Page:Encyclopædia Britannica, Ninth Edition, v. 10.djvu/63

standard coils, the centre of its multiplier being near the centre of the whole arrangement, and the axes of all the c0Ils comeIdent. A multiple arc is then (I -b i'oI'IIIed, one branch of which contains the / coils and the other /“ the galvanometcr, so that the magnetic actions oppose each other. The resist- anccs ot' the two branches are then adjusted till the galvanometer needle gives no indication when a current is sent through the multiple are. The whole arrangement will be understood from fig. 8. lf 1: and S bc,thc resistances in the branches containing the galvanometer and coils respectively, then the constant of the galvanomcter is to that of the coils as It: S; so that when the latter is calculated^[1] the former is known.

Fig. 8.

The constant of the galvanonietcr G being known, the value of a. current producing a dellcxion 9 is given in absolute measure by

$\textstyle \mathrm {I} ={\frac {\mathrm {H} }{\mathrm {G} }}\tan \theta$,

H being the. horizontal component of the earth’s magnetic force.

In many cases it is necessary to correct for the torsion of the sus- pending iibre. The value of this correction is easily found by turning the multiplier^[2] through 90° either way, and observing how far the needle follows it. The reader will find all necessary details in Maxwell, vol. ii., secs. 4:32, 742.

In all cases where 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 0 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 galvanometcr. If the object simply is to calibrate the galvanomcter without reducing its indications to absolute measure, the standard coils may be replaced by a‘ single coil of sullicient 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 resistance of the galvanomctcr, and they can be rapidly inter- changed. By adjustingf the ratio of the currents in the branches of the multiple are Inay be varied as we please, and by varying c the current in one of the branches can always be brought to a standard strength, say that which produces unit deflcxion 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.

Fig. 9.

On 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 Varlcy’s construction are used.

When a current is to be detected which produces a very small or quite insensible permanent dctlexion,the following proecss, called the method of multiplication, is sometimes used. The eriod of oscilla- tion of the needle is first found; then, the needle Teing 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 intermittcd 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 ol'the current is equal to that wasted by the damping of the needle.

It is obvious that this process is more ctl'ective 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^[3]are bv far the most convenient; the dead-beat arrangement is essential for rapid work.

If a ditl'erential galvanometer of given dimensions be used (see art. Electricity, p. 44), and if the resistance of the battery is negligible Compared with the other resistances used, the wire with which it is wound should be chosen so that its resistance is one- third of the resistance to be measured.^[4]

It is shown in the art. Electricity (p. 44) that, in arranging a \Vheatstonc’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 battory are given, and the resist- ance of the galvanomcter (of given dimensions) is at our disposal, then the resistance of the galvanometer ought to be equal to that of the multiple are which remains between the terminals of the galvanomcter when the battery is disconnected from the bridge.^[5]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 galva- nometer 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. 41 with respect to 3/ and x, we get

$\textstyle \mathrm {B} \mathrm {G} -y^{2}x^{2}\mathrm {R} ^{2}=x\left\lbrace y^{2}\left(\mathrm {R} +\mathrm {G} \right)\mathrm {R} -\mathrm {G} \left(\mathrm {R} +\mathrm {G} \right)\right\rbrace$,
$\textstyle \mathrm {B} \mathrm {G} -y^{2}x^{2}\mathrm {R} ^{2}=y\left\lbrace x^{2}\left(\mathrm {R} +\mathrm {B} \right)\mathrm {R} -\mathrm {B} \left(\mathrm {R} +\mathrm {G} \right)\right\rbrace$

the solution of which is obviously

$\textstyle y={\sqrt {\frac {\mathrm {G} \left(\mathrm {R} +\mathrm {B} \right)}{\mathrm {R} \left(\mathrm {R} +\mathrm {G} \right)}}}$

$\textstyle x={\sqrt {\frac {\mathrm {B} \left(\mathrm {R} +\mathrm {G} \right)}{\mathrm {R} \left(\mathrm {R} +\mathrm {B} \right)}}}$

whence we have $\textstyle S={\sqrt {\mathrm {R} \mathrm {G} {\frac {\mathrm {R} +\mathrm {B} }{\mathrm {R} +\mathrm {G} }}}}$ $\textstyle T={\sqrt {\mathrm {R} \mathrm {B} {\frac {\mathrm {R} +\mathrm {G} }{\mathrm {R} +\mathrm {B} }}}}$ and $\textstyle U={\sqrt {\mathrm {B} \mathrm {G} }}$ 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 17: and G.^[6]

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 lleymond in .llonatsbcr. d. Bert. Acad., 1869—70.

(g. ch.)

G A L V E S T O N^[7]

Copyright, 1879, by A. & C. Black.

GALVESTON, a city and port of entry on the coast of Texas, United States of North America, situated about 340 miles to the westward of the mouth of the South Pass of the Mississippi River, on the south side of the entrance into Galveston Bay, in 29° 18′ N. lat. and 94° 47′ long. west from Greenwich. It is the principal port and the largest city in the State, is the seat of justice of Galveston County, and is located on the inner shore of Galveston Island, about 2 miles from its most north-easterly point, known as Fort Point. The city therefore faces the main Texas shore, being separated from it by West Bay, lying between the island and the mainland. The principal portion of the county lies on the mainland fronting the two bays above named, its general surface, like that of the island, being low and level, and the soil sandy.

Galveston Island is a low sandy island, about 28 miles long and 1$\scriptstyle {\frac {1}{2}}$ to 3$\scriptstyle {\frac {1}{2}}$ miles wide, stretching along the coast of Texas in a north-easterly and south-westerly direction, and forming the gulf coast-line throughout its entire length.

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1. See for such calbuljdi—onshlaxwell, vol. ii., chaps. xiv. and xv.
2. Or the piece to which the fibre is attached, if it is not rigidly attached to the multiplier.
3. See Sir W. Thomson on resistance measurement, Proc. R. S., 1862, p. 313.
4. Schwendler, Phil. JIag., 1872.
5. 2‘bid., 1866.
6. Heaviside, ibid., 1873.
7. This is reprinted here from the work entitled Galveston, by Maj.-Gen. Q. A. Gillmore, U. S. Engineers. New York, Charles Scribner’s Sons, 1879. Copyright, 1879, by A. & C. Black.