another wire carrying a small current, such as a telephone or bell wire, and causing the latter to become highly heated. Hence the necessity of protecting all wiring from an excessive current. This is commonly done by interposing, at some suitable place in the wiring, a short length of metal similar to solder called a "fuse," which melts at the maximum temperature the circuit is capable of sustaining without danger. The melting of the fuse breaks the circuit, thus preventing the flow of the current. In electric welding and heating the resistance is so arranged as to heat the metal to the required degree.

This property of resistance is also important in considering the composition of batteries, and also upon their arrangement or grouping. The metals and chemicals that are used in the various cells differ greatly in the potential force they produce, and likewise in the resistance they offer to the flow of the current. A comprehensive consideration of chemical composition of cells requires a considerable knowledge of chemistry, and is outside the scope of these studies. A separate article on " Batteries," soon to be published in this magazine, will describe the more common types in use and the properties peculiar to each. A brief statement of the general characteristics of all cells is desirable at this time, to enable a proper summary of this and the previous chapters.

A cell is commonly composed of two metals of different potentials which are acted upon by an acid. A current flows when, by means of a wire or other substance, a complete circuit is established. The force of a current is termed the electromotive force (abbreviated E. M. F., or E.), and is expressed in volts. As applied to batteries, this difference of potential or pressure or voltage is dependent upon what metals are used rather than on their size. The greater the difference in the tendency of the metals to combine chemically with the acid, the greater the E. M. F.

The anode is the metal in the cell by which the current enters and which is dissolved during the action of the cell. The kathode is the metal by whi(?h the current leaves the cell, which remain's constant or receives a deposit of some residium of the chemical action of the cell. These two terms have other applications analogous to these, which will be considered in the appropriate place.

The E. M. F. produced by a cell is rarely the exact difference in potential of the metals compos-ing it. This is due to the resistance which the current meets and overcomes, mostly in the liquids of the cell. This resistance may be reduced by using larger pieces of metal or placing them nearer together. It is increased by the continued action of the cell, which causes a change in the chemical composition of the liquids, and also generates gases which attach to the surface of one of the metals, reducing the surface which may be acted upon. This is termed " polarization."

These chemical changes continue so long as the current flows, and are proportional to the volume of the current flowing.

With the information which has been presented in this and previous studies clearly in the mind, the relations existing between the E. M. F., resistance and current flow should be evident, and, knowing any two of these factors, the other can be found. Briefly, the E. M. F. (volts) divided by the resistance (ohms) will give the current (amperes).

The current (amperes) multiplied by the resistance (ohms) will give the E. M. F. (volts).

The E. M. F. (volts) divided by the current (amperes) will give the resistance (ohms).

These fundamental laws of electrical work should be studied until thoroughly memorized and understood, as this will do much to simplify many features of electrical study hereafter to be presented.