A Treatise on Electricity and Magnetism, Vol. 1 (1881) — part 19 of 28

If P now leaves the spring a it carries with it the charge aV. As P leaves A its potential diminishes, and it diminishes still more when it comes within the influence of C'> which is negatively electrified.

If when P comes within C' its coefficient of induction on C' is — C', and its capacity is (? + c', then, if U is the potential of P the charge on P is

If C'V'=aV,

then at this point U the potential of P will be reduced to zero.

Let P at this point come in contact with the spring / which is connected with the earth. Since the potential of P is equal to that of the spring there will be no spark at contact.

This conductor C", by which the carrier is enabled to be connected to earth without a spark, answers to the contrivance called a regenerator in heat-engines. We shall therefore call it a .Re- generator.

Now let P move on, still in contact with the earth-spring /, till it comes into the middle of the inductor £, the potential of which is V. If — B is the coefficient of induction between P and B at this point, then, since U= 0 the charge on P will be — BV.

When P moves away from the earth-spring it carries this charge with it. As it moves out of the positive inductor B towards the

300 ELECTROSTATIC INSTRUMENTS. [214.

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

A' + a'

and if JB7 is greater than of 7' 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 _Z?', during which motion it acquires a positive charge BV 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 #Fand gained a charge B'7'. Hence the total gain of positive electricity is BV'-aV.

Similarly the total gain of negative electricity is BY — 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 C7=a'7'.

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. In- struments 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 sensitive may be used in electrical measurements, provided we can make the measurement depend on

2 1 5.] COULOMB'S TORSION BALANCE. 301

the absence of electrification. For instance, if we have two charged bodies A and B we may use the method described in Chapter I to determine which body has the greater charge. Let the body A be carried by an insulating support into the interior of an insulated closed vessel C. Let C be connected to earth and again insulated. There will then be no external electrification on C. Now let A be removed, and B introduced into the interior of C, and the elec- trification of C tested by an electroscope. If the charge of B is equal to that of A there will be no electrification, but if it is greater or less there will be electrification of the same kind as that of J?, or the opposite kind.

Methods of this kind, in which the thing to be observed is the non-existence of some phenomenon, are called null or zero methods. They require only an instrument capable of detecting the existence of the phenomenon.

In another class of instruments for the registration of phe- nomena the instruments may be depended upon to give always the same indication for the same value of the quantity to be registered, but the readings of the scale of the instrument are not proportional to the values of the quantity, and the relation between these readings and the corresponding value is unknown, except that the one is some continuous function of the other. Several electrometers depending on the mutual repulsion of parts of the instrument which are similarly electrified are of this class. The use of such instruments is to register phenomena, not to measure them. Instead of the true values of the quantity to be measured, a series of numbers is obtained, which may be used afterwards to determine these values when the scale of the instrument has been properly investigated and tabulated.

In a still higher class of instruments the scale readings are proportional to the quantity to be measured, so that all that is required for the complete measurement of the quantity is a know- ledge of the coefficient by which the scale readings must be multiplied to obtain the true value of the quantity.

Instruments so constructed that they contain within themselves the means of independently determining the true values of quan- tities are called Absolute Instruments.

Coulomb's Torsion Balance. 215.] A great number of the experiments by which Coulomb

302 ELECTROSTATIC INSTRUMENTS. [215.

established the fundamental laws of electricity were made by mea- suring the force between two small spheres charged with electricity, one of which was fixed while the other was held in equilibrium by two forces, the electrical action between the spheres, and the torsional elasticity of a glass fibre or metal wire. See Art. 38.

The balance of torsion consists of a horizontal arm of gum-lac, suspended by a fine wire or glass fibre,, and carrying at one end a little sphere of elder pith, smoothly gilt. The suspension wire is fastened above to the vertical axis of an arm which can be moved round a horizontal graduated circle, so as to twist the upper end of the wire about its own axis any number of degrees.

The whole of this apparatus is enclosed in a case. Another little sphere is so mounted on an insulating stem that it can be charged and introduced into the case through a hole, and brought so that its centre coincides with a definite point in the horizontal circle described by the suspended sphere. The position of the suspended sphere is ascertained by means of a graduated circle engraved on the cylindrical glass case of the instrument.

Now suppose both spheres charged, and the suspended sphere in equilibrium in a known position such that the torsion-arm makes an angle 0 with the radius through the centre of the fixed sphere. The distance of the centres is then 2 a sin \ 0, where a is the radius of the torsion-arm, and if F is the force between the spheres the moment of this force about the axis of torsion is Fa cos J 0.

Let both spheres be completely discharged, and let the torsion- arm now be in equilibrium at an angle <£ with the radius through the fixed sphere.

Then the angle through which the electrical force twisted the torsion-arm must have been 0— (f>, and if M is the moment of the torsional elasticity of the fibre, we shall have the equation

Hence, if we can ascertain JJf, we can determine F, the actual force between the spheres at the distance 2 a sin \0.

To find Mt the moment of torsion, let /be the moment of inertia of the torsion-arm, and T the time of a double vibration of the arm under the action of the torsional elasticity, then

In all electrometers it is of the greatest importance to know what force we are measuring. The force acting on the suspended

2 I 5.] INFLUENCE OF THE CASE. 303

sphere is due partly to the direct action of the fixed sphere, but partly also to the electrification, if any, of the sides of the case.

If the case is made of glass it is impossible to determine the electrification of its surface otherwise than by very difficult mea- surements at every point. If, however, either the case is made of metal, or if a metallic case which almost completely encloses the apparatus is placed as a screen between the spheres and the glass case, the electrification of the inside of the metal screen will depend entirely on that of the spheres, and the electrification of the glass case will have no influence on the spheres. In this way we may avoid any indefiniteness due to the action of the case.

To illustrate this by an example in which we can calculate all the effects, let us suppose that the case is a sphere of radius £, that the centre of motion of the torsion-arm coincides with the centre of the sphere and that its radius is a ; that the charges on the two spheres are E1 and E, and that the angle between their positions is 6 ; that the fixed sphere is at a distance «1 from the centre, and that r is the distance between the two small spheres.

Neglecting for the present the effect of induction on the dis- tribution of electricity on the small spheres, the force between them will be a repulsion

_EEl -T'

and the moment of this force round a vertical axis through the centre will be

The image of Et due to the spherical surface of the case it a point

in the same radius at a distance — with a charge —El — , and the

#! «i

moment of the attraction between E and this image about the axis of suspension is

b* . a — sm 0

aa, sin 0

( aa^ A aa\ )i

••}»-»?««+ VI

If 7), the radius of the spherical case, is large compared with a

304 ELECTKOSTATIC INSTRUMENTS. [216.

and al , the distances of the spheres from the centre, we may neglect the second and third terms of the factor in the denominator. The whole moment tending to turn the torsion- arm may then be written

Electrometers for the Measurement of Potentials.

216.] In all electrometers the moveable part is a body charged with electricity, and its potential is different from that of certain of the fixed parts round it. When, as in Coulomb's method, an insulated body having a certain charge is used, it is the charge which is the direct object of measurement. We may, however, connect the balls of Coulomb's electrometer, by means of fine wires, with different conductors. The charges of the balls will then depend on the values of the potentials of these conductors and on the potential of the case of the instrument. The charge on each ball will be approximately equal to its radius multiplied by the excess of its potential over that of the case of the instrument, provided the radii of the balls are small compared with their distances from each other and from the sides or opening of the case.

Coulomb's form of apparatus, however, is not well adapted for measurements of this kind, owing to the smallness of the force between spheres at the proper distances when the difference of po- tentials is small. A more convenient form is that of the Attracted Disk Electrometer. The first electrometers on this principle were constructed by Sir W. Snow Harris*. They have since been brought to great perfection, both in theory and construction, by Sir W. Thomson f.

When two disks at different potentials are brought face to face with a small interval between them there will be a nearly uniform electrification on the opposite faces and very little electrification on the backs of the disks, provided there are no other conductors or electrified bodies in the neighbourhood. The charge on the positive disk will be approximately proportional to its area, and to the difference of potentials of the disks, and inversely as the distance between them. Hence, by making the areas of the disks large

• Phil. Trans. 1834.

f See an excellent report on Electrometers by Sir W. Thomson. Report of the British Association, Dundee, 1867.

217.]

PRINCIPLE OF THE GUARD-RING.

305

and the distance between them small, a small difference of potential may give rise to a measurable force of attraction.

The mathematical theory of the distribution of electricity over two disks thus arranged is given at Art. 202, but since it is im- possible to make the case of the apparatus so large that we may suppose the disks insulated in an infinite space, the indications of the instrument in this form are not easily interpreted numerically.

217.] The addition of the guard-ring to the attracted disk is one of the chief improvements which Sir W. Thomson has made on the apparatus.

Instead of suspending the whole of one of the disks and determ- ining the force acting upon it, a central portion of the disk is separated from the rest to form the attracted disk, and the outer ring forming the remainder of the disk is fixed. In this way the force is measured only on that part of the disk where it is most regular, and the want of uniformity of the electrification near the

COUMTERPOIse

Fig. 19.

edge is of no importance, as it occurs on the guard-ring and not on the suspended part of the disk.

Besides this, by connecting the guard-ring with a metal case surrounding the back of the attracted disk and all its suspending apparatus, the electrification of the back of the disk is rendered

VOL. i. x

306 ELECTROSTATIC INSTRUMENTS, [217.

impossible, for it is part of the inner surface of a closed hollow conductor all at the same potential.

Thomson's Absolute Electrometer therefore consists essentially of two parallel plates at different potentials, one of which is made so that a certain area, no part of which is near the edge of the plate, is moveable under the action of electric force. To fix our ideas we may suppose the attracted disk and guard-ring uppermost. The fixed disk is horizontal, and is mounted on an insulating stem which has a measurable vertical motion given to it by means of a micrometer screw. The guard-ring is at least as large as the fixed disk ; its lower surface is truly plane and parallel to the fixed disk. A delicate balance is erected on the guard-ring to which is suspended a light moveable disk which almost fills the circular aperture in the guard-ring without rubbing against its sides. The lower surface of the suspended disk must be truly plane, and we must have the means of knowing when its plane coincides with that of the lower surface of the guard-ring, so as to form a single plane interrupted only by the narrow interval between the disk and its guard-ring.

For this purpose the lower disk is screwed up till it is in contact with the guard-ring, and the suspended disk is allowed to rest upon the lower disk, so that its lower surface is in the same plane as that of the guard-ring. Its position with respect to the guard- ring is then ascertained by means of a system of fiducial marks. Sir W. Thomson generally uses for this purpose a black hair attached to the moveable part. This hair moves up or down just in front of two black dots on a white enamelled ground and is viewed along- with these dots by means of a piano convex lens with the plane side next the eye. If the hair as seen through the lens appears straight and bisects the interval between the black dots it is said to be in its sighted position, and indicates that the sus- pended disk with which it moves is in its proper position as regards height. The horizontality of the suspended disk may be tested by comparing the reflexion of part of any object from its upper surface with that of the remainder of the same object from the upper surface of the guard-ring.

The balance is then arranged so that when a known weight is placed on the centre of the suspended disk it is in equilibrium in its sighted position, the whole apparatus being freed from electrification by putting every part in metallic communication. A metal case is placed over the guard-ring so as to enclose the

2 1 7.] THOMSON'S ABSOLUTE ELECTROMETER. 307

balance and suspended disk, sufficient apertures being left to see the fiducial marks.

The guard-ring, case, and suspended disk are all in metallic communication with each other, but are insulated from the other parts of the apparatus.

Now let it be required to measure the difference of potentials of two conductors. The conductors are put in communication with the upper and lower disks respectively by means of wires, the weight is taken off the suspended disk, and the lower disk is moved up by means of the micrometer screw till the electrical attraction brings the suspended disk down to its sighted position. We then know that the attraction between the disks is equal to the weight which brought the disk to its sighted position.

If W be the numerical value of the weight, and g the force of gravity, the force is Wg, and if A is the area of the suspended disk, D the distance between the disks, and V the difference of the potentials of the disks *,

• - 
  

• Let us denote the radius of the suspended disk by E, and that of the aperture of the guard-ring by R', then the breadth of the annular interval between the disk and the ring will be B = R'—R.

If the distance between the suspended disk and the large fixed disk is D, and the difference of potentials between these disks is F, then, by the investigation in Art. 201, the quantity of electricity on the suspended disk will be

I SD SD

where a = B^^-, or a = 0.220635 (R'- -R).

If the surface of the guard-ring is not exactly in the plane of the surface of the suspended disk, let us suppose that the distance between the ^ fixed ^ disk and the guard -ring is not D but D + z = I?, then it appears from the investigation in Art. 225 that there will be an additional charge of electricity near the edge of the disk on account of its height z above the general surface of the guard-ring. The whole charge in this case is therefore, approximately,

and in the expression for the attraction we must substitute for A, the area of the disk, the corrected quantity

(R'*-IP) -~^ + 8 (B + K) (D'-

where E = radius of suspended disk,

R'= radius of aperture in the guard-ring, D = distance between fixed and suspended disks, D'= distance between fixed disk and guard-ring, a = 0.220635 (X?-K).

When a is small compared with D we may neglect the second term, and when D' — D is small we may neglect the last term.

X 2

308 ELECTROSTATIC INSTRUMENTS. [218.

If the suspended disk is circular, of radius R, and if the radius of the aperture of the guard-ring is R'> then

A = i* (-ffi2 + IP), and V= 4 D

218.] Since there is always some uncertainty in determining the micrometer reading corresponding to D = 0, and since any error in the position of the suspended disk is most important when D is small, Sir W. Thomson prefers to make all his measurements depend on differences of the electromotive force T. Thus, if V and V are two potentials, and D and If the corresponding distances,

For instance, in order to measure the electromotive force of a galvanic battery, two electrometers are used.

By means of a condenser, kept charged if necessary by a re- plenisher, the lower disk of the principal electrometer is maintained at a constant potential. This is tested by connecting the lower disk of the principal electrometer with the lower disk of a secondary electrometer, the suspended disk of which is connected with the earth. The distance between the disks of the secondary elec- trometer and the force required to bring the suspended disk to its sighted position being constant, if we raise the potential of the condenser till the secondary electrometer is in its sighted position, we know that the potential of the lower disk of the principal electrometer exceeds that of the earth by a constant quantity which we may call T.

If we now connect the positive electrode of the battery to earth, and connect the suspended disk of the principal electrometer to the negative electrode, the difference of potentials between the disks will be V+ v, if v is the electromotive force of the battery. Let D be the reading of the micrometer in this case, and let I? be the reading when the suspended disk is connected with earth, then

In this way a small electromotive force v may be measured by the electrometer with the disks at conveniently measurable distances. When the distance is too small a small change of absolute distance makes a great change in the force, since the force varies inversely as the square of the distance, so that any

2I9-] GAUGE ELECTROMETER. 309

error in the absolute distance introduces a large error in the result unless the distance is large compared with the limits of error of the micrometer screw.

The effect of small irregularities of form in the surfaces of the disks and of the interval between them diminish according to the inverse cube and higher inverse powers of the distance, and what- ever be the form of a corrugated surface, the eminences of which just reach a plane surface, the electrical effect at any distance which is considerable compared to the breadth of the corrugations, is the same as that of a plane at a certain small distance behind the plane of the tops of the eminences. See Arts. 197, 198.

By means of the auxiliary electrification, tested by the auxiliary electrometer, a proper interval between the disks is secured.

The auxiliary electrometer may be of a simpler construction, in which there is no provision for the determination of the force of attraction in absolute measure, since all that is wanted is to secure a constant electrification. Such an electrometer may be called a gauge electrometer.

This method of using an auxiliary electrification besides the elec- trification to be measured is called the Heterostatic method of electrometry, in opposition to the Idiostatic method in which the whole effect is produced by the electrification to be measured.

In several forms of the attracted disk electrometer, the attracted disk is placed at one end of an arm which is supported by being attached to a platinum wire passing through its centre of gravity and kept stretched by means of a spring. The other end of the arm carries the hair which is brought to a sighted position by altering the distance between the disks, and so adjusting the force of the electric attraction to a constant value. In these electro- meters this force is not in general determined in absolute measure, but is known to be constant, provided the torsional elasticity of the platinum wire does not change.

The whole apparatus is placed in a Leyden jar, of which the inner surface is charged and connected with the attracted disk and guard-ring. The other disk is worked by a micrometer screw and is connected first with the earth and then with the conductor whose potential is to be measured. The difference of readings multiplied by a constant to be determined for each electrometer gives the potential required.

219.] The electrometers already described are not self-acting, but require for each observation an adjustment of a micrometer

310 ELECTKOSTATIC INSTRUMENTS. [219.

screw, or some other movement which must be made by the observer. They are therefore not fitted to act as self-registering instruments, which must of themselves move into the proper position. This condition is fulfilled by Thomson's Quadrant Electrometer.

The electrical principle on which this instrument is founded may be thus explained : —

A and B are two fixed conductors which may be at the same or at different potentials. C is a moveable conductor at a high potential, which is so placed that part of it is opposite to the surface of A and part opposite to that of B, and that the proportions of these parts are altered as C moves.

For this purpose it is most convenient to make C moveable about an axis, and make the opposed surfaces of A, of B, and of C portions of surfaces of revolution about the same axis.

In this way the distance between the surface of C and the opposed surfaces of A or of B remains always the same, and the motion of C in the positive direction simply increases the area opposed to B and diminishes the area opposed to A.

If the potentials of A and B are equal there will be no force urging C from A to £, but if the potential of C differs from that of B more than from that of A, then C will tend to move so as to increase the area of its surface opposed to B.

By a suitable arrangement of the apparatus this force may be made nearly constant for different positions of C within certain limits, so that if C is suspended by a torsion fibre, its deflexions will be nearly proportional to the difference of potentials between A and B multiplied by the difference of the potential of C from the mean of those of A and B.

C is maintained at a high potential by means of a condenser provided with a replenisher and tested by a gauge electrometer, and A and B are connected with the two conductors the difference of whose potentials is to be measured. The higher the potential of C the more sensitive is the instrument. This electrification of C, being independent of the electrification to be measured, places this electrometer in the heterostatic class.

We may apply to this electrometer the general theory of systems of conductors given in Arts. 93, 127.

Let A, B, C denote the potentials of the three conductors re- spectively. Let a, b, c be their respective capacities,^ the coefficient of induction between B and <?, % that between C and A, and r that

2I9-]

QUADRANT ELECTROMETER.

311

between A and B. All these coefficients will in general vary with the position of (?, and if C is so arrang-ed that the extremities of A and B are not near those of Cas long as the motion of Cis confined within certain limits, we may ascertain the form of these coefficients. If 0 represents the deflexion of C from A towards B, then the part of the surface of A opposed to C will diminish as 0 increases. Hence if A is kept at potential 1 while B and Care kept at potential 0, the charge on A will be a = #0— aO, where a0 and a are constants, and a is the capacity of A.

If A and B are symmetrical, the capacity of B is b — b0 + aO.

The capacity of C is not altered by the motion, for the only effect of the motion is to bring a different part of C opposite to the interval between A and B. Hence c = c0.

The quantity of electricity induced on C when B is raised to potential unity is p = p0—a$.

The coefficient of induction between A and C is q = $0 + ad.

The coefficient of induction between A and B is not altered by the motion of C, but remains r = r0 .

Hence the electrical energy of the system is

and if 0 is the moment of the force tending to increase 0,

0 = — , A, .5, C being supposed constant, ad

CAa ;

or = a

In the present form of Thomson's Quadrant Electrometer the conductors A and B are in the form of a cylindrical box completely divided into four quadrants, separately insu- lated, but joined by wires so that two opposite quadrants are connected with A and the two others with B.

The conductor C is suspended so as to be capable of turning about a vertical axis, and may consist of two opposite flat quadrantal arcs supported rig 20

by their radii at their extremities. In the position of equilibrium these quadrants should be partly

312 ELECTROSTATIC INSTRUMENTS. [22O.

within A and partly within B, and the supporting radii should be near the middle of the quadrants of the hollow base, so that the divisions of the box and the extremities and supports of C may be as far from each other as possible.

The conductor C is kept permanently at a high potential by being connected with the inner coating of the Leyden jar which forms the case of the instrument. B and A are connected, the first with the earth, and the other with the body whose potential is to be measured.

If the potential of this body is zero, and if the instrument be in adjustment, there ought to be no force tending to make C move, but if the potential of A is of the same sign as that of (7, then C will tend to move from A to B with a nearly uniform force, and the suspension apparatus will be twisted till an equal force is called into play and produces equilibrium. Within certain limits the deflexions of C will be proportional to the product

By increasing the potential of C the sensibility of the instrument may be increased, and for small values of J (A + B) the deflexions will be nearly proportional to (A—B) C.

On the Measurement of Electric Potential.

220.] In order to determine large differences of potential in ab- solute measure we may employ the attracted disk electrometer, and compare the attraction with the effect of a weight. If at the same time we measure the difference of potential of the same conductors by means of the quadrant electrometer, we shall ascertain the absolute value of certain readings of the scale of the quadrant electrometer, and in this way we may deduce the value of the scale readings of the quadrant electrometer in terms of the potential of the suspended part, and the moment of torsion of the suspension apparatus.

To ascertain the potential of a charged conductor of finite size we may connect the conductor with one electrode of the electro- meter, while the other is connected to earth or to a body of constant potential. The electrometer reading will give the potential of the conductor after the division of its electricity between it and the part of the electrometer with which it is put in contact. If K denote the capacity of the conductor, and K' that of this part

221.] MEASUREMENT OF POTENTIAL. 313

of the electrometer, and if 7, V denote the potentials of these bodies before making contact, then their common potential after making contact will be

K+K'

Hence the original potential of the conductor was

If the conductor is not large compared with the electrometer, K' will be comparable with K, and unless we can ascertain the values of K and R' the second term of the expression will have a doubtful value. But if we can make the potential of the electrode of the electrometer very nearly equal to that of the body before making contact, then the uncertainty of the values of K and K' will be of little consequence.

If we know the value of the potential of the body approximately, we may charge the electrode by means of a ' replenisher ' or other- wise to this approximate potential, and the next experiment will give a closer approximation. In this way we may measure the potential of a conductor whose capacity is small compared with that of the electrometer.

To Measure the Potential at any Point in the Air.

221.] First Method. Place a sphere, whose radius is small com- pared with the distance of electrified conductors, with its centre at the given point. Connect it by means of a fine wire with the earth, then insulate it, and carry it to an electrometer and ascertain the total charge on the sphere.

Then, if V be the potential at the given point, and a the radius of the sphere, the charge on the sphere will be — Va — Q, and if V be the potential of the sphere as measured by an elec- trometer when placed in a room whose walls are connected with the earth, then Q = ya,

whence V+ 7'= 0,

or the potential of the air at the point where the centre of the sphere was placed is equal but of opposite sign to the potential of the sphere after being connected to earth, then insulated, and brought into a room.

This method has been employed by M. Delmann of Creuznach in

314 ELECTROSTATIC INSTRUMENTS. [222.

measuring the potential at a certain height above the earth's surface.

Second Method. We have supposed the sphere placed at the given point and first connected to earth, and then insulated, and carried into a space surrounded with conducting matter at potential zero.

Now let us suppose a fine insulated wire carried from the elec- trode of the electrometer to the place where the potential is to be measured. Let the sphere be first discharged completely. This may be done by putting it into the inside of a vessel of the same metal which nearly surrounds it and making it touch the vessel. Now let the sphere thus discharged be carried to the end of the wire and made to touch it. Since the sphere is not electrified it will be at the potential of the air at the place. If the electrode wire is at the same potential it will not be affected by the contact, but if the electrode is at a different potential it will by contact with the sphere be made nearer to that of the air than it was before. By a succession of such operations, the sphere being alternately discharged and made to touch the electrode, the poten- tial of the electrode of the electrometer will continually approach that of the air at the given point.

222.] To measure the potential of a conductor without touching it, we may measure the potential of the air at any point in the neighbourhood of the conductor, and calculate that of the conductor from the result. If there be a hollow nearly surrounded by the conductor, then the potential at any point of the air in this hollow will be very nearly that of the conductor.

In this way it has been ascertained by Sir W. Thomson that if two hollow conductors, one of copper and the other of zinc, are in metallic contact, then the potential of the air in the hollow surrounded by zinc is positive with reference to that of the air in the hollow surrounded by copper.