Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/304

 negative receiver $$A'$$ its potential will be increasingly negative. At the middle of $$A'$$, if it retained its charge, its potential would be

$-\frac{A'V'+BV}{A'+a'} $

and if $$BV$$ is greater than $$a'V'$$ its numerical value will be greater than that of $$V'$$. Hence there is some point before $$P$$ reaches the middle of $$A'$$ where its potential is $$-V'$$. At this point let it come in contact with the negative receiver-spring $$a'$$. There will be no spark since the two bodies are at the same potential. Let $$P$$ move on to the middle of $$A'$$ still in contact with the spring, and therefore at the same potential with $$A'$$. During this motion it communicates a negative charge to $$A'$$. At the middle of $$A'$$ it leaves the spring and carries away a charge $$-a'V'$$ towards the positive regenerator $$C$$, where its potential is reduced to zero and it touches the earth-spring $$e$$. It then slides along the earth-spring into the negative inductor $$B'$$, during which motion it acquires a positive charge $$B'V'$$ which it finally communicates to the positive receiver $$A$$, and the cycle of operations is repeated.

During this cycle the positive receiver has lost a charge $$aV$$ and gained a charge $$B'V'$$. Hence the total gain of positive electricity is

$B'V'-aV $

Similarly the total gain of negative electricity is $$BV-a'V' $$.

By making the inductors so as to be as close to the surface of the carrier as is consistent with insulation, $$B$$ and $$B'$$ may be made large, and by making the receivers so as nearly to surround the carrier when it is within them, $$a$$ and $$a'$$ may be made very small, and then the charges of both the Leyden jars will be increased in every revolution.

The conditions to be fulfilled by the regenerators are

$C'V'=aV $ and $CV=a'V' $.

Since $$a$$ and $$a'$$ are small the regenerators do not require to be either large or very close to the carriers.

On Electrometers and Electroscopes.

214.] An electrometer is an instrument by means of which electrical charges or electrical potentials may be measured. Instruments by means of which the existence of electric charges or of differences of potential may be indicated, but which are not capable of affording numerical measures, are called Electroscopes.

An electroscope if sufficiently sensible may be used in electrical measurements, provided we can make the measurement depend on