Radio-activity/Chapter 3

by Ernest Rutherford

 

CHAPTER III.

METHODS OF MEASUREMENT.

53. Methods of Measurement. Three general methods have been employed for examination of the radiations from radio-active bodies, depending on

(1) The action of the rays on a photographic plate.

(2) The ionizing action of the rays on the surrounding gas.

(3) The fluorescence produced by the rays on a screen of platinocyanide of barium, zinc sulphide, or similar substance.

The third method is very restricted in its application, and can only be employed for intensely active substances like radium or polonium.

The photographic method has been used very widely, especially in the earlier development of the subject, but has gradually been displaced by the electrical method, as a quantitative determination of the radiations became more and more necessary. In certain directions, however, it possesses distinct advantages over the electrical method. For example, it has proved a very valuable means of investigating the curvature of the path of the rays, when deflected by a magnetic or electric field, and has allowed us to determine the constants of these rays with considerable accuracy.

On the other hand, as a general method of study of the radiations, it is open to many objections. A day's exposure is generally required to produce an appreciable darkening of the sensitive film when exposed to a weak source of radiation like uranium and thorium. It cannot, in consequence, be employed to investigate the radiations of those active products which rapidly lose their activity. Moreover, W. J. Russell has shown that the darkening of a photographic plate can be produced by many agents which do not give out rays like those of the radio-active bodies. This darkening of the plate is produced under the most varied conditions, and very special precautions are necessary when long exposures to a weak source of radiation are required.

The main objection to the photographic method, however, lies in the fact that the radiations which produce the strongest electrical effect are very weak photographically. For example, Soddy^[1] has shown that the photographic action of uranium is due almost entirely to the more penetrating rays, and that the easily absorbed rays produce in comparison very little effect. Speaking generally, the penetrating rays are the most active photographically, and, under ordinary conditions, the action on the plate is almost entirely due to them.

Most of the energy radiated from active bodies is in the form of easily absorbed rays which are comparatively inactive photographically. These rays are difficult to study by the photographic method, as the layer of black paper which, in many cases, is required in order to absorb the phosphorescent light from active substances, cuts off at the same time most of the rays under examination. These easily absorbed rays will be shown to play a far more important part in the processes occurring in radio-active bodies than the penetrating rays which are more active photographically.

The electrical method, on the other hand, offers a rapid and accurate method of quantitatively examining the radiations. It can be used as a means of measurement of all the types of radiation emitted, excluding light waves, and is capable of accurate measurement over an extremely wide range. With proper precautions it can be used to measure effects produced by radiations of extremely small intensity.

54. Electrical Methods. The electrical methods employed in studying radio-activity are all based on the property of the radiation in question of ionizing the gas, i.e. of producing positively and negatively charged carriers throughout the volume of the gas. The discussion of the application of the ionization theory of gases to measurements of radio-activity has been given in the last chapter. It has been shown there that the essential condition to be fulfilled for comparative measurements of the intensity of the radiations is that the electrical field shall in all cases be strong enough to obtain the maximum or saturation current through the gas.

The electric field required to produce practical saturation varies with the intensity of the ionization and consequently with the activity of the preparations to be examined. For preparations which have an activity not more than 500 times that of uranium, under ordinary conditions, a field of 100 volts per cm. is sufficient to produce a practical saturation current. For very active samples of radium, it is often impossible to obtain conveniently a high enough electromotive force to give even approximate saturation. Under such conditions comparative measurement can be made by measuring the current under diminished pressure of the gas, when saturation is more readily obtained.

The method to be employed in the measurement of this ionization current depends largely on the intensity of the current to be measured. If some very active radium is spread on the lower of two insulated plates as in Fig. 1, and a saturating electric field applied, the current may readily be measured by a sensitive galvanometer of high resistance. For example, a weight of ·45 gr. of radium chloride of activity 1000 times that of uranium oxide, spread over a plate of area 33 sq. cms., gave a maximum current of 1·1 × 10^{-8} amperes when the plates were 4·5 cms. apart. In this case the difference of potential to be applied to produce practical saturation was about 600 volts. Since most of the ionization is due to rays which are absorbed in passing through a few centimetres of air, the current is not much increased by widening the distance between the two plates. In cases where the current is not quite large enough for direct deflection, the current may be determined by connecting the upper insulated plate with a well insulated condenser. After charging for a definite time, say one or more minutes, the condenser is discharged through the galvanometer, and the current can readily be deduced.

55. In most cases, however, when dealing with less active substances like uranium or thorium, or with small amounts of active material, it is necessary to employ methods for measuring much smaller currents than can be detected conveniently by an ordinary galvanometer. The most convenient apparatus to employ for this purpose is one of the numerous types of quadrant electrometer or an electroscope of special design. For many observations, especially where the activity of the two substances is to be compared under constant conditions, an electroscope offers a very certain and easy method of measurement. As an example of a simple apparatus of this kind, a brief description will be given of the electroscope used by M. and Mme Curie in many of their earlier observations.

Fig. 11.

The connections are clearly seen from Fig. 11. The active material is placed on a plate laid on top of the fixed circular plate P, connected with the case of the instrument and with earth. The upper insulated plate P´ is connected with the insulated gold-leaf system LL´. S is an insulating support and L the gold-leaf.

The system is first charged to a suitable potential by means of the rod C. The rate of movement of the gold-leaf is observed by means of a microscope. In comparisons of the activity of two specimens, the time taken by the gold leaf to pass over a certain number of divisions of the micrometer scale in the eyepiece is observed. Since the capacity of the charged system is constant, the average rate of movement of the gold-leaf is directly proportional to the ionization current between P and P´, i.e. to the intensity of the radiation emitted by the active substance. Unless very active material is being examined, the difference of potential between P and P´ can easily be made sufficient to produce saturation.

When necessary, a correction can be made for the rate of leak when no active material is present. In order to avoid external disturbances, the plates PP´ and the rod C are surrounded by metal cylinders, E and F, connected with earth.

56. A modified form of the gold-leaf electroscope can be used to determine extraordinarily minute currents with accuracy, and can be employed in cases where a sensitive electrometer is unable to detect the current. A special type of electroscope has been used by Elster and Geitel, in their experiments on the natural ionization of the atmosphere. A very convenient type of electroscope to measure the current due to minute ionization of the gas is shown in Fig. 12.

Fig. 12.

This type of instrument was first used by C. T. R. Wilson^[2] in his experiments of the natural ionization of air in closed vessels. A brass cylindrical vessel is taken of about 1 litre capacity. The gold-leaf system, consisting of a narrow strip of gold-leaf L attached to a flat rod R, is insulated inside the vessel by the small sulphur bead or piece of amber S, supported from the rod P. In a dry atmosphere a clean sulphur bead or piece of amber is almost a perfect insulator. The system is charged by a light bent rod CC´ passing through an ebonite cork^[3]. The rod C is connected to one terminal of a battery of small accumulators of 200 to 300 volts. If these are absent, the system can be charged by means of a rod of sealing-wax. The charging rod CC´ is then removed from contact with the gold-leaf system. The rods P and C and the cylinder are then connected with earth.

The rate of movement of the gold-leaf is observed by a reading microscope through two holes in the cylinder, covered with thin mica. In cases where the natural ionization due to the enclosed air in the cylinder is to he measured accurately, it is advisable to enclose the supporting and charging rod and sulphur bead inside a small metal cylinder M connected to earth, so that only the charged gold-leaf system is exposed in the main volume of the air.

In an apparatus of this kind the small leakage over the sulphur bead can be eliminated almost completely by keeping the rod P charged to the average potential of the gold-leaf system during the observation. This method has been used with great success by C. T. R. Wilson (loc. cit.). Such refinements, however, are generally unnecessary, except in investigations of the natural ionization of gases at low pressures, when the conduction leak over the sulphur bead is comparable with the discharge due to the ionized gas.

57. The electric capacity C of a gold-leaf system about 4 cms. long is usually about 1 electrostatic unit. If V is the decrease of potential of the gold-leaf system in t seconds, the current i through the gas is given by

i = CV/t.

With a well cleaned brass electroscope of volume 1 litre, the fall of potential due to the natural ionization of the air was found to be about 6 volts per hour. Since the capacity of the gold-leaf system was about 1 electrostatic unit

i = 1 × 6/(3600 × 300) = 5·6 × 10^{-6} E.S. units = 1·9 × 10^{-15} amperes.

With special precautions a rate of discharge of 1/10 or even 1/100 of this amount can be measured accurately.

The number of ions produced in the gas can be calculated if the charge on an ion is known. J. J. Thomson has shown that the charge e on an ion is equal to 3·4 × 10^{-10} electrostatic units or 1·13 × 10^{-19} coulombs.

Let q = number of ions produced per second per cubic centimetre
          throughout the volume of the electroscope,

    S = volume of electroscope in cubic centimetres.

If the ionization be uniform, the saturation current i is given by i = qSe. Now for an electroscope with a volume of 1000 c.c., i was equal to about 1·9 × 10^{-15} amperes. Substituting the values given above

q = 17 ions per cubic centimetre per second.

With suitable precautions an electroscope can thus readily measure an ionization current corresponding to the production of 1 ion per cubic centimetre per second.

The great advantage of an apparatus of this kind lies in the fact that the current measured is due to the ionization inside the vessel and is not influenced by the ionization of the external air or by electrostatic disturbances^[4]. Such an apparatus is very convenient for investigating the very penetrating radiations from the radio-elements, since these rays pass readily through the walls of the electroscope. When the electroscope is placed on a lead plate 3 or 4 mms. thick, the ionization in the electroscope, due to a radio-active body placed under the lead, is due entirely to the very penetrating rays, since the other two types of rays are completely absorbed in the lead plate. If a circular opening is cut in the base of the electroscope and covered with thin aluminium of sufficient thickness to absorb the α rays, measurements of the intensity of the β rays from an active substance placed under it, can be made with ease and certainty.

58. A modified form of electroscope, which promises to be of great utility for measuring currents even more minute than those to be observed with the type of instrument already described, has recently been devised by C. T. R. Wilson^[5]. The construction of the apparatus is shown in Fig. 13.

The case consists of a rectangular brass box 4 cms. × 4 cms. × 3 cms. A narrow gold-leaf L is attached to a rod R passing through a clean sulphur cork. Opposite the gold-leaf is fixed an insulated brass plate P, placed about 1 mm. from the wall of the box. The movement of the gold-leaf is observed through two small windows by means of a microscope provided with a micrometer scale. The plate P is maintained at a constant potential (generally about 200 volts). The electrometer case is placed in an inclined position as shown in the figure, the angle of inclination and the potential of the plate being adjusted to give the desired sensitiveness. The gold-leaf is initially connected to the case, and the microscope adjusted so that the gold-leaf is seen in the centre of the scale. For a given potential of the plate, the sensitiveness depends on the angle of tilt of the case. There is a certain critical inclination below which the gold-leaf is unstable. The most sensitive position lies just above the critical angle. In a particular experiment Wilson found that with an angle of tilt of 30° and with the plate at a constant potential of 207 volts, the gold-leaf, when raised to a potential of one volt above the case, moved over 200 scale divisions of the eyepiece, 54 divisions corresponding to one millimetre.

Fig. 13.

In use, the rod R is connected with the external insulated system whose rise or fall of potential is to be measured. On account of the small capacity of the system and the large movement of the gold-leaf for a small difference of potential, the electroscope is able to measure extraordinarily minute currents. The apparatus is portable. If the plate P be connected to one pole of a dry pile the gold-leaf is stretched out towards the plate, and in this position can be carried without risk of injury. 59. Electrometers. Although the electroscope can be used with advantage in special cases, it is limited in its application. The most generally convenient apparatus for measurement of ionization currents through gases is one of the numerous types of quadrant electrometer. With the help of auxiliary capacities, the electrometer can be used to measure currents with accuracy over a wide range, and can be employed for practically every kind of measurement required in radio-activity.

The elementary theory of the symmetrical quadrant electrometer as given in the text-books is very imperfect. It is deduced that the sensibility of the electrometer—measured by the deflection of the needle for 1 volt P.D. between the quadrants—varies directly as the potential of the charged needle, provided that this potential is high compared with the P.D. between the quadrants. In most electrometers however, the sensibility rises to a maximum, and then decreases with increase of potential of the needle. For electrometers in which the needle lies close to the quadrants, this maximum sensibility is obtained for a comparatively low potential of the needle. A theory of the quadrant electrometer, accounting for this action, has been recently given by G. W. Walker^[6]. The effect appears to be due to the presence of the air space that necessarily exists between adjoining quadrants.

Fig. 14.

Suppose that it is required to measure with an electrometer the ionization current between two horizontal metal plates A and B (Fig. 14) on the lower of which some active material has been spread. If the saturation current is required, the insulated plate A is connected with one pole of a battery of sufficient E.M.F. to produce saturation, the other pole being connected to earth. The insulated plate B is connected with one pair of quadrants of the electrometer, the other pair being earthed. By means of a suitable key K, the plate B and the pair of quadrants connected with it may be either insulated or connected with earth. When a measurement is to be taken, the earth connection is broken. If the positive pole of the battery is connected with A, the plate B and the electrometer connections immediately begin to be charged positively, and the potential, if allowed, will steadily rise until it is very nearly equal to the potential of A. As soon as the potential of the electrometer system begins to rise, the electrometer needle commences to move at a uniform rate. Observations of the angular movement of the needle are made either by the telescope and scale or by the movement of the spot of light on a scale in the usual way. If the needle is damped so as to give a uniform motion over the scale, the rate of movement of the needle, i.e. the number of divisions of the scale passed over per second, may be taken as a measure of the current through the gas. The rate of movement is most simply obtained by observing with a stop-watch the time taken for the spot of light, after the motion has become steady, to pass over 100 divisions of the scale. As soon as the observation is made, the plate B is again connected with earth, and the electrometer needle returns to its original position.

In most experiments on radio-activity, only comparative measurements of saturation currents are required. If these measurements are to extend over weeks or months, as is sometimes the case, it is necessary to adopt some method of standardizing the electrometer from day to day, so as to correct for variation in its sensibility. This is done most simply by comparing the current to be measured with that due to a standard sample of uranium oxide, which is placed in a definite position in a small testing vessel, always kept in connection with the electrometer. Uranium oxide is a very constant source of radiation, and the saturation current due to it is the same from day to day. By this method of comparison accurate observations may be made on the variation of activity of a substance over long intervals of time, although the sensibility of the electrometer may vary widely between successive measurements.

60. Construction of electrometers. As the quadrant electrometer has gained the reputation of being a difficult and uncertain instrument for accurate measurements of current, it may be of value to give some particular details in regard to the best method of construction and insulation. In most of the older types of quadrant electrometers the needle system was made unnecessarily heavy. In consequence of this, if a sensibility of the order of 100 mms. deflection for 1 volt was required, it was necessary to charge the Leyden jar connected to the needle to a fairly high potential. This at once introduced difficulties, for at a high potential it is not easy to insulate the Leyden jar satisfactorily, or to charge it to the same potential from day to day. This drawback is to a large extent avoided in the White pattern of the Kelvin electrometer, which is provided with a replenisher and attracted disc for keeping the potential of the needle at a definite value. If sufficient trouble is taken in insulating and setting up this type of electrometer, it proves a very useful instrument of moderate sensibility, and will continue in good working order for a year or more without much attention.

Simpler types of electrometer of greater sensibility can however be readily constructed to give accurate results. The old type of quadrant electrometer, to be found in every laboratory, can readily be modified to prove a useful and trustworthy instrument. A light needle can be made of thin aluminium, of silvered paper or of a thin plate of mica, covered with gold-leaf to make it conducting. The aluminium wire and mirror attached should be made as light as possible. The needle should be supported either by a fine quartz fibre or a long bifilar suspension of silk. A very fine phosphor bronze wire of some length is also very satisfactory. A magnetic control is not very suitable, as it is disturbed by coils or dynamos working in the neighbourhood. In addition, the zero point of the needle is not as steady as with the quartz or bifilar suspension

When an electrometer is used to measure a current by noting the rate of movement of the needle, it is essential that the needle should be damped sufficiently to give a uniform motion of the spot of light over the scale. The damping requires fairly accurate adjustment. If it is too little, the needle has an oscillatory movement superimposed on the steady motion; if it is too great, it moves too sluggishly from rest and takes some time to attain a state of uniform motion. With a light needle, very little, if any, extra damping is required. A light platinum wire with a single loop dipping in sulphuric acid is generally sufficient for the purpose.

With light needle systems and delicate suspensions, it is only necessary to charge the needle to a potential of a few hundred volts to give a sensibility of several thousand divisions for a volt. With such low potentials, the difficulty of insulation of the condenser, with which the needle is in electrical connection, is much reduced. It is convenient to use a condenser such that the potential of the needle does not fall more than a few per cent. per day. The ordinary short glass jar partly filled with sulphuric acid is, in most cases, not easy to insulate to this extent. It is better to replace it by an ebonite (or sulphur) condenser^[7] such as is shown in Fig. 15.

Fig. 15.

A circular plate of ebonite about 1 cm. thick is turned down until it is not more than 1/2 mm. thick in the centre. Into this circular recess a brass plate B fits loosely. The ebonite plate rests on another brass plate C connected with earth. The condenser thus formed has a considerable capacity and retains a charge for a long time. In order to make connection with the needle, a small glass vessel D, partly filled with sulphuric acid, is placed on the plate B and put in connection with the needle by means of a fine platinum wire. The platinum wire from the needle dips into the acid, and serves to damp the needle. In a dry atmosphere, a condenser of this kind will not lose more than 20 per cent. of its charge in a week. If the insulation deteriorates, it can readily be made good by rubbing the edge of the ebonite A with sand-paper, or removing its surface in a lathe.

If a sufficient and steady E.M.F. is available, it is much better to keep the battery constantly connected with the needle, and to avoid the use of the condenser altogether. If a battery of small accumulators is used, their potential can be kept at a constant value, and the electrometer always has a constant sensibility.

61. A very useful electrometer of great sensibility has been devised by Dolezalek^[8]. It is of the ordinary quadrant type with a very light needle of silvered paper, spindle shaped, which lies fairly close to the quadrants. A very fine quartz suspension is employed. In consequence of the lightness of the needle and its nearness to the quadrants, it acts as its own damper. This is a great advantage, for difficulties always arise when the wire dips into sulphuric acid, on account of the thin film which collects after some time on the surface of the acid. This film obstructs the motion of the platinum wire dipping into the acid, and has to be removed at regular intervals. These instruments can readily be made to give a sensibility of several thousand divisions for a volt when the needle is charged to about one hundred volts. The sensibility of the electrometer passes through a maximum as the potential of the needle is increased. It is always advisable to charge the needle to about the value of this critical potential. The capacity of the electrometer is in general high (about 50 electrostatic units) but the increased sensibility more than compensates for this. The needle may either be charged by lightly touching it with one terminal of a battery, or it may be kept charged to a constant potential through the quartz suspension.

Dolezalek states that the fibre can be made sufficiently conducting for the purpose by dipping it into a dilute solution of calcium chloride or phosphoric acid. I have not found this method satisfactory in dry climates as in many cases the fibre practically loses its conductivity after a few days exposure to dry air.

In addition to its great sensibility, the advantage of this instrument is in the steadiness of the zero and in the self-damping.

A sensibility of 10,000 millimetre divisions per volt can be readily obtained with this electrometer, if a very fine fibre be used. The use of such high sensibilities cannot, however, be recommended except for very special experiments. The period of swing of the needle under these conditions is several minutes and the natural leak of the testing vessels employed, as well as electrostatic and other disturbances, make themselves only too manifest. If measurements of minute currents are required, an electroscope of the type described in Section 56 is much to be preferred to a very sensitive electrometer. The electroscope readings in such a case are more accurate than similar measurements made by an electrometer.

For most measurements in radio-activity, an electrometer which has a sensibility of 100 divisions per volt is very suitable, and no advantage is gained by using an electrometer of greater sensibility. If still smaller effects require to be measured, the sensibility may be increased to several thousand divisions per volt.

62. Adjustment and screening. In adjusting an electrometer, it is important to arrange that the needle shall lie symmetrically with regard to the quadrants. This is best tested by observing whether the needle is deflected on charging, the quadrants all being earthed. In most electrometers there is an adjustable quadrant, the position of which may be altered until the needle is not displaced on charging. When this condition is fulfilled, the zero reading of the electrometer remains unaltered as the needle loses its charge, and the deflection on both sides of the zero should be the same for equal and opposite quantities of electricity.

The supports of the quadrants require to be well insulated. Ebonite rods are as a rule more satisfactory for this purpose than glass. In testing for the insulation of the quadrants and the connections attached, the system is charged to give a deflection of about 200 scale divisions. If the needle does not move more than one or two divisions after standing for one minute, the insulation may be considered quite satisfactory. When a suitable desiccator is placed inside the tight-fitting electrometer case, the insulation of the quadrants should remain good for months. If the insulation of the ebonite deteriorates, it can easily be made good by removing the surface of the ebonite in a lathe.

In working with a sensitive instrument like the Dolezalek electrometer, it is essential that the electrometer and the testing apparatus should be completely enclosed in a screen of wire-gauze connected with earth, in order to avoid electrostatic disturbances. If an apparatus is to be tested at some distance from the electrometer, the wires leading to it should be insulated in metal cylinders connected with earth. The size of the insulators used at various points should be made as small as possible, in order to avoid disturbances due to their electrification. In damp climates, paraffin, amber, or sulphur insulates better than ebonite. The objection to paraffin as an insulator for sensitive electrometers lies in the difficulty of getting entirely rid of any electrification on its surface. When paraffin has been once charged, the residual charge, after diselectrifying it with a flame, continues to leak out for a long interval. All insulators should be diselectrified by means of a spirit-lamp or still better by leaving some uranium near them. Care should be taken not to touch the insulation when once diselectrified.

In accurate work it is advisable to avoid the use of gas jets or Bunsen flames in the neighbourhood of the electrometer, as the flame gases are strongly ionized and take some time to lose their conductivity. If radio-active substances are present in the room, it is necessary to enclose the wires leading to the electrometer in fairly narrow tubes, connected with earth. If this is not done, it will be found that the needle does not move at a constant rate, but rapidly approaches a steady deflection where the rate of loss of charge of the electrometer and connections, due to the ionization of the air around them, is balanced by the current to be measured. This precaution must always be taken when observations are made on the very penetrating rays from active substances. These rays readily pass through ordinary screens, and ionize the air around the electrometer and connecting wires. For this reason it is impossible to make accurate measurements of small currents in a room which is used for the preparation of radio-active material. In course of time the walls of the room become radio-active owing to the dissemination of dust and the action of the radio-active

emanations^[9]. 63. Electrometer key. For work with electrometers of high sensibility, a special key is necessary to make and break from a distance the connection of the quadrants with earth in order to avoid electrostatic disturbances at the moment the current is to be measured. The simple key shown in Fig. 16 has been found very satisfactory for this purpose. A small brass rod BM, to which a string is attached, can be moved vertically up and down in a brass tube A, which is rigidly attached to a bent metal support connected with earth. When the string is released, this rod makes contact with the mercury M, which is placed in a small metal vessel resting on a block of ebonite P. The electrometer and testing vessel are connected with the mercury. When the string is pulled, the rod BM is removed from the mercury and the earth connection of the electrometer system is broken. On release of the string, the rod BM falls and the electrometer is again earthed. By means of this key, which may be operated at any distance from the electrometer, the earth connection may be made and broken at definite intervals without any appreciable disturbance of the needle. Fig. 16. 64. Testing apparatus. The arrangement shown in Fig. 17 is very convenient for many measurements in radio-activity. Two parallel insulated metal plates A and B are placed inside a metal vessel V, provided with a side door. The plate A is connected with one terminal of a battery of small storage cells, the other pole of which is earthed; the plate B with the electrometer, and the vessel V with earth. The shaded areas in the figure indicate the position of ebonite insulators. The active material to be tested is spread uniformly in a shallow groove (about 5 cms. square and 2 mms. deep) in the brass plate A. In order to avoid breaking the battery connection every time the plate A is removed, the wire from the battery is permanently connected with the metal block N resting on the ebonite support. In this arrangement there is no

possibility of a conduction leak from the plate A to B, since the earth-connected vessel V intervenes.

Fig. 17.

An apparatus of this kind is very convenient for testing the absorption of the radiations by solid screens, as well as for making comparative studies of the activity of different bodies. Unless very active preparations of radium are employed, a battery of 300 volts is sufficient to ensure saturation when the plates are not more than 5 centimetres apart. If substances which give off a radio-active emanation are being tested, the effect of the emanation can be eliminated by passing a steady current of air from a gas bag between the plates. This removes the emanation as fast as it is produced.

If a clean plate is put in the place of A, a small movement of the electrometer needle is always observed. If there is no radio-active substance in the neighbourhood, this effect is due to the small natural ionization of the air. We can correct for this natural leak when necessary.

65. We have often to measure the activity due to the emanations of thorium or radium, or the excited activity produced by those emanations on rods or wires. A convenient apparatus for this purpose is shown in Fig. 18. The cylinder B is connected with the battery in the usual way, and the central conductor A with the electrometer. This central rod is insulated from the external cylinder by an ebonite cork, which is divided into two parts by a metal ring CC´ connected to earth. This ring acts the part of a guard-ring, and prevents any conduction leak between B and A. The ebonite is thus only required to insulate satisfactorily for the small rise of potential produced on A during the experiment. In all accurate measurements of current in radio-activity the guard-ring principle should always be used to ensure good insulation. This is easily secured when the ebonite is only required to insulate for a fraction of a volt, instead of for several hundred volts, as is the case when the guard-ring is absent.

Fig. 18.

66. For measurements of radio-activity with an electrometer, a steady source of E.M.F. of at least 300 volts is necessary. This is best obtained by a battery of small cells simply made by immersing strips of lead in dilute sulphuric acid, or by a battery of small accumulators of the usual construction. Small accumulators of capacity about one-half ampere-hour can now be obtained at a moderate price, and are more constant and require less attention than simple lead cells.

In order to measure currents over a wide range, a graduated series of capacities is required. The capacity of an electrometer and testing apparatus is usually about 50 electrostatic units or ·000056 microfarads. Subdivided condensers of mica are constructed in which capacities varying from ·001 to ·2 microfarads are provided. With such a condenser, another extra capacity is required to bridge over the gap between the capacity of the electrometer and the lowest capacity of the condenser. This capacity of value about 200 electrostatic units can readily be made by using parallel plates or still better concentric cylinders. With this series of capacities, currents may be measured between 3 × 10^{-14} and 3 × 10^{-8} amperes—a range of over one million. Still larger currents can be measured if the sensibility of the electrometer is reduced, or if larger capacities are available.

In a room devoted to electrometer measurements of radio-activity, it is desirable to have no radio-active matter present except that to be tested. The room should also be as free from dust as possible. The presence of a large quantity of dust in the air (see section 31) is a very disturbing factor in all radio-active measurements. A larger E.M.F. is required to produce saturation on account of the diffusion of the ions to the dust particles. The presence of dust in the air also leads to uncertainty in the distribution of excited activity in an electric field (see section 181).

67. Measurement of Current. In order to determine the current in the electrometer circuit by measuring the rate of movement of the needle, it is necessary to know both the capacity of the circuit and the sensibility of the electrometer.

Let C = capacity of electrometer and its connections in E.S. units,
    d = number of divisions of the scale passed over per second,
    D = sensibility of the electrometer measured in scale divisions
                for 1 volt P.D. between the quadrants.

The current i is given by the product of the capacity of the system and the rate of rise of potential.

Thus i = Cd/(300D) E.S. units,
= Cd/(9 × 10^{11}D) amperes.

Suppose, for example,

C = 50, d = 5, D = 1000;
then i = 2·8 × 10^{-13} amperes.

Since the electrometer can readily measure a current corresponding to a movement of half a scale division per second, we see that an electrometer can measure a current of 3 × 10^{-14} amperes, which is considerably below the range of the most sensitive galvanometer.

The capacity of the electrometer itself must not be considered as equal to that of the pair of quadrants and the needle when in a position of rest. The actual capacity is very much larger than this, on account of the motion of the charged needle. Suppose, for example, that the needle is charged to a high negative potential, and kept at the zero position by an external constraint. If a quantity Q of positive electricity is given to the electrometer and its connections, the whole system is raised to a potential V, such that Q = CV, where C is the capacity of the system. When however the needle is allowed to move, it is attracted into the charged pair of quadrants. This corresponds to the introduction of a negatively charged body between the quadrants, and in consequence the potential of the system is lowered to V´. The actual capacity C´ of the system when the needle moves is thus greater than C, and is given by

C´V´ = CV.

Thus the capacity of the electrometer is not a constant, but depends on the potential of the needle, i.e. on the sensibility of the electrometer.

An interesting result of practical importance follows from the variation of the capacity of the electrometer with the potential of the needle. If the external capacity attached to the electrometer is small compared with that of the electrometer itself, the rate of movement of the needle for a constant current is, in some cases, independent of the sensibility. An electrometer may be used for several days or even weeks to give nearly equal deflections for a constant current, without recharging the needle, although its potential has been steadily falling during the interval. In such a case the decrease in sensibility is nearly proportional to the decrease in capacity of the electrometer, so that the deflection for a given current is only slightly altered. The theory of this action has been given by J. J. Thomson^[10].

68. The capacity of the electrometer and its connections cannot be measured by any of the commutator methods used for the determination of small capacities, for in such cases the needle does not move, and the capacity measured is not that of the electrometer system when in actual use. The value of the capacity may, however, be determined by the method of mixtures.

Let C = capacity of electrometer and connections,
    C_{1} = capacity of a standard condenser.

The electrometer and its connections are charged to a potential V_{1} by a battery, and the deflection d_{1} of the needle is noted. By means of an insulated key, the capacity of the standard condenser is added in parallel with the electrometer system. Let V_{2} be the potential of the system, and d_{2} the new deflection.

Then CV_{1} = (C + C_{1}) V_{2},
(C + C_{1})/C = V_{1}/V_{2} = d_{1}/d_{2},

and C = C_{1} d_{2}/(d_{1} - d_{2}).

Fig. 19.

A simple standard capacity for this purpose can be constructed of two concentric brass tubes the diameters of which can be accurately measured. The external cylinder D (Fig. 19) is mounted on a wooden base, which is covered with a sheet of metal or tin-foil connected to earth. The tube C is supported centrally on ebonite rods at each end. The capacity is given approximately by the formula

C = l/(2 log_{e}(b/a)),

where b is the internal diameter of D, a the external diameter of C,

and l the length of the tubes.

The following method can be used in some cases with advantage. While a testing vessel is in connection with the electrometer, a sample of uranium is placed on the lower plate A. Let d_{2} and d_{1} be the number of divisions passed over per second by the needle with and without the standard capacity in connection.

Then (C + C_{1})/C = d_{1}/d_{2},
and C = C_{1} d_{2}/(d_{1} - d_{2}).

This method has the advantage that the relative capacities are expressed in terms of the motion of the needle under the actual conditions of measurement.

69. Steady deflection method. The methods of measurement previously described depend upon the rate of angular movement of a suspended gold-leaf or of an electrometer needle. The galvanometer can only be employed for measurements with intensely active matter. A need, however, has long been felt for a method in which ordinary ionization currents can be measured by means of a steady deflection of an electrometer needle. This is especially the case, where measurements have to be made with active substances whose activity alters rapidly in the course of a few minutes.

This can obviously be secured if the electrometer system (one pair of quadrants being earthed) is connected to earth through a suitable high resistance. A steady deflection of the electrometer needle will be obtained when the rate of supply of electricity to the electrometer system is balanced by the loss due to conduction through the resistance. If the high resistance obeys Ohm's law, the deflection should be proportional to the ionization current to be measured.

A simple calculation shows that the resistance required is very great. Suppose, for example, that a current is to be measured corresponding to a rate of movement of the needle of 5 divisions per second, with a sensibility of 1000 divisions per volt, and where the capacity of the electrometer system is 50 electrostatic units. This current is equal to 2·8 × 10^{-13} amperes. If a steady deflection of 10 divisions is required, which corresponds to a rise of potential of the system of 1/100 of a volt, the resistance should be 36,000 megohms. For a deflection of 100 divisions, the resistance should be 10 times as large. Dr Bronson^[11], working in the laboratory of the writer, has recently made some experiments in order to devise a practical method for measurements of this character. It is difficult to obtain sufficiently high and constant resistances to answer the purpose. Tubes of xylol had too great a resistance, while special carbon resistances were not sufficiently constant. The difficulty was finally got over by the use of what may be called an "air resistance." The arrangement of the experiment is shown in Fig. 20.

Fig. 20.

The electrometer system was connected with the upper of two insulated parallel plates AB, on the lower of which was spread a layer of a very active substance. An active bismuth plate, coated with radio-tellurium, which had been obtained from Sthamer of Hamburg, proved very convenient for this purpose.

The lower plate B was connected to earth. The charge communicated to the upper plate of the testing vessel CD and the electrometer system leaked away in consequence of the strong ionization between the plates AB, and a steady deflection was obtained when the rate of supply was equal to the rate of discharge.

This air resistance obeyed Ohm's law over a considerable range, i.e. the steady deflection was proportional to the current. It is advisable, in such an arrangement, to test whether the deflection is proportional to the ionization current over the range required for measurement. This can readily be done by the use of a number of metal vessels filled with a constant radio-active substance like uranium oxide. The effect of these, when placed in the testing vessel, can be tested separately and in groups, and in this way the scale can be calibrated accurately.

The plates AB were placed inside a closed vessel to avoid air currents. The contact difference of potential between the plates AB, which shows itself by a steady deflection when no radio-active matter is present in CD, was for the most part eliminated by covering the surface of the plates A and B with very thin aluminium foil.

This method proved very accurate and convenient for measurement of rapid changes in activity, and possesses many advantages over the ordinary rate-method of use of an electrometer. A thin layer of radium of moderate activity would probably serve in place of the radio-tellurium, but the emanation and the [Greek: beta] and [Greek: gamma] rays emitted from it would be a possible source of disturbance to the measurements. The deflection of the electrometer needle in this arrangement is independent of the capacity of the electrometer system, and thus comparative measurements of current can be made without the necessity of determining the capacity in each case.

70. Quartz piezo-electrique. In measurements of the strength of currents by electrometers, it is always necessary to determine the sensibility of the instrument and the capacity of the electrometer and the apparatus attached thereto. By means of the quartz piezo-electrique devised by the brothers MM. J. and P. Curie^[12], measurements of the current can be made with rapidity and accuracy over a wide range. These measurements are quite independent of the capacity of the electrometer and external circuit. The essential part of this instrument consists of a plate of quartz which is cut in a special manner. When this plate is placed under tension, there is a liberation of electricity equal in amount but opposite in sign on the two sides of the plate. The plate of quartz AB (Fig. 21) is hung vertically and weights are added to the lower end. The plate is cut so that the optic axis of the crystal is horizontal and at right angles to the plane of the paper.

Fig. 21.

The two faces A and B are normal to one of the binary axes (or electrical axes) of the crystal. The tension must be applied in a direction normal to the optic and electric axes. The two faces A and B are silvered, but the main portion of the plate is electrically insulated by removing a narrow strip of the silvering near the upper and lower ends of the plate. One side of the plate is connected with the electrometer and with the conductor, the rate of leak of which is to be measured. The quantity of electricity set free on one face of the plate is accurately given by

Q = 063(L/b)F,

where L is the length of the insulated portion of the plate, b the

thickness AB, and F the weight attached in kilogrammes. Q is then given in electrostatic units.

Suppose, for example, that it is required to measure the current between the plates CD (Fig. 21) due to some radio-active material on the plate C, for a given difference of potential between C and D. At a given instant the connection of the quadrants of the electrometer with the earth is broken. The weight is attached to the quartz plate, and is held in the hand so as to apply the tension gradually. This causes a release of electricity opposite in sign to that given to the plate D. The electrometer needle is kept at the position of rest as nearly as possible by adjusting the tension by hand. The tension being fully applied, the moment the needle commences to move steadily from zero is noted. The current between the plates CD is then given by Q/t where t is the time of the observation. The value of Q is known from the weight attached.

In this method the electrometer is only used as a detector to show that the system is kept at zero potential. No knowledge of the capacity of the insulated system is required. With practice, measurements of the current can be made in this way with rapidity and certainty.

1. Soddy, Trans. Chem. Soc. Vol. 81, p. 860, 1902.
2. Wilson, Proc. Roy. Soc. Vol. 68, p. 152, 1901.
3. If the apparatus is required to be air-tight, the gold-leaf system can be charged by means of a piece of magnetized steel wire, which is made to touch the rod R by the approach of a magnet.
4. It is sometimes observed that the motion of the gold-leaf, immediately after charging, is irregular. In many cases, this can be traced to air currents set up in the electroscope in consequence of unsymmetrical heating by the source of light used for illumination.
5. Wilson, Proc. Camb. Phil. Soc. Vol. 12, Part II. 1903.
6. Walker, Phil. Mag. Aug. 1903.
7. Strutt, Phil. Trans. A, p. 507, 1901.
8. Dolezalek, Instrumentenkunde, p. 345, Dec. 1901.
9. It is very desirable that care should be taken not to release large quantities of the radium emanation inside a laboratory. This emanation has a slow rate of decay and is carried by currents of air throughout the whole building and finally leaves behind an active deposit of very slow rate of change (see chapter XI.). Eve (Nature, March 16, 1905) has drawn attention to the difficulty of making refined radio-active measurements under such conditions.
10. J. J. Thomson, Phil. Mag. 46, p. 537, 1898.
11. Bronson, Amer. Journ. Science, Feb. 1905.
12. J. and P. Curie, C. R. 91, pp. 38 and 294, 1880. See also Friedel and J. Curie, C. R. 96, pp. 1262 and 1389, 1883, and Lord Kelvin, Phil. Mag. 36, pp. 331, 342, 384, 414, 453, 1893.