a column of mercury at o° C. of 1 sq. mm. section and nearly 105 cm. in length. It is 1,000,000,000 (or 10") times the absolute unit. The ohm is usually designated by the symbol w.

Note.--The ohm here given (called the 'B.A' ohm) is now found to be a little too small; i.e. it is not quite 10" times the absolute unit.

(iii.) As unit of current, the ampère. This is the current given by 1 volt E.M.F. when the total resistance is 1 ohm. From Ohm's law it is clear that the ampère must be orth, the absolute

108

1099

unit of current. We have then, generally,

§ 2. Resistance Coils, and Resistance Boxes. In electrical measurements we need, as standards of reference, resistances of known magnitude; just as in chemical investigations we need to use 'weights' of known magnitude. We must therefore have at our disposal convenient multiples and sub-multiples of the ohm. Now a column of mercury is obviously a very unmanageable unit; whereas coils of wire are very convenient, and should be durable also, if carefully made. While, therefore, we can keep our mercury column as the unit to which to refer, we can for purposes of use make copies of it in wire. Coils are made some having 1 ohm resistance, others having 2, 3, 4 . . 10. . . 50 ... 100 . . . 1,000, &c., ohms resistance, and such standards of resistance are very durable and occupy but little space.

...

For the making of coils we choose some wire which fulfils as far as possible the following conditions: (i.) it should not corrode; (ii.) its resistance should not alter with time or with a moderate amount of bending; (iii.) it should not alter much with temperature; (iv.) it should not be too expensive. The wire which is best for the purpose is an alloy of copper, zinc, and nickel; or of silver and platinum.

The alteration with time, &c., can only be checked by periodic testing. As to temperature, either the coils are arranged so that they can be immersed in water at some standard temperature, or there may be used a 'correction formula' which will approximately allow for the rise in resistance with rise in temperature.

The wire is covered with an insulating material, and is wound

in a particular way, so as to obviate as far as possible induction effects; the wire being doubled on itself before winding, so that all through the coil there are equal currents in opposite directions lying side by side. When

ment in a resistance box. Into the circuit we introduce the thick brass piece T T'. This is not continuous, but is divided into portions connected by the resistance coils. The gaps, however, can be filled up by well-fitting brass plugs, and when all these plugs are in their places, there is between T and T' a continuous thick brass conductor of practically no resistance. The removal

of any plug throws into the circuit that resistance coil which in the figure lies below that plug. Hence, by a suitable removal of plugs we can throw into the circuit any resistance that is contained in the box.

The figure indicates that the coils are so wound as to obviate errors due to induction (see Chapter XXI.).

§3. Wheatstone's Rheostat.-We will now mention an instrument intended for the measurement of resistances continuously, the resistance box above described being evidently discontinuous.

Note. We may here remark that on account of certain defects of contact, &c., that appear to be inherent in the very nature of a Wheatstone's rheostat, this instrument cannot be used in any but very rough measurements.

Its chief use is as a continuously adjustable resistance, in cases where it is not desired to measure the resistance thus introduced.

A and B are two parallel cylinders, A being of brass and B of wood. A fine uniform wire can be wound from A on to B, or

FIG. i.

vice versa. The wire that is on A is in good contact with the brass of A, and thus forms one conductor with the cylinder. The wire that is on B is wound in a spiral groove cut in the wood, and is thus insulated. In the figure the wire is represented as partly on that portion of B which is nearest to the spectator, and partly on the further portion of A. One end of the wire is attached to a brass ring on

B, this brass ring being in connection with the terminal o by means of a brass spring that presses against it. The other end of the wire is attached to the far end of the brass cylinder A, and then is in connection, by means of the cylinder itself and a spring that presses against it, with the other terminal n. By turning the handled we can wind more or less of the wire on to the cylinder B where it is insulated, and so throw more or less of it into the circuit. That portion of the wire which is on A gives no appreciable resistance, being then practically part of a very thick brass conductor.

By noticing against what mark on the graduated scale (seen in the figure between the two cylinders) the wire stands, we can read off the integral number of turns of the handle d, the fractions of one turn being read from a graduated circle round which the handled turns.

We can use this instrument in two main ways.

I. Method of substitution.-In the figure, R is the rheostat ; m m' are two mercury cups between which either the unknown resistance x, or a thick

copper piece of no resistance, can be inserted; and G is a galvanometer

We first measure the deflexion a when x is in the circuit. We then replace x by a thick copper piece, and wind in a

measured length of rheostat wire of resistance / until we have the same deflexion a as before.

Then, if the E.M.F. E has remained constant, we can easily show by Ohm's law that

x = 1.

II. Method of comparison of deflexions.-Here we use a measuring galvanometer; e.g. a tangent galvanometer in which, if a be the angle of deflexion, the current-strength C is given by the relation C=k. tan a, where k is some constant. Let E be the E.M.F. of the battery, x the unknown resistance, R the resistance of rest of the circuit.

Let a be the deflexion when x is not in the circuit. Then

(i.)

Now introduce the resistance x, and let the new deflexion

Next remove x, and introduce some measured resistance, and let the new deflexion be az. Then we have

By subtracting (i.) from (ii.) and from (iii.) respectively, and by

Q

dividing the one result by the other, we finally eliminate both R

which gives us x in terms of known quantities.

Both the above methods assume that E is constant. Now E varies with time, rendering method (I.) inaccurate; and in method (II.) E varies not only with time, but with the strength of the current flowing.

The Wheatstone's bridge method, next to be described, is free from the above and other objections.

§ 4. Wheatstone's Bridge, General Principle.-Fig. i. represents diagrammatically the principle of Wheatstone's bridge.

Let the current from A to C divide into two branches ABC and A B'C; and let the resistance A B be measured by r, BC by r', A B' by s, and B' C by s'.

Then A is at one potential VA, and C at a lower potential Vc; and along both branches the potential falls from VA to Vc proportionally with the resistance. If (r+r') be great as compared with (s + s'), then the fall through A B C is gradual as compared with the 'steeper' fall through A B' C. But whatever proportion