This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 129.100.58.76

This content was downloaded on 11/11/2014 at 20:52

Please note that terms and conditions apply.

A capacitance-resistance hygrometer

View the table of contents for this issue, or go to the journal homepage for more

1955 J. Sci. Instrum. 32 425

(http://iopscience.iop.org/0950-7671/32/11/305)

Home Search Collections Journals About Contact us My IOPscience

A capacitance-resistance hygrometer By C. L. CUTTING, B.Sc., Ph.D., and A. C. JASON, B.Sc., Ph.D., Torry Research Station, Department of Scientific

and Industrial Research, and J. L. WOOD, M.A., Ph.D., Sir John Cass College, London, E.C.3

[Paper first received 13 April, and in final form 23 July, 19551

A new type of hygrometer is described. Indications of relative humidity are given by changes of the electrical properties of anodized aluminium oxide layers. The calibration is independent of temperature from 0 to 80” C, and of the air speed. The instrument is extremely sensitive, and may be easily adapted for continuous recording and control. A theory accounting for the

observations is outlined.

The need for a simple, stable hygrometer which is capable of indicating and recording relative humidity over a wide range of conditions has long been recognized. Most indirect instruments suffer from such disadvantages as hysteresis, long-period drift, large temperature coefficients, or high sensitivity to contamination. Although absolute methods, e.g. chemical or dew-point determinations avoid these defects, they are not suitable for continuous recording or instrumen- tation. For this it is desirable that the indication of humidity be presented directly in the form of an electrical parameter without the need for complex ancillary equipment. Two further desirable features for successful instrumentation are that the speed of response be rapid, and that no temperature measurement be required additionally.

It is believed that the instrument described in this paper possesses a number of these advantages, which are not found together in other hygrometers. Although the capacitance- resistance hygrometer was originally developed to study various problems involved in the processing and preservation of fish, it was considered to have wider application. For this reason a detailed investigation was undertaken.

The hygrometer consists essentially of a condenser having as dielectric a porous film of alumina. It behaves as an electrical transducer responding to changes of relative humidity by variation of its capacitance and resistance.

G E N E R A L P R I N C I P L E S

Porous oxide layers formed on aluminium by anodization in acid electrolytes provide, by virtue of their structure, a large surface area for adsorption. Isotherms for the adsorption of water on to these layers are similar in form to those cited for bulk powdered alumina by Taylor(’) and Gregg,@) and follow a Brunauer, Emmett and Teller equation.(3)

In general it is to be expected that the capacitance of a condenser formed between two conducting layers would vary with the adsorption of water vapour into the dielectric. The resulting changes in capacitance, most simply calculated on an additive(4) basis, would however be relatively small. Even at saturation, the quantity of water contained in the layer could not thus give rise to a dielectric constant greatly exceeding 20.

In fact, on approaching saturation, the apparent dielectric constants of such porous films are observed often to exceed 10oO. Indeed on occasion capacitances indicating dielectric constants greater than SO00 have been observed.

A theory has been put forward to explain these observations and is briefly outlined following the sections describing the principal features of this anomalous behaviour.

C O N S T R U C T I O N OF H U M I D I T Y S E N S I T I V E E L E M E N T

Any method of anodizing which yields porous aluminium oxide layers will produce humidity sensitive elements, but, for reasons which will be given, sulphuric acid is to be pre- ferred as electrolyte. The temperature, the concentration of the acid, the current density and the anodizing time may each be varied widely so that, depending on the selection of these variables, a great variety of thicknesses and structures can be produced.(’-*) In the examples given the oxide layers were formed as follows, unless otherwise stated:

material:

electrolyte: temperature: 30” C; current densify: various values from 10 to 120 mA/cm2 were

used; modiring time: 30 gin; cathode:

aluminium rod, 0.158 cm diameter 99.5 %

sulphuric acid 17.5% per volume; pure ;

stainless steel, lead or aluminium.

The thicknesses of the films thus formed are 0.62 f 0.02 microns per milliammeter per square centimetre (obtained by micrometer measurement before and after chsmically removing the oxide).

Observations of the characteristics of elements formed on aluminium rod of 99.998% punty and on high-duty aluminium-alloy wire show that there is no critical dependence on the purity of the aluminiuii.

Rods may be anodized either singly or in groups. Great care should be taken to degrease them in an organic solvent beforehand. After removal from the electrolyte, the rods are thoroughly washed and then allowed to soak for several hours in distilled water. Details of the succeeding stages in the construction are shown in Fig. 1. The untreated alumin- ium surface of each rod A is insulated with “capping solution” B which is made to overlap the oxide surface G for about 3 mm. A thin layer of a porous conducting material G is deposited on the oxide and extended over the insulation so that electrical connexion may be made to it by winding a few turns of fine copper wire D round the overlap. These turns are coated with a thick layer of Aquadag E and, after this has dried, the connexion is secured with a little Perspex cement F. The element is then in the form of a robust “probe” which can be handled without fear of breaking the connexion to the outer conducting layer. This layer is most conveniently formed by painting on to the oxide a thin coating of Aquadag which has been diluted three or four times with distilled water. However, provided that the

VOL. 32, NOVEMBER 1955 4*

425 JOURNAL OF SCIENTIFIC INSTRUMENTS

C. L. Cutting, A. C. conducting layer is porous, it may consist of chemically deposited silver or, preferably, of an evaporated metallic film.

An element need not take the precise form described and may be of any shape or size as long as the resistance of the conducting layer is low. (For example, an element may be constructed of a 30 s.w.g. aluminium alloy wire, the sensitive

A

'D

Fig. 1. Construction of hygrometer

portion having an area of less than 1 mm2.) Whatever the form of construction, it is essential that the connexion to the conducting layer be made as described; otherwise if connexion is made by contact over the oxide surface itself, water vapour becomes trapped at high humidities and this leads to slow response and apparent hysteresis. It is advisable not to extend the conducting layer to those parts of the anodized surface formed on sharp edges in order to reduce the vulnerability to mechanical damage.

C A L I B R A T I O N

(i) Vapour pressure and temperature control. Any of the well-known methods for calibrating hygrometerdg) may be used, at room temperature. For the purpose of providing a steady stream of air containing water vapour at any desired vapour pressure and temperature, an open-circuit, two- temperature method(lO) is convenient. An arrangement of this method which is suitable for calibrating probes is shown in Fig. 2. Air is fed into a saturator A , containing filter paper B dipping into a pool of distilled water C. This is surrounded by a jacket D through which water circulates at a temperature f l indicated by a thermometer E. The water bath is main- tained at a temperature tZ(>tl) by the contact thermometer F operating a heater G through a suitable relay. H is a stirrer motor. Air, saturated at temperature f,, is conducted through a serpentine tube J to tubes K containing elements L. These are supported by tightly fitting corks in holders M sealed into the system inside tubes N by standard taper glass joints 0 a:?d mercury P. The relative humidity in the tubes L is given by the ratio of the saturated vapour pressures at tl and t2. The serpentine tube is introduced between the saturator and the elements to ensure temperature equilibration of the air stream. The elements are held entirely beneath the surface level of the water so that their temperature is equal to that of the bath. The anodized areas are situated well down in the tubes K, where they are continuously swept by a flow of vapour.

In principle, almost any alternating current bridge method involving phase

(ii) Capacitance and resistance nieasrrrmrents.

Jason and J. L. Wood

and the series resistance method, both described by Hague,(") were used. In both arrangements the balance is independent of frequency. Small inaccuracies resulting from stray capacitances and self capacitances of the bridge components are negligible compared to the increases of capacitance to be measured. Lead capacities are normally negligible but it is sometimes necessary to apply a correction when remote measurements involve lengthy leads.

Except in the section dealing with frequency effects, all bridge measurements given were obtained at 1000 cis.

Fig. 2. Open-circuit, two-temperature method for calibrating hygrometers

E F F E C T S O F W A T E R V A P O U R O N C A P A C I T A N C E A S D R E S I S T A K C E

balance may be employed. The parallel resistance method, JOURNAL OF SCIENTIFIC INSTRUMENTS 426

Fig. 3 provides an illustration of typical measurements of the equivalent parallel capacitance C,, and resistance Rp, of an element at various relative humidities. The readings were all made at a constant temperature t2 of 30" C.

The form of the dependence of Cp and Rp on relative humidity is determined primarily by the conditions employed in anodizing and the frequency at which measurements are made, and accord with the predicted theoretical behaviour discussed below.

In Fig. 3 the points plotted for increasing humidity (ringed) and decreasing humidity (unringed), between 0 and 90% relative humidity, show that any effects due to hysteresis in the sorption of water by the oxide film are less than those due to the scatter of the points themselves. The measure- ments were made at periods from 10min to 12h after the change of relative humidity. However, if 90% r.h. was exceeded for more than about 10min hysteresis in the

VOL. 32, NOVEMBER 1955

A capacitance-resistance hygrometer

direction of increased capacity was observed on decreasing the humidity. The adsorption of water by alumina also shows a considerable positive hysteresis at high humidities. It is therefore not surprising that the hygrometer characteristics reflect this effect to a certain degree.

I( humidity increasinq B o humidity decreabinq

\ y. / ,.

2

Relative humidity p td) Fig. 3. Variation of equivalent parallel capacity and

resistance with relative humidity

- 4days x 29 53

0 128

Relatlve humidity p ( X ) (a) (b)

105,

loz*oo Io'' 2 0 ' b:O ' IO0 Relative humidlty p (%) Rclatwe humidi ty p (%)

( c ) (4 Fig. 4. The effect of aging on the capacitance isotherms of elements anodized in various electrolytes. Capacitance

measured by ballistic method at 100 s-'

(a) Initial effect for an element anodized in sulphuric acid. (6, c, d) Long-term effects for an element anodized in chromic,

oxalic and sulphuric acids.

A G E I N G A N D R E P R O D U C I B I L I T Y

In the few months immediately after formation, ageins occurs which results in a reduction of Cp and an incrsase ir Rp at any given humidity. These effects are initially ver) rapid, but the rate of change soon becomes small, and aftei some time (see Fig. 4) the isotherms do not change further. This figure shows the effect of ageing on the capacity oi elements formed in various electrolytes. When there is nc further change with time, only those formed in sulphuric acid are sensitive over a wide range of relative humidity. This is the reason for preferring sulphuric acid for the electrolyte in anodization.

It should be noted that the capacitances presented in Fig. 4 were obtained ballistically by the repeated charging and dis- charging of the condenser.

When a number of elements are prepared by anodizing the batch simultaneously, their capacitance characteristics are comparable. Thus for such a group of five samples, the indication of relative humidity showed a standard deviation from the mean calibration of 3.4% over the entire range from 0 to 90% r.h.

I N F L U E N C E O F T E M P E R A T U R E

A typical example of the influence of temperature on the capacitance and resistance characteristics of an element is illustrated in Figs. 5 and 6. The most important feature

4 0 I ? " ' ' ( 60 80 100

Fig.

Relative humidity p

5. Influence of temperature on the capacity characteristics of an element

material: element No. 19011; pure aluminium rod. electrolyte: sulphuric acide 17.5% per volume. temperature: 40' C. current density: 120 mA/cm*. anodizing time: 30 min. anodized area: 0.61 cm2.

revealed in these figures is that, in the range of temperature investigated (20-80' C), capacity and resistance are each functions of relative humidity rather than of vapour pressure. Although the scatter is here rather greater than in Fig. 3, there are no systematic variations with temperature.

As a consequence of the theory discussed later, i t was anticipated that at temperatures below 0' C, a marked change in the characteristics would be found. For this reason, the investigation of the effect of temperature was at a later date extended to the sub-freezing point range. Figs. 7 and S show that the characteristics remain substantially

VOL. 32, NOVEMBER 1955 427 JOURXAL OF SCIENTIFIC Ih'STRUMENTS

C. L. Cutting, A. C. Jason and J. L. Wood

constant down to a temperature of -15" C, but that a sharp change in these curves occurs before -30" C is reached.

At temperatures above 100" C the elements still show sensitivity to changes in relative humidity; even at 400" C

0 L

Id ' 20 ' 40 ' 60 ' so ' IO0 Relative humidity p (46)

Fig. 6. Influence of temperature on the resistance characteristics of an element. (Conditions identical with

those for Fig. 5 )

105r

I 0 -30

'0'6 20 40 bo i o IO0 Relative humidity p (%)

Fig. 7. Variation of capacitance with relative humidity at lower temperatures

both capacitance and resistance are found to vary with the relative humidity. However, it appears probable that exposure of elements to these higher temperatures causes irreversible changes in the room temperature characteristics.

T R A N S I E N T R E S P O N S E

The response of the capacitance of a typical element to rapid changes in the relative humidity is presented in Fig. 9. The times indicate the period elapsed after transference from the first relative humidity shown, to the second. These humidities were provided by constant humidity bottles. Measurements, made by the ballistic method (repetition rate ~ W S - : ) , are given in terms of galvanometer current. Analysis of the kinetics of surface adsorption(12) shows that

water molecules are usually rapidly sorbed on to surfaces, and the mean time taken to penetrate into the pores of an aluminium oxide film is probably less than a second. This is

Fig. 8.

1 , 0 2 0 4 0 6 0 0 0 100

Relative humidity p &)

Variation of resistance with relative at lower temperatures

humidity

compatible with the short response time of the elements shown in Fig. 9 and with the assumption made in the theory that the effects described are dependent on the surface conduction along the pore sides.

Time (I)

Fig. 9. Response characteristics of an element anodized in sulphuric acid

T H E O R Y

The principal requirement of any theoretical treatment is to account for the remarkably large variation of the capaci- tance of the porous oxide layers as the humidity increases

JOURNAL OF SCIENTIFIC INSTRUMENTS 428 VOL. 32, NOVEMBER 1955

A capacitance-resistance hygrometer

toward saturation. The dielectric constant, based on the distance d between the two conductors (Fig. lo), together with the area and measured capacitance, may rise to a value of more than 1000 (see earlier section on general principles). Such a large value could not be accounted for by any geo- metrical disposition of the adsorbed water, nor by any reasonable modification of the dipoles of the adsorbed water

Fig. 10. Pore structure

molecules. An explanation is however provided by the observation that the capacitances of porous oxide layers measured in situ in the anodizing bath are very high. The electrolyte penetrates the pores, so that this outer conductor then follows the contours of the oxide surface. Between the base of each pore and the metal there is a very thin layer of alumina (b N 120A). The contribution of these pore bases to the capacitance is therefore large. A calculation may be simply made by considering the pores to be cylindrical. Estimating from electron micrographs that the cross-sectional area s at the base be 10% of the superficial area, the capacitance of the pore bases in a 3 cm long rod sample is 53 OOO pF. This figure is based on a dielectric constant of 12.0 for alumina.

With oxide layers mounted as described in an earlier section, the capacitances observed at relative humidities approaching saturation are of this magnitude. This suggests that as the humidity increases, water is progressively adsorbed on the walls of the pores. The resistance RI down the walls decreases, becoming very small at saturation. The observed

ourer conducfor I

l j _

metal

Fig. 11. Equivalent circuit of a single pore

capacitance thus changes from that of a condenser, distance d between plates (CO N 400 pF) when dry, to that of a condenser with the outer conductor following the oxide surface (C, N 53 000 pF) at saturation.

The observed characteristics may be quantitatively accounted for on this basis. The equivalent circuit of the porous layer based on this model is shown in Fig. 11. In addition to R,, CO and C,, as above, R2 is the leakage resis- tance through the pore base. The leakage through the entire thichess d of the oxide is negligible at the frequencies used in the measurements. The equivalent parallel capacitance and resistance of a pore are then

For the entire layer two formally identical equations result, the symbols then referring to the oxide layer as a whole. It is now assumed that the variation of R, and C, with relative humidity is negligible compared with that of RI. E it were possible to measure RI directly at each relative humidity, the isotherms for R, versus relative humidity and for Cp versus relative humidity could be predicted. However, as this is not possible, RI is obtained from the measured value of Rp [equation (2 ) ] , at each relative humidity, and from these the capacity isotherm calculated. An example is shown in Fig. 12. For comparison, C,, the capacity which would be

4 0 -

h U Q

m Q 30- 4

0 V

0 !2 20- c ,. - U 0 a

s 10-

a=observed o =calculated

Fig. 12. Calculated and observed values of Cp obtained from measured values of Rp

C2 = 40 x 1OjpF. Rr = 2530 R.

expected in the absence of the pore effect, is shown on the same scale.

SOME C O N S E Q U E N C E S O F T H E T H E O R Y A N D T H E I R E X P E R I M E N T A L V E R I F I C A T I O N

It will be noticed that the sensitivity of C, to changes in humidity is greatest at intermediate relative humidities. The theory above suggests that by modifying the length d of the pores, the maximum sensitivity range may be altered. Thus by choosing anodizing conditions to give a small

VOL. 32, NOVEMBER 1955 429 JOURNAL OF SCENTlFIC INSTRUMENTS

C. L. Cutting, A. C.

thickness d, the resistance R, wiU become small at lower relative humidities. The greatest sensitivity will then be in this range, while at high humidities C, will be approximately C, + CO, and will not greatly vary. By making d large, the maximum sensitivity will be shifted to higher humidities. The three isotherms shown (Fig. 13) illustrate this effect.

4 0 r

I

d = 6 p /

!

I I I

I d-12p j d=25p

I I G I

0 40 8 0 0 40 8 0 0 2 0 6 0 I00 Relative humidity p (%I

Fig. 13. Effect of oxide film thickness on Cp isotherm

A number of other observations have been made which confirm the mechanism put forward here. Thus oxide layers formed in other acid electrolytes also show the effect. Such layers are porous. In contrast, layers formed in neutral electrolytes, which are nonporous, show no great variation of capacity or resistance with humidity changes.

The effect should be independent of the nature of the outer conductor, provided this does not penetrate the pores. The Aquadag graphite particles are greater than lOOO8, in diameter and so cannot enter the pores (diameter - 120 A). We have found similar isotherms when the outer layer is formed of evaporated aluminium. Minor changes in the outer conductor, due to damage, or repainting with Aquadag, do not impair the functioning.

The adsorption of water vapour on alumina follows a Brunauer, Emmett and Teller equation,c3) so that the quantity of water adsorbed is a function principally of the relative humidity, and comparatively independent of temperature. RI is highly dependent on this quantity of adsorbed water (i.e. in the typical isotherm, Fig. 12, the calculated values of R, vary from 160 fi to 20 MQ). In comparison, the depen- dence of RI on temperature appears to be small. This accounts for the observation that the isotherm characteristics in the range 20-80°C show no noticeable dependence on temperature, provided comparison is made on a relative humidity scale. Further, this interpretation suggests that a phase change of the adsorbed water, by markedly affecting R, would resuit in a sharp change in the isotherms. Such an abrupt alteration in the temperature sensitivity has in fact been found between -15 and -3O'C (Figs. 7 and 8). Further work is in progress at the Tony Research Station on the low temperature characteristics, which will provide a mGre detailed knowledge of the phase transition of the adsorbed water.

Eflect offrequency. The resistance R, along the length of the outer conducting layer of an element is normally not negligible. If the layer consists of Aquadag for example, this resistance is usually about lo00 fi/cm. The element is thus equivalent to an open ended transmission line. In deriving equations (1) and (2 ) no account was taken of this finite outer conductor resistance. When this is taken into

JOURNAL OF SCENTIFIC INSTRUMENTS 4

Jason and J. L. Wood

consideration the resulting impedance Xo of the element is equal to Z/(RLX) coth d(RL/X) , where 1/X = 1/R, + 2.irfiCq(13) The bridge measures the two components of X,,.

Provided RL is small compared with 1x1, Xo is closely equal to X. However, at higher frequencies this is not so. From equations ( 1 ) and (2), it is apparent that C, and Rp both decrease as the frequency increases, and ultimately 1 XI becomes comparable with R,.

By making R, extremely small, X = Xo so that the bridge readings at higher frequencies would then give R, and Cp directly. This was effected by forming the porous outer conductor of evaporated aluminium on which was wound a spiral of 1 mm pitch of 4Os.w.g. aluminium wire. This reduced the effective value of RI. to less than 1 fi. Capaci- tance and resistance measurements, made on this element in the range of frequency from 50 cis to 10 kc/s at selected relative humidities from 0 to 100% at 20" C, are shown in Figs. 14 and 15. It will be noted that C, and Rp decrease

40 U a

Fig. 14. Effect of frequency on capacity C, of oxide layer

D~ 20 4 0 bo 80 IO0 Relative humidity p (40)

Fig. 15. Effect of frequency on resistance Rp of oxide

,30 VOL. 32, NOVEMBER 1955 layer

A capacitance-resistance hygrometer

with increasing frequency at all relative humidities, as expected from equations (1) and (2). The results are in quantitative agreement with these equations, the constants C, and R2 being dependent on the frequency.

A notable consequence of the combination of equations (1) and (2) is that at higher frequencies Rp should pass through a minimum as the humidity tends toward saturation, while C, continues to increase. This has indeed been found for all frequencies greater than 1 kc/s.

If elements with Aquadag outer conductors are used at higher frequencies, the transmission line effect results in the measured parallel capacity being less than Cp, while the measured parallel resistance is greater than Rp. This has been directly confirmed by preparing two elements anodized simultaneously; one with an evaporated aluminium outer layer, the other with Aquadag.

Effects ofother vapours. It is appropriate to mention here that the effects of other vapours on the elements are con- sistent with the influence of their conductivity in the condensed phase on R,, the pore side resistance.

D I S C U S S I O N

It is evident from the data presented that the hygrometer is capable of measuring relative humidity with considerable precision (see Fig. 3, where the mean deviation is less than or equal to k2.0xr.h.) over a wide range of operating conditions. The instrument is considered to offer the follow- ing advantages : (a) the characteristics are almost independent of temperature from 0 to 80" C ; (b) elements anodized simultaneously have the same calibration curve, if due care is taken in their construction; (c) the characteristics may be conveniently modified by a suitable choice of anodizing conditions; ( d ) the hygrometer displays the humidity in terms of electrical parameters convenient for continuous recording and control; (e) the physical size and shape of elements may be widely varied to suit particular applications; (f) the velocity of the air stream flowing past the instrument does not affect the readings; (8) remote readings are possible; (h) the response time is relatively rapid; (i) after the initial period of aging, the calibration is stable, provided no major chemical contamination occurs; ( j ) the elements are reason- ably robust and not unduly sensitive to physical shock.

As considerable interest has been shown in the use of these elements for purposes of recording and control of relative humidity, the following examples of our experience are given.

Instrumentation of the hygrometer for purposes of con- tinuous recording is easily carried out by utilizing the ballistic capacity method. In this way both anodized plates and rods have been used to provide a continuous record of the atmospheric humidity.

The humidity in cold stores has been similarly recorded. Among trial industrial applications has been the continuous measurement of relative humidity in the intergranular spaces of phosphate fertilizer emerging from a dryer on a moving belt: the relative humidity was found to provide an approxi- mate indication of the dryness of the product.

A wind tunnel of cross-section approximately 3 ft?, used

for air-drying experiments, has had its relative humidity at air speeds up to 20 ft/s kept constant within &0.25%.

The instrument suffers from the following disadvantages: (a) At relative humidities of 90% or more the response is slow, and there is a small irreversible drift. This gives rise to positive hysteresis on returning to lower relative humidities Further prolonged exposure to saturation destroys the sensitivity of the element. (b) Applied voltages greater than 80 % of the final formation voltage cause temporary electrical breakdown in the oxide. (c) Contamination by surface migration of oil or grease prevents the instrument functioning.

It is concluded that provided precautions are taken to avoid these conditions, the instrument is a useful hygrometer. Work on further development, in particular a detailed investigation of the ballistic method, is in progress.

A C K N O W L E D G E M E N T S

The work described in this paper was carried out as part of the programmes of the Food Investigation Organization of the Department of ScieotSc and Industrial Research, and of the Sir John Cass College.

The authors wish to acknowledge the assistance of Mr. R. R. Haddow and Mr. A. Lees who carried out much of the experimental work.

R E F E R E N C E S

(1) TAYLOR, H. S . J. Amer. Chem. Soc., 56, p. 1685 (1934). (2) GREGG, S. J. J. Chem. Soc., p. 563 (1946). (3) BRUNAUER, S. Ahorption of Gases and Vapors, equation

(37), p. 153 (Princeton: Princeton University Press, (1943).

(4) BOTTCHER, C. J. F. Theory of Electric Polarization, equation (6.45), p. 188 (London: Elsevier Publishing Co., 1952).

(5) ZAUSCHER, H.'voN. Ann. Phys. [Leipzig], 23, p. 597 (1 93 5).

(6) NAPIER, D. H., and WESTWOOD, J. V. Met. Znd., 76, p. 123 (1950).

(7) BAHN, R., and BOTTCHER, 0. Z. Phys., 135, p. 376 (1953).

(8) CHARLESBY, A. Proc. Phys. Soc. [London] B, 66, p. 317 (1953).

(9) WEXLER, A., and BROMBACHER, W. G. Nat. Bur. Sfand., Circular 512 (1951).

(10) CVTTWG, C. L., and JASON, A. C. J. Sci. Insfrum., 30, p. 338 (1953).

(11) HAGUE. A.C. Bridge Methods, 4th ed., pp. 329 and 335 (London: Sir Isaac Pitman and Sons Ltd., 1938).

( 12) DE BOER, J. H. The Dynamical Character of Adsorption, p. 30 (London: Oxford University Press, 1952).

(13) SMYTHE, W. R. Static and Dynamic Electricity, 2nd ed., p. 377 (London: McGraw-Hill Book Co. Ltd., 1952).

VOL. 32, NOVEhlBER 1955 43 1 JOURNAL OF SCIENTIFIC INSTRUMENTS