Page:Elementary Text-book of Physics (Anthony, 1897).djvu/312

298 always taken in the space between the plates as equal to $$2\pi \sigma$$ (§ 57). Every unit on the attracted disk is attracted with this force, and the total attraction, which is measured by means of the balance or spring, is $$F = 2\pi \sigma^2 S.$$ Substituting this value of $$\sigma$$ in the former equation, we get which gives the difference of potential between the two plates in terms which are all measurable in absolute units.

Thomson's quadrant electrometer is an instrument which is not used for absolute measurement, but being extremely sensitive to minute diflerences of potential, it enables us to compare them with each other and with some known standard. The construction of the apparatus can best be understood from Fig. 81. Of the four metallic quadrants which are mounted on insulating supports, the two marked $$P$$ and the two marked $$N$$ are respectively in conducting contact by means of wires. The body $$C,$$ technically called the needle, is a thin sheet of metal, suspended symmetrically just above the quadrants by two parallel silk fibres, forming what is known as a bifilar suspension. When there is no charge in the apparatus, the axes of symmetry of the needle lie above the spaces which separate the quadrants.

To use the apparatus, the needle is maintained at a high, constant potential, and the two points, the difference of potential between which is desired, are joined to the pairs of quadrants $$P$$ and $$N.$$ The needle is deflected from its normal position, and the amount of deflection is an indication of the difference of potential between the two pairs of quadrants.

262. Electrical Machines.—Electrical machines may be divided into two classes: those which depend for their operation upon friction, and those which depend upon induction.

The frictional machine, in one of its forms, consists of a