the strength of the magnet-the deflecting torque is produced by a stationary magnet acting on a moving coil conveying the current to be measured, but, although phosphor-bronze strips are used to convey the current into and out of the coil, as in Fig. 76, they are made as thin as possible so as to exert but a very slight control. The main part of the control is produced by the attraction of the stationary magnet on some tiny hard steel magnets, which are inserted at various places inside the coil. Weakening the large stationary magnet therefore diminishes both the deflecting and the controlling torques in nearly the same proportion, and so leaves the sensibility of the instrument practically unchanged.

152

CHAPTER III.

DIFFERENCE OF POTENTIAL, AND RESISTANCE.

40. Difference of Potentials-41. Potential of the Earth Arbitrarily called Nought; Positive and Negative Potentials-42. Electrometer-43. Ohm's Law-44. Resistance-45. Ohm-46. Volt47. Current Method of Comparing P.Ds.-48. Reason for Using High Resistance Galvanometers for P.D. Measurements-49. Voltmeter-50. Ammeters Used as Voltmeters-51. Moving Coil Voltmeter-52. Calibrating a Deflectional Voltmeter--53. Voltmeters Used as Ammeters-54. Gold-Leaf Electroscope-55. Sensibility of Gold-Leaf Electroscopes-56. No Force Inside a Closed Conductor Produced by Exterior Electrostatic Action-57. Potential due to Exterior Electrostatic Action Uniform at All Points Inside a Closed Conductor-58. Voltmeters must be Enclosed in a Conducting Case-59. The Potential of a Conductor -60. The Potential of a Body Depends Partly on its Position Relatively to other Bodies-61. The Potential of a Body Depends Partly on its Size and Shape-62. The Potential of a Body Depends Partly on a Third Condition: the Quantity of Electricity63. No Electricity at Rest Inside a Conductor-64. Comparing Quantities of Electricity-65. Quantity of Electricity Produced by Rubbing two Bodies together-66. Conduction and Induction67. Testing the Sign of the Electrification of a Body-68. Screening Outside Space from Inside Electrostatic Action-69. Electric Density-70. Examples Showing the Difference between Potential, Quantity, and Density.

40. Difference of Potentials.--When a current of electricity is flowing through a wire, it has the same strength at all cross-sections of the wire. If, for example, the wire be cut anywhere, and a galvanometer be put in circuit, the galvanometer will always show the same deflection while the same current is flowing; or if several galvanometers, or ammeters, be placed at different parts of the same circuit, each instrument will be found to indicate the same current. In the same way, in the case of a water-pipe, the quantity of water passing every cross-section of the pipe per second is exactly the same as soon as the flow of water becomes steady. Just at the commencement, when, for example, some water has

entered at one end of the pipe, and none has flowed out at the other—when the pipe is filling in fact-the flow at different cross-sections may be different; so also, in many cases, just at the moment after completing an electric circuit, the current will differ at different crosssections. But as soon as the flow in each case becomes a steady one this difference disappears, and the strength of the water current—that is, the number of gallons of water passing per minute (not, of course, the velocity of the particles of water)—is the same at all parts of the pipe, even if the pipe be broad at some points and narrow at others. In the same way the strength of the electric current flowing through a single circuit is "uniform" at all parts of the circuit, independently of the thickness of the conductor, and of the material of which it is made.

But although the stream of water is the same at all parts of the pipe, the pressure per square inch of the water is by no means the same, even if the pipe be quite horizontal and of uniform cross-section. This pressure per square inch of the water on the pipe, which is the same as the pressure per square inch of one portion of the water on another portion adjacent to it, becomes less and less as we proceed in the direction of the flow. It is, in fact, this difference of pressure, or "loss of head" as it is sometimes called, that causes the flow to take place against the friction of the pipe, the difference of pressure at any two points, in the case of a steady flow through a horizontal pipe of uniform sectional area, being balanced by the frictional resistance of that length of pipe for that particular rate of flow.

Quite analogous with this there is, in the case of an electric current flowing through a conductor, a "difference

* Uniform refers to space, constant to time. The height of the houses in a street is generally not uniform, but it is constant so long as there is no change made in the height of the houses. If water be run out of a cistern the level at all parts of the surface of the water is uniform, but it is not constant, since it steadily falls as the water runs out.

of potentials" between any two points in the conductor, and this difference of potentials, or "potential difference," or "P.D." as it may be shortly called, is needed to overcome the resistance of the conductor, or opposition that it offers to the passage of an electric current through it. In fact the analogy between difference of potentials and difference of fluid pressure is so

marked that the name "pressure is now frequently used to stand for difference of potentials.

The pressure per square inch of the water at any point of a tube conveying a stream can be ascertained by attaching a vertical stand-pipe to the tube, and observing to what height the water is forced up in this stand-pipe, and if at a number of points, P1, P2, P3, P4 P5, P (Fig. 77), in a glass tube, tt, conveying a stream of water, a series of vertical glass stand-pipes, 81 82 So, be tixed,

the height to which the water is forced up in them will show the distribution of pressure along the tube. If the tube tt be straight and of uniform cross-section, and if the flow be a steady one, the tops of the water-columns in the stand-pipes will be found to all lie in one straight line, 91 92 96, therefore, if the length P1 P2 of the uniform tube be equal to the length P4 P5, the difference between P11, the height of water in the stand-pipe s1, and P2 Q2, the height of water in the stand-pipe s2, is exactly equal to the difference between P494 and P. Q. Also, if the length P1 P be three times the length P4 P5, the difference between P191 and P424 is equal to three times the difference between P494 and P5 Q5. Or, in other words, when there is a steady flow of liquid through a uniform tube, the difference of pressure between any two points is proportional to the distance between these points. And this is true whatever the inclination of the tube tt to the horizontal, provided that the tube is straight and of uniform cross-section everywhere.

If the tap T and the screw pinch-cock 8, be fully open, and the screw pinch-cock s2 be fairly open, the stream of water through the tube t t will be rapid, and the slope of pressure—that is, the line Q1 Q2... Q joining the tops of the columns of water in the stand-pipes -will be steep. If now the pinch-cock s2 be screwed up a little so as to impede the passage of the water, the flow will be decreased, and the slope of pressure R R Rg will be less inclined to the horizontal than 9192... 96.

As the pinch-cock s, is more and more screwed up the pressure line will become more and more horizontal until, when the flow is entirely checked, the line H1 H2 He joining the tops of the columns of water in the stand-pipes becomes quite horizontal and at the same level as the water in the cistern C1.

It will be noted that if there be any flow, the level of the water in the first stand-pipe s1 is less than that in the cistern itself, which is seen through a little glass