1902 Encyclopedia > Galvanometer

Galvanometer




GALVANOMETER, an instrument used for indicating or measuring currents of electricity, wherein advantage is taken of the force exerted by such currents on movable magnets in their neighbourhood. When a galvanometer is used for indicating merely, without measuring, it is sometimes called a galvanoscope. If we consider only such instruments as have come into actual use, this definition is strict enough for practical purposes. If we were to consider all the instruments that have been or might be made, some would come under the definition whose resemblance to the modern galvanometer would not at first sight be apparent. Such, for instance, is the electromagnetic balance of Becquerel, which consists of two bar magnets hung from the scale pans of a delicate balance each in the axis of a cylindrical bobbin of wire—one being over, the other under its corresponding bobbin (see fig. 1). The north poles of both magnets hang

!
Fig. 1.

downwards, and the current to be measured is sent round tho^ bobbin, so that each of the magnets is repelled. Weights are put into the left-hand scale until equilibrium in the original position is restored. The weight thus added is proportional to the current strength, so long as the induced magnetism of the magnets can be neglected. This instrument has fallen into disuse.

see art. ELECTRICITY, vol. viii. p. 13.

In a complete galvanometer of modern construction the following parts may occur :—(1) the coil or multiplier, (2) the needle or movable magnet or magnets, (3) the astatizing apparatus, (4) the deflecting or adjusting magnet, (5) the graduation or reading apparatus, (6) the damping apparatus, (7) accompanying the galvanometer, as a piece of auxiliary apparatus, we may also have a box of shunts. It would be easy to make a more minute enumeration of parts, but the above will serve our present purpose. On the other hand, it is not always that each of the above organs is represented separately; some may be wanting in certain cases, and the functions of two or more may be combined.
1. The multiplier or coil consists of a ring-shaped
channel of elliptical, rectangular, or circular shape—usually
the last, the cross section being in general rectangular.
Into this is wound, as closely and regularly as possible, a
quantity of silk-covered wire. The material chosen for the
wire is usually copper, which should be as soft as possible
in order to secure high conductivity. White silk is preferred
for the insulating covering, on account of its freedom from
iron, though this is for most purposes a needless refinement.
Great care should be taken that the wire is dry when it is
wound. It is usual, in order to secure and render perman-
ent the insulation, to steep the whole coil in melted paraffin ;
after this has been done, there is little risk of loss of insula-
tion, provided the layers have been carefully tested during
the winding. The idea of the multiplier in sensitive
galvanometers is to bring the greatest number of coils of
wire within the least possible distances of the magnet. It
is evident, therefore, that the insulating covering should be
as thin as is consistent with good insulation; this considera-
tion assumes great importance when coils of very fine wire
have to be wound. After the wire has reached a certain
fineness the proportion of space occupied by insulating
matter is so great that further reduction of the section of
the wire simply increases the resistance without enabling
us to pack more turns into the same space. In general the
section of the wire ought to be chosen with reference to the
use which the galvanometer is intended to serve. The
following ideal case will enable the reader to comprehend
the principle which regulates the choice of multiplier
under given circumstances. Suppose the dimensions of the
channel, and the whole space which the wire is to fill, to be
given, and the whole external resistance also given, then it
may be shown that the section of the wire8 ought to be
I chosen so that the resistance of the galvanometer shall be equal to the external resistance. The case contemplated here is that where we have a simple external circuit; many cases can be reduced to this at once, and we shall consider below a more complicated case of considerable practical importance. Theoretically the section of the wire ought to
I vary with the distance of the winding from the axis of the coil. The law is that the diameter of the wire in each layer ought to be proportional to the linear dimension of that layer. This is sometimes roughly carried out in practice by winding the outer layers of thicker wire than the inner.4 The proper form of the longitudinal section of the coil depends on the use for which the instrument is destined, and will be more properly discussed when we describe particular instruments. In a certain class of galvanometers called differential, the wire on the coil is wound double, so that two currents can be sent through side by side in the same or in opposite directions.
2. The needle consists of a piece of magnetized steel,
3 In this and all that follows the silk covering is either neglected or is supposed to vary in thickness as the diameter of the wire.
4 The cross section of the coil is not a matter of indifference in sensitive galvanometers ; but the question is hardly of sufficient importance to need discussion here. Information on the subject will be found in W. Weber's Electrodynamische Maasbestimmungen, Thl. ii.; H. Weber, Pogg. Ann., 1869 ; Maxwell's Electricity and Magnetism, vol. ii. sees. 716 sqq.: Jenkin's Electricity and Mag-netism, cap. xiii. sec. 9.

which should be as hard as possible. Watch-spring steel is sometimes used, and file steel is recommended by some authorities. The hardness is important for two reasons,— in the first place, to ensure that the permanent magnetism of the needle shall not alter. This is of small importance where permanent deflections are to be observed, provided we can be sure that the direction of the magnetic axis does not alter. In the second place the induced magnetism is less in hard than in soft steel, though not so much less as some writers would lead us to suppose. The best way of avoiding induced magnetism would be to make the needle spherical in form; the advantage thus gained, however, would in most cases be counterbalanced by other defects.
The form of the needle has been much varied by different constructors. In the earlier instruments they were made very long, and were suspended like compass needles by means of a jewelled cup playing on a steel point. We have heard on good authority that for some purposes, such as mounting tangent galvanometer needles, this method of suspension, if carefully carried out, really answers very well. By far the most usual mode of suspension, however, is by means of a raw silk fibre, or by a bundle of such fibres. Weber introduced the use of heavy magnets whose moment of inertia and time of oscillation were great. For many purposes such needles have great advantages—where, for instance, the time of oscillation, the logarithmic decrement, or the extent of swing of the needle has to be observed. Where, on the contrary, the galvanometer is to be used merely as an indicator, particularly in detecting transient currents, a light needle of small moment of inertia should be used. Continental constructors, no doubt unduly influenced by a reverence for Weber's methods, have failed to realize this; and we have seen few, if indeed any, instruments by them really well suited for measuring resistances with the Wheatstone's bridge. This principle has been carried farthest in the galvanometers of Sir William Thomson, in some of which the needle with all its appurtenances weighs little over a grain.
In some galvanometers (e.g., certain telegraphic reading instruments) the needle is movable about a horizontal axis, and is weighted so as to be vertical in its undisturbed position. Owing to the friction at the points where the axis is supported, this method of suspension is useless for sensitive instruments.
3. When, as i3 usual, the galvanometer magnet is movable in a horizontal plane, the force which balances the electromagnetic force of the current in the multiplier is the horizontal component of the earth's magnetic force. Each of these forces is proportional to the magnetic moment of the galvanometer needle, and consequently the ratio of the forces, on which depends the magnitude of the deflexion of the needle, is independent of the magnetic moment of the needle. We cannot therefore increase the sensitiveness of the galvanometer by simply increasing the magnetic moment of the needle. The action of the earth can, how-ever, be counteracted, and the needle rendered more or less astatic in one or other of two ways.
One way is to fix on the same axis of suspension two parallel magnets, whose magnetic moments are as nearly as possible equal, and which are turned opposite ways. The whole system is suspended so that one of the magnets swings inside the multiplier and the other over it, as in fig. 2. In more modern instruments, such as those constructed by Messrs Elliot Brothers, the multiplier consists of two equal coils placed one vertically over the other, each enclosing one of the magnets of the astatic system, as in fig. 3. Another method is to place a magnet, or a system of magnets, in the neighbourhood of the galvanometer, so as to counteract the earth's force. In general, one magnet will suffice, placed vertically under or over the galvanometer, in the magnetic meridian, its north pole of course pointing north. For convenience this magnet should be mounted on a vertical graduated rod, with a rough and a fine adjustment.
In adjusting the sensi-
tiveness of the galvano-
meter, it will be useful to
recollect that the couple
tending to bring the
needle back to its posi-
tion of equilibrium varies
directly as the square of
the number of oscilla-
tions which the needle
executes in a given time
when no current is pass-
ing through the multi-
plier. As the astatizing
magnet is brought nearer lig-2.

and nearer to the galvanometer, the oscillations of the needle will be seen to become slower and slower, till at last the equilibrium becomes unstable, and the needle turns round through 180°; after which, on causing the magnet to approach still farther, the rapidity of oscillation increases. If the damping be very strong, and the mirror very light, an intermediate stage called the aperiodic state is passed through.
i. The normal position of the magnetic
axis of the needle, when no current is
passing, is parallel to the windings of
the multiplier. It is particularly neces-
sary that it should be in this position
when the galvanometer is being used
as a measuring instrument, and it is
advisable in any case, since this is the
position in which for a given current the 3-
electromagnetic action on the needle is greatest. The final adjustment might of course be made by moving the multiplier, but it is far more convenient to move the needle, a magnet being used for the purpose. Sometimes the astatizing magnet is used, but it is better to have a much weaker magnet for the fine adjustment, suspended like the astatizer on a vertical axis, having a vertical motion and a motion of rotation. It is better still to use a magnet placed with its axis in the axis of the multiplier, so that it can be slid backwards and forwards at pleasure. We have seen two such magnets placed side by side, with their north and south and their south and north poles together; this gives a differential adjustment which is very convenient. The main advantage of placing magnets in this way is that we can alter the direction of the lines of force with a minimum effect on the strength of the magnetic field.
sufficient for ordinary purposes.





5. The graduation or reading apparatus in the older instruments consisted of a pointer or index fixed to the magnet (very often it was the magnet itself), playing over a circular graduation centred as nearly as possible in the axis of rotation of the needle. The mirror method of read-ing which prevails in most modern instruments was origin-ally suggested by Poggendorff, and carried out in practice by Gauss and Weber. A mirror is rigidly attached to the magnet, so that the reflecting face passes as nearly as pos-sible through the vertical axis of rotation of the needle. The glass of the mirror should be very thin, otherwise a greater or less correction for its thickness will be necessary. In the subjective method of reading, a scale is fixed before the mirror, which is usually plane (it must be well made to

be of any use), and the image of the scale is observed by means of a telescope fixed over or under the centre of the scale. The scale divisionsare seen to pass the wires of the telescope, and if a circular scale be used, whose centre is in the axis of suspension of the mirror, the difference between the numbers on the cross wires in any two positions of the magnet is a measure of twice the deflection of the magnet. A correction is necessary when a straight scale is used. The reader who has occasion to use the method will find practical instructions, with tables of corrections, in Wiedemann's Galvanismus, Bd. ii. sec. 181 sqq.; Maxwell's Electricity and Magnetism, vol. ii. sec. 450 sqq. In the objective method, which is more usually practised in this country, the mirror is concave, and reflects the image of a fixed illumin-ated slit (often furnished with a vertical wire where greater accuracy is desired) upon a graduated scale. The readings are proportional to double the deflexion of the needle, or to the tangent of the double deflexion, according as the scale is circular or straight.
6. By damping is meant the decrease of the extent of the
oscillations of the galvanometer needle arising from the
dissipation of energy through the resistance of the air, the
action of currents induced in neighbouring metallic circuits,
the viscosity of the suspension fibre, and so on. There is
always more or less damping owing to the first two causes,
and possibly the third; but in many cases, where it is de-
sirable that the oscillations should subside very quickly, the
damping is purposely increased. In the older instruments
the damping arrangement consisted of masses of copper
surrounding the magnet. This is carried to the extreme in
Wiedemann's tangent galvanometer, where the needle is
ring-shaped, and swings in a ring-shaped cavity not much
larger than itself, in the heart of a mass of copper. In the
dead-beat galvanometers of Sir William Thomson the
magnet with its attached mirror is enclosed in a flat cell,
in which it can just move freely to the required extent.
The damping, due to the pumping of the air backwards and
forwards round the edges of the mirror, is so great that the
needle swings off to its position of equilibrium, and remains
there without oscillating at all. The same result is attained
in Varley's construction by immersing the needle in a cell
filled with liquid.
7. The box of shunts is simply a set of resistances;
generally there are three,—Lth, ^th, and -g^-g-th of the
resistance of the multiplier. When it is required to reduce
the sensibility of the galvanometer, the terminals of one of
these, say the ^th, are connected with the terminals of the
multiplier; we thus have a multiple arc in place of the
galvanometer, and the current is divided between its
branches in the ratio of their conductivities, so that one-
hundredth of the whole current flows through the galvano-
meter. By means of such a box as we have described, we
can therefore send through the galvanometer the whole of
any current, or the tenth, hundredth, or thousandth part.
It must not be forgotten that the introduction of the shunt
diminishes the whole resistance of the galvanometer circuit.
In most cases, however, this is of little moment; where
necessary, the alteration may be either compensated or
allowed for.

Sensitive Galvanometers.—In galvanometers of this class everything is disposed so as to bring the greatest possible number of turns of wire into the neighbourhood of the needle. The needle is therefore made as small and compact as possible, and the windings embrace it as closely as pos-sible, the opening in the centre of the coil being reduced to a minimum. The astatic multiplier (fig. 4) is an instru-ment of this kind which was formerly much used. The

coil is of flat, rectangular shape, with a narrow central
opening just large enough to allow one of the magnets of
the astatic system
to swing freely.
The other magnet
swings over a gra-
duated circle placed
on the top of the
coil, and serves also
as an index. Some-
times a mirror and
scale aresubstituted
for the index and
graduated circle.
The sole on which
the coil stands is
movable on a fixed
piece which can be
levelled by means
of three screws. A
graduation is often
furnished to mea-
sure the angle of
rotation of the coil
about a vertical FlG- 4.—Astatic multiplier,
axis; this is useful when the galvanometer has to be graduated or corrected for the torsion of the fibre.
In the galvanometers of Sir William Thomson, which are the most sensitive hitherto constructed, the central opening of the coil is circular, being just large enough to allow free play to a small concave mirror a centimetre or so in diameter. Usually the coil is wound in two halves, which can be screwed together with a septum between them, in which is placed the arrangement for suspending the mirror and magnets. In dead-beat instruments the coil is often wound in a single piece, and the mirror is arranged in a cell, glazed back and front, and fitted into a tube which slides into the core of the coil.
Fig. 5 represents a very convenient form of Thomson's
galvanometer, the only specimen of its kind we have seen. The peculiarity of its construction consists in the connexion between the scale and the galvanometer, which saves much trouble in adjusting the instrument. It was constructed by Elliot Brothers for the British Association Committee on Electrical Standards. Such a galvanometer as this, pro-vided with a high and low resistance coil, would meet all the wants of most laboratories.
3 This arrangement is that adopted by White of Glasgow in the galvanometers made by him after Sir Wm. Thomson's pattern.
In another form called the marine galvanometer, the mirror is strung on a fibre stretched between two fixed points In order to keep the needle from being influenced

by the rolling of the ship, its centre of gravity is carefully adjusted so as to be iu the axis of suspension. The mirror is enclosed in a narrow cell which just allows it room to deflect to the required extent, and damps the oscillation so effectually that the instrument is " dead beat." In order to destroy the directive action of the earth, the inconveni-ence of which in a galvanometer for use on board ship is obvious, the case of this galvanometer is made of thick soft iron, which completely encloses the whole, leaving only a small window for the ingress and egress of the ray of light by means of which the motions of the mirror are read; a flat horse-shoe magnet placed on the top of the case still farther overpowers the earth's force and directs the mirror.
All these galvanometers may, of course, be wound double
and used differentially. When this is the small
auxiliary compensating coil is often used to correct the inequality of the magnetic fields due to the two sets of windings. This auxiliary coil is usually mounted on a spindle in the axis of the main coil, and can be moved backwards and forwards till a current passing through it and one set of windings in one direction, and through the other set of windings in the other direction, does not sensibly deflect the mirror.
The astatic arrangement described above (p. 51, fig. 4) is often adopted. A galvano-meter of this construction by Elliot Brothers is shown in fig. 6. It may be questioned, how-ever, whether for ordinary purposes the additional sensi-bility thus gained compensates for the increased complexity and cost of the instrument.
Standard Galvanometers.— When galvanometers are intended for measuring currents, there must be some law connecting the indications of the needle with the strength of the current in the multiplier. It is therefore of great importance that slight variations in the position of the magnet should not introduce large or irregular (incalculable) variations into the indications of the instrument. Accordingly in standard instru-ments the windings are much farther removed from the mag-net than in sensitive galvanometers, and in the best forms the multiplier is so disposed that it produces a uniform field of magnetic force around the needle.
The earliest forms of standard galvanometer were the tangent and sine compasses invented by Pouillet. The first of these consists simply of a single vertical coil of wire, with a magnet suspended at its centre, whose deflexion may be read in any of the various ways already described. If the length of the magnet be very small, the magnetic field in its neighbourhood may be regarded as uniform, and the electromagnetic couple will be propor-tional to cos 6, 6 being the deflexion from the plane of the windings. If the windings be arranged so as to be in the magnetic meridian, the couple due to the earth's action tending to bring the magnet back to its position of equilibrium will be proportional to sin 0, hence the current strength will be proportional to tan 0.
If the multiplier be movable about a vertical axis through angles which can be measured in any way, the instrument may be used as a sine compass. The current is applied and the multiplier turned round after the magnet until the axis of the latter is again parallel to the windings. The current strength is now clearly proportional to sin 6, where 0 is the deflexion of the multiplier from the mag-netic meridian. When the instrument is used in this way, the needle being always brought into the same position relative to the windings, the uniformity of the magnetic field is a matter of indifference, and there is no necessity for the needle to be short.
Gaugain attempted to improve the tangent galvanometer by suspending the magnet ex-centrically at a point in the axis of the coil distant from the centre by half the radius of the coil. This, however, is in reality the reverse of an improvement.

channels cut in a cylindrical block of hard wood, each an inch broad and an inch deep. The radius of the bottom of each channel is one inch, and the distance between them is half an inch. The cylin-drical perforation in the core of the multiplier is If inch in diameter—large enough to allow the needle to swing freely without causing irregular air currents, &c. Into the ends of the core are screwed two caps containing a piece of plane parallel glass and a plano-convex lens respectively, the former for subjective, the latter for objective reading. By means of a slit and screw in the stem which supports the instrument, a horizontal bar can be fixed parallel to the axis of the multiplier. On this a deflecting magnet can be mounted, so that the galvanometer can he used as a magnetometer.
A real advance, however, was made by Helmholtz, who placed two equal parallel and vertical coils, one on each side of the magnet, each at a distance from it equal to half the common radius. In fig. 19, at the end of his second volume, Maxwell gives a diagram of the lines of force due to two equal parallel circular circuits, from which it will be seen that the magnetic field at the centre of such an arrangement of currents is very approximately uniform. This approximation may be carried Still farther by adding a third FIG. 7.—Galvanometer designed coil parallel to the two Others, HJ Professor Maxwell, and equidistant from them. The wireis wound in two parallel
In some examples of Helm-holtz's galvanometer the windings are arranged on a conical surface, so that the ratio of the radius of each to the distance of its plane from the centre of the magnet shall be 2 :1. In reality this is unnecessary, provided the ratio of the depth and breadth of the usual rectangular channel be properly adjusted (see Maxwell, vol. ii. sec. 713). Fig. 7 represents
of the kind
galvanometer described.





Reduction of Galvanometer Indications.—"When the position of every layer of wire in the multiplier is known with sufficient accuracy, and the multiplier arranged so as to produce a sensibly uniform field, the electromagnetic action per unit of current can be calculated for every position of the magnet. In this case the galvanometer is an absohde instrument. When we possess one absolute instrument it is easy to evaluate the indications of any other in absolute measure by means of it; we have only to pass the same current through both galvanometers in series and compare the readings. The best way, however, to construct a standard galvano-meter is to provide for uniformity of field in the core of the multiplier; and find the resultant electromagnetic force for unit current, or, as it is called, the constant of the instrument, by comparison with a pair of equal standard coils of large diameter (18 in. to 24 in.). These are arranged vertically on the same axis, the distance between them being equal to the mean radius, just as in Helmholtz's galvanometer. The galvanometer to be tested is placed symmetrically between tht

standard coils, the centre of its multiplier being near the centre of the whole arrangement, and the axes of all the coils coincident. A multiple arc is then formed, one branch of which contains the coils and the other the galvanometer, so that the magnetic actions oppose each other. The resist-ances of the two branches are then adjusted till the gal-vanometer needle gives no indication when a current is sent through the multiple arc. The whole arrangement will be understood from fig. 8. if R and S be the resistances in the branches containing the galvanometer and coils respectively, then the constant of the galvanometer is to that of the coils as It: S; so that when the latter is calculated the former is known.
The constant of the galvanometer G being known, the value of a current producing a deflexion 0 is given in absolute measure by
I = 5tan B, G
H being the horizontal component of the earth's magnetic force.
In many cases it is necessary to correct for the torsion of the suspending fibre. The value of this correction is easily found by turning the multiplier through 90° either way, and observing how far the needle follows it. The reader will find all necessary details in Maxwell, vol. ii., sees. 452, 742.
In all cases whei great accuracy is required it is advisable to graduate, or, as it is sometimes said, to calibrate the galvanometer, that is, to compare the electromagnetic couple exerted by the multi-plier when the needle is deflected through an angle 6 with that when the needle is parallel to the windings. It is easy to see that this may be done by means of the arrangement described above for finding the constant of a galvanometer. If the object simply is to calibrate the galvanometer without reducing its indications to absolute measure, the standard coils may be replaced by a single coil of sufficient magnetic moment placed in the axis of the multi-plier. Another method of calibration, which is simpler, and in some respects more satisfactory, although possibly more laborious, will be understood from fig. 9. The resistance a is equal to the

Fig. 9.
resistance of the galvanometer, and they can be rapidly interchanged. By adjusting/the ratio of the currents in the branches of the multiple arc may be varied as we please, and by varying e the current in one of the branches can always be brought to a standard strength, say that which produces unit deflexion of the galvanometer needle. We can thus, by repeatedly interchanging a and b, compare the deflexions produced by a series of currents whose strengths are given multiples of the standard strength. If the experimenter has two galvanometers at his disposal the interchanges may of course be avoided.
Chi the Use of the Galvanometer.—We may add a few remarks on the different uses to which a galvanometer may be put.
Detection of Currents.—One of the commonest of all the uses of a galvanometer is to indicate the currents sent through telegraph wires or cables. In the case of submarine cables, where the currents are often very feeble, dead-beat galvanometers of Thomson's or Varley's construction are used.
When a current is to be detected which produces a very small or quite insensible permanent deflexion, the following process, called the method of multiplication, is sometimes used. The period of oscilla-tion of the needle is first found ; then, the needle being at rest or only swinging through a very small arc, the current is applied through half the period of oscillation so as to urge the needle in the direction in which it is going, then intermitted for half a period, then applied again, and so on. If a current in the supposed direction really exist, the oscillations of the magnet will gradually increase, until the energy supplied by the intermittent action of the current is equal to that wasted by the damping of the needle.
It is obvious that this process is more effective the smaller the damping of the needle ; it leads to no advantage whatever with a dead-beat instrument.
Resistance Measuring.—In comparing resistances, sensitive galvanometers of Sir William Thomson's construction are by far the most convenient; the dead-beat arrangement is essential for rapid work.
If a differential galvanometer of given dimensions be used (see art. ELECTRICITY, p. 44), and if the resistance of the battery is negligible compared with tho other resistances used, the wire with which it is wound should bo chosen so that its resistance is one-third of the resistance to be measured.
It is shown in the art. ELECTRICITY (p. 44) that, in arranging a Wheatstone's bridge to measure a given resistance, all the arms of the bridge and the battery and galvanometer should have equal resistances. As a rule, all these are not at our disposal. If the resistances of the arms and of the battery are given, and the resistance of the galvanometer (of given dimensions) is at our disposal, then the resistance of the galvanometer ought to be equal to that of the multiple arc which remains between the terminals of the galvanometer when the battery is disconnected from the bridge. This may be deduced at once from the expression given in vol. viii. p. 44.
Again, the resistance to be measured and the battery and galvanometer resistance being given, we may inquire what is the best arrangement of the arms of the bridge.
Differentiating the expression given in vol. viii. p. 44 witk respect to y and z, we get
/B(R+G).
BG-2/ 2 R =z{2^(R+G)R-G(K+B)} , BG-y z R =y{2 (R+B)R-B(B+G)} ;
R(R+B)
the solution of which is obviously
/G(R+B)
V R(R+G)'
whence we have s= */KG 'gifl' T= */KB' S^B ' AND U=^BG-determining the resistances of the disposable arms.
It appears that, when B and G are given, the resistance of the arm opposite to the resistance to be measured ought always to be the geometric mean between B and G.
In a certain class of observations a needle with large moment of
inertia is used. The methods in use are mostly due to Gauss and
Weber. For an account of these methods the reader is referred to
Maxwell, chap. xvi. He should also consult a paper by Du Bois
Eeymond in Monatsbcr. d. Berl. Acad., 1869-70. (G. CH.)



Footnotes

For another definition see the article ELECTROMETER.
For a brief history of the construction of galvanometric apparatus

This is not exactly true where there is damping : hut the rule is sufficient for ordinary purposes


See art. ELECTRICITY, p. 43.
E.g., in above case by introducing into the galvanometer circuit
_^ths, x^nrths, TVAths, respectively of the resistance of the multiplier.

3 This arrangement is that adopted by White of Glasgow in the galvanometers made by him after Sir Wm. Thomson's pattern.

This can he done most easily by means of a mirror attached to
the multiplier and adjusted so as to be parallel to the windings.

s See Maxwell, Electricity and Magnetism, vol. ii. sees. 712, 713.

See for such calculations Maxwell, vol. ii., chaps, xiv. and xv.
Or the piece to which the fibre is attached, if it is not rigidly
attached to the multiplier.

Schwendler, Phil. Mag., 1872. 5 Id., ibid., 1866.
6 Heaviside, ibid., 1873.
Or the piece to which the fibre is attached, if it is not rigidly
attached to the multiplier.
Schwendler, Phil. Mag., 1872. 5 Id., ibid., 1866.
6 Heaviside, ibid., 1873.
Or the piece to which the fibre is attached, if it is not rigidly
Or the piece to which the fibre is attached, if it is not rigidly
attached to the multiplier.




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