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192 plate, and the character of these is different according as the point is positive or negative. Figures 9 and 10 represent discharges from positive and negative points respectively.

The discharge from a negative point is in some gases very much influenced by the purity of the gas; thus Warburg found that the discharge from a negative point in nitrogen increased about fifty times by removing the last trace of oxygen from the nitrogen, though this had little or no effect upon the discharge from a posi- tive point. This can be accounted for by the discovery of Franck and Hertz that in very pure nitrogen the electron does not become a negative ion and has a very high mobility. This is true for the inert gases as well as for nitrogen, and Pryzibram has shown that the difference between the discharges from positive and negative points is exceptionally large in these gases.

Electrical Wind. The electrified ions starting from the point in a point discharge sets the gas in the neighbourhood of the point in motion producing a current of air, called the " electrical wind." The momentum gained by the air is lost by the point, so that there is a backward force acting on the point, which has often been measured. This force, as well as the electrical wind, is smaller when the point is negative than when it is positive; this difference is especially marked at pressures low enough to make the negative ion have an abnormally large mobility.

Relation between Potential Difference and Current. The po- tential difference required to maintain a discharge will depend upon the current passing in the discharge. The relation between the current and potential difference for discharge through gases is often a very complicated one. We should expect that this would be so, for in the spark discharge, for example, the potential difference is made up of the cathode fall of potential (this in- creases with the current) and a uniform force along the rest of the discharge, and this force in many cases diminishes as the current increases. Thus whether increases of current produce an in- crease or decrease in the potential difference will depend on the relative contributions of these two parts.

I

FIG. 11

C.urren*.

A curve of which the ordinates are the potential difference between the electrodes and the abscissae the current through the gas is called

the " characteristic curve " for the discharge. Suppose that the current sent through a gas by a battery of cells of electromotive force Eo is required. If R is the resistance of the curves connecting the battery with the electrodes in the gas, then E Ri is the potential difference between the electrodes in the gas, and one relation between this potential V and the current is represented by the straight line V = Eo Rt. The other relation is that represented by the char- acteristic curve; the values of the current through the gas and the potential difference between the electrodes will be determined by the points of intersection of this straight line and the character- istic curve. Unless the straight line cuts the curve there can be no discharge through the gas ; on the other hand, the straight line may cut the characteristic curve in more than one point, indicating that there is more than one type of discharge. Some of these types may, however, be unstable and thus impossible to realize. Thus, for example, if the current is increased by Si the difference of potential given by the battery between the electrodes' is diminished by R5i; if V is the potential difference between the electrodes required to send a current t through the gas, then, when the current is increased

by Si, the increase in the potential required is-j-8i; thus unless

-f-Si is less than RSi, or ( -r- + R J Si be positive, the dimin-

ished potential supplied by the battery will not be sufficient to maintain the increase in the current, this increase will stop, the current will return to its original value, and the discharge will be

stable; thus if R +-^ is positive the discharge will be stable. If,

however, R+r is negative the fall in potential required to main-

tain the increased current is so great that, in spite of the diminu- tion of the potential difference supplied by the battery, the residue is great enough to maintain the increased current, the increase in the current will continue, and the discharge will be unstable. Thus

the condition for stability is that R+-J- should be positive, a re-

sult first given by Kaufman. This result is equivalent to the con- dition that for stability the straight line must, at the point where it cuts the characteristic curve, fall more steeply than the tangent to the curve at that point. Thus if APQB is the characteristic curve, and if the straight line cuts it at PQ, the type of discharge represented by P is unstable, and that by Q stable. Keeping the electromotive force of the battery constant and increasing the resistance will make the straight line steeper, and Q will move to the left and the current through the tube will decrease; when the line gets so steep that it touches the curve at S, the minimum value of the current consistent with the maintenance of this type of dis- charge by the electromotive force supplied by the battery will be reached, and any further diminution of the current will result in the extinction of this type of discharge. It is a well-known fact that the existence of most types of luminous discharges requires the current to be above a certain critical value which depends upon the external force. The electric arc is perhaps the most familiar example of this; as the characteristic curve for the arc discharge is

a rectangular hyperbola represented by the equation

a-\ '

We can easily show that if the external electric force is E, the maxi- mum resistance which can be introduced into the circuit without extinguishing the arc is (E a) 2 /4&, and the smallest current com- patible with the existence of the arc 2&/(E a). For any stable type of discharge we see that an increase in the external electro- motive force will result in an increase of current; at a point corre- sponding to an unstable condition it produces a diminution.

Structure of the Discharge. The structure of the discharge at atmospheric pressure is on so fine a scale that its details can only be made out with difficulty; as the pressure is reduced the scale gets larger and larger, until, when the pressure is reduced to that due to a millimetre or so of mercury, the details of the structure become very conspicuous. The appearance of the discharge at

such a pressure is shown in fig. 12, and we see that it is built up of several constituents of very different types. We have already