conductor at constant temperature, is known as "Ohm's Law," since it was first published by Ohm in 1827, although not exactly in the form here given. And it is important to notice that all experiments that have been made to test its accuracy, even when made with the most sensitive instruments yet constructed, have failed to detect any inaccuracy in this law.

It is sometimes stated that Ohm's law is self-evident, but that misconception has arisen first from the law being so extremely simple, and secondly from its wide use in electrical calculations having led people to gradually imagine that no connection between P.D. and current for a given conductor, other than direct proportionality, could exist.

So far, however, from this being the case, it is still possible that with very large currents, especially when flowing through conductors of great width, some slight want of proportionality between P.D. and current may be detected, even when the current is absolutely steady, and the conductor absolutely at the same temperature, and in every other respect in the same physical condition. At present, however, the law must be regarded as being rigorously true without exception.

44. Resistance. Since the ratio of the P.D. to the current has a constant value for each conductor this ratio has been called by a special name—the “resistance’ of the conductor, and gradually people have grown to think and speak about the electric resistance of a wire as being a definite property which belongs to the wire like its length and its cross-section.

If, however, the ratio of P.D. to current had been no more constant for a given conductor than is the ratio of pressure to flow for a given tube carrying a liquid stream, it is practically certain that this conception would not have come into existence. Therefore the mere statement that a definite wire has a definite resistance is in itself an assertion, although not of course a proof, that Ohm's law is true.

seen,

The analogy between the distribution of water pres sure and of electric potential is a very useful one for students to use, as it enables them better to grasp the meaning of electric potential; but, like many analogies, it must not be carried too far; for not merely, as we have is the ratio of difference of pressure to the quantity of a fluid flowing per second not constant for a given pipe, but any bend made in a straight pipe, even when the cross-section of the pipe is in no way decreased, causes a diminution in the flow for the same difference in pressure between its two ends; whereas bending a wire through which a steady electric current is flowing, has no effect on the electric stream. Even a sudden expansion in a pipe, that is an enlargement of the bore, for a short distance checks the fluid stream, whereas if the cross-section of a conductor be made larger for a short portion of its whole length, either no change whatever is observed in the current, or the change, if noticeable, is always an increase and never a diminution in the steady current flowing.

45. Ohm. Various units of resistance, differing slightly from one another, have been adopted from time to time, and called the " ohm," but the value that was definitely recommended to the Board of Trade in 1892 by the Committee appointed to advise them, was defined thus: "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 centimetres may be adopted as one ohm"; and at the Electrical Congress held in Chicago in 1893, this value was unanimously accepted by the Chamber of Delegates, composed of members nominated by the Governments of the United States, Great Britain, France, Italy, Germany, Mexico, Austria, Switzerland, Sweden, and British North America.

Finally, for the purpose of distinguishing this unit

of resistance from any other, it was decided to call it by the name of the "international ohm."

A brief sketch of the history of the British system of electrical units, now the system of the world, is given in the Appendix, page 568. It should be read by all those who are interested in seeing how the interdependence of electrical theory and practice, each on the other, has led to the building-up of a complete system of electrical standards, now accepted by all nations as a common heritage.

Eventually the international ohm will be so generally used that no other unit of resistance will be met with, and probably the adjective international will then be dropped. For some years, however, the "B.A. unit of resistance," the legal ohm" (so called because it was legalised in France), and the "international ohm" must be carefully distinguished from one another. Their relative values are given in the following table :—

TABLE IV.

RATIOS OF THE PRACTICAL UNITS OF RESISTANCE.

I international ohm 1.00235 legal ohm.
I international ohm = 1·01358 B.Ā. unit.

I legal ohm

I legal ohm

I B.A. unit
I B.A. unit

=0·99765 international ohm.

1 01120 B.A. unit.

0.98660 international ohm. = 0·98892 legal ohm.

46. Volt. Since the ratio of the P.D. maintained between the terminals of a conductor to the current that flows in it is constant, it follows that the P.D. that must be maintained at the terminals of a resistance of one international ohm when a current of one ampere passes through it must have a perfectly definite value. This value is taken as the practical unit of P.D., and called the "international volt.”

If, instead of basing our unit of P.D. on the international ohm, we base it on the B.A. unit of resistance or on the legal ohm, then we obtain the "B.A. volt" and the "legal volt." And the equations connecting the values of the three volts are exactly the same as those connecting the three ohms, viz. :—

There is, however, but one ampere, viz. that defined in § 6, page 23.

Example 22.-With a P.D. of 100 international volts maintained between the terminals of a glow lamp a current of 0.3 passes through it, what is the resistance of the lamp? Answer.-333-3 international ohms.

Example 23.-If the P.D. be reduced to 98 international volts and the resistance of the filament remain as before, what current will pass through it?

Answer.-0.294 ampere. Example 24.-By how much per cent. does the international volt exceed the B.A. volt?

Answer.-1.36 per cent. Example 25.-A P.D. of 7 international volts is maintained between the terminals of a resistance of 2,475 legal ohms, what is the current that passes?

Answer.-002835 ampere.

Example 26.-The standard P.D. employed by the London Electric Supply Corporation is 2,400 legal volts, what is that in international volts?

Answer.-2,394 international volts.