of these two bodies can be secured by connecting these terminals together with a piece of wire, thick or thin. For if there be any difference of potential, a momentary current will flow through this wire which will annihilate the P.D.

Furter, if the terminals be joined respectively by wires woh any two conductors A and B, momentary currents lead flow, and the potentials of the needle and inductors will become respectively the same as those of a and B. In fact, we may say generally, that if any number of conductors be touched together, or be joined by wires, and if no current be flowing between any of the bodies, the conductors and wires are all at the same potential. To be strictly correct, this general proposition requires that all the conductors should be made of the same material, and be at the same temperature.

This last proposition can be stated briefly and completely thus :—the potential of all parts of a conducting system composed of the same material at the same temperature and on which electricity is at rest is uniform.

In order to ensure that the electric force exerted on the needle shall be wholly due to the P.D. between it and the inductors, and that no part of this force shall be caused by the attraction of external bodies, the interior of the glass shade is coated with a conducting transparent varnish devised by Mr. Mather and the author, the composition, and action of which explained in § 58, page 200.

are

The spindle of the needle in the electrometer (Fig. 83) moves in guides top and bottom, the upper guide being clearly seen in Fig. 83a, which shows the top of the needle and of the inductors rather larger than full size; hence the instrument may be turned upside down, or carried about without its being necessary to clamp the needle, and without there being any risk of breaking the thin phosphor-bronze strip supporting it.

If now, in addition to sending a steady stream of water through the tube tt (Fig. 77, page 154), the water in the

tube be used as a conductor and a steady electric current be sent through it, the various P.Ds. between the pairs of points P1 and P2, P2 and P3, &c., can easily be measured with the electrometer just described by simply dipping wires, attached respectively to the terminals of the electrometer, into the water in the various pairs of standpipes S1 and S2, S2 and s, &c. For, since this no electric current in the water in a stand-pipe

t, there can be no P.D. between the different parts of the water in the same stand-pipe; hence the water in the standpipes can be used simply as extensions of the wires attached to the terminals of the electrometer. When the screw pinch-cock 8 is fully open, so that the tube tt is throughout of uniform bore, it will be found that the P.Ds. between the different pairs of points are related to one another in exactly the same way as are the differences between the water pressures for the same pairs of points.

Thus the distribution of potential along a uniform conductor conveying a steady electric current is exactly analogous with the distribution of fluid pressure along a uniform tube, through which flows a steady stream of liquid.

43. Ohm's Law. But if instead of measuring the P.D. between different points along a conductor through which flows a steady current we measure the P.D. between two fixed points in a given conductor through which different currents are flowing, then the P.D. does not vary with the current in the same way that the difference of pressure between two points in a given tube varies with the stream of fluid flowing through it. Let us consider the second case first :-Keep the level of water in the reservoir c1 (Fig. 77) constant in the way already described, open the screw pinch-cock 82 a certain amount, the screw pinch-cock s1 being fully open, and, when the stream has become steady, measure with the graduated glass the number of cubic centimetres of water that flow through the tube tt per second, also the difference of pressure between two fixed points in the

tube P, and P for example. Next open the pinch-cock s a little more, and again measure the number of cubic centimetres of water per minute that flow out of the tube, as well as the difference between the height of the water in the stand-pipes s, and Sg. If such measurements be made for several different steady rates of flow, numbers Curve connecting Rate of Flow of Water with Loss of Head.

Flow in cubic centimetres per second

like the following will be obtained, and when plotted they give the curve seen in Fig. 84, concave to the axis along which difference of level is plotted.

If the numbers in the third column were all the same it would tell us that the ratio of the difference of level to the number of cubic centimetres flowing per second-that is, the ratio of pressure to current—was a constant for a given pipe. In that case the points on the curve in Fig. 84 would all lie in one straight line, and to double, treble, quadruple the current would require exactly double, treble, quadruple the pressure. But the numbers in the third column steadily increase as the current increases, and if we examine the numbers in the first two columns we find that to increase, for example, the flow from 1.20 to 4.76 cubic centimetres per second —that is, to make the current not quite four times as great--we have to increase the difference of level from 6.9 to 36-2 centimetres-that is, to increase the pressure more than five times.

The quantity of water, therefore, that flows per second through a given pipe does not increase as rapidly as the difference of pressure between two fixed points in it, or, in other words, we must more than double, treble the difference of pressure to produce twice, three times the flow, even although the tube through which the water flows remains absolutely unchanged. It might, therefore, have been expected that the same sort of inequality would be found in the ratio connecting the P.D. between two fixed points in a conductor and the current flowing through it.

But that is not the case, for if the conductor K (Fig. 85) remains at the same temperature, and be not changed in any way, experiment shows that the P.D. between two fixed points, K1, K in it, measured by the electrometer E (in the way described in § 42, page 165), is directly proportional to the current flowing through this conductor, the currents being measured relatively to one another by any suitable galvanometer G,* *for which the law connecting current

*For the details of the construction of the galvanometer illustrated in Fig. 85, see § 38, page 148.

G*

and deflection has been obtained by a relative calibration as described in § 12, page 46.

For carrying out these tests the current can be conveniently produced with a battery, BB, of what are known as "dry cells" (see § 140, page 457), or of "accumulators" (see Vol. II.); and its strength can be varied by

altering the number of cells employed. This alteration in the number of cells that are used in the different tests, can be easily effected by means of the mercury switch-board, ss, seen in front of the battery of cells in Fig. 85. The construction, and mode of using such a mercury switch-board, will be found described in § 162, page 539.

This experimental result, that the ratio of the P.D. to the current, if steady, is absolutely constant for a given