Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/427

334.] misled by the analogy between electricity and heat, entertained an opinion of this kind, and was thus, by means of an erroneous opinion, led to employ the equations of Fourier to express the true laws of conduction of electricity through a long wire, long before the real reason of the appropriateness of these equations had been suspected.

Mechanical Illustration of the Properties of a Dielectric.

334.] Five tubes of equal sectional area $$A,\, B,\, C,\,  D$$ and $$P$$ are arranged in circuit as in the figure. $$A,\, B,\, C$$ and $$D$$ are vertical and equal, and $$P$$ is horizontal.

The lower halves of $$A,\, B,\, C,\, D$$ are filled with mercury, their upper halves and the horizontal tube $$P$$ are filled with water.

A tube with a stopcock $$Q$$ connects the lower part of $$A$$ and $$B$$ with that of $$C$$ and $$D,$$ and a piston $$P$$ is made to slide in the horizontal tube.

Let us begin by supposing that the level of the mercury in the four tubes is the same, and that it is indicated by $$A_0,\, B_0,\, C_0,\, D_0,$$ that the piston is at $$P_0,$$ and that the stopcock $$Q$$ is shut.

Now let the piston be moved from $$P_0$$ to $$P_1,$$ a distance $$a.$$ Then, since the sections of all the tubes are equal, the level of the mercury in $$A$$ and $$C$$ will rise a distance $$a,$$ or to $$A_1$$ and $$C_1,$$ and the mercury in $$B$$ and $$D$$ will sink an equal distance $$a,$$ or to $$B_1$$ and $$D_1.$$

The difference of pressure on the two sides of the piston will be represented by $$4a.$$

This arrangement may serve to represent the state of a dielectric acted on by an electromotive force $$4a.$$

The excess of water in the tube $$D$$ may be taken to represent a positive charge of electricity on one side of the dielectric, and the excess of mercury in the tube $$A$$ may represent the negative charge on the other side. The excess of pressure in the tube $$P$$ on the side of the piston next $$D$$ will then represent the excess of potential on the positive side of the dielectric.