1240
ANALYTICAL CHEMISTRY
circuit, with respect to the grid circuit. Small capacitance changes may be followed by using ta-o such oscillators and measuring the beat-frequency between them as a titration is carried oat ivhich affects only one. Such an instrument using a modifi.dColpitts circuit has hem descrihed hy West, Burkhalter, and Broussard (26). Because the Colpitts oscillator remains "in tune" as changes a.re made across t,he terniinals of the coil, changes in its grid or p1at)evoltages or currcnts should be a good indication of changes in t,hc cffrct,ive over-all conductance of a cell. Andcrson, Bettis, :\rid R,rvinson ( 1 ) ha,vc: described a titration instrument. based on the grid-dip circuit., whirh is of the Colpitts type, in n-hieh the grid current is measurrd to indicate thtn course of the: rcvrction in i he, tit,ration vcvsel. For motleixte loading, it appears that this inst,mment responds ptimiiliiy to c:ffectivo over-all contluct:tnce vh:mges of t,hc titration vewscl, rvhich are related to t h o rontluotance changes of i he solutioii as discumed previously. In all the preceding discu3:sion i t has beon aHumrd that changes In conductance have small effect oii frequencj.. A(tuaIly, in niost cases, the conductanw may bc made large hg choicc of cell geometry and roncentration range, and it may be powsihlr to load the circuit sl.ific-iently to damp,cwthe osc:illat,ion eoinplctely. n'herever t,ht vonductanw effect is great enough t,o affcct tho frequericy appreciably, anti t h e oscillat,oi,isbrought back to mnriiiiui~i i'estinance by adjust#nient of the varid)le cqmcitor, R part of the adjustment will kw c:ompensatiori for tlic nonductanw change it5 iiidicat.ed by Formula 5 . C o ~ i ~ c ~ s ~ ~ o i iifd fi rnegqlu~t,~ i i c:h:tnge r~~ is measured, :I part of t.hc eharigv will t)c due to conductnnce chntiges. As is indic,:ttt.d k)y the d:it:t of Figure 3, thc cbffect, due to t,he effective over-all collductance change may eithri, add to or d ) t , r a c , tfrom t8hreffect, due to the effective capacitancc, change of ~ h cell. c In some titiittioiiy i i rapid conductance change near the end point may work i n opposition to the rapwittirice ehmgc and Icss Sharp than ivonld othcrmake the end-point c~etc~~.iiiiii:~tion wise be ewpected.
LITERATURE CITED
Anderson. B., Hettis. E. S., and Revinson. D., .-~NAL. CHEM., 22, 743 (1950).
Anderson, K., and Revinson, D.. Ihid., 22, 1372 (1950). Blaedel, W.J., Burkhalter, T. S.,Flom, D. G., Hare, G., and Jensen, F. W., Ibid., 2 4 , 1 9 8 (1952). Blaedel, W.J., and hialmstadt, TI. V.. Ihid., 22, i 3 4 fl950). Ihid., p. 1410. Ibid., 2 3 , 4 7 1 (1951). Blake, G. G., d n a l y s t , 7 5 , 3 2 (1950). Blake, G. G., Chtmistry &Industry, 1946, 28. Blake, 0. G., J . S c i . I n s t r i r n i m i f s , 22, 174 (1945). Ihid., 2 4 , 7 7 (1947). Critchfield, P. E., "High-Frequency Study of the ('yunides of
Cobalt amd Nirkel." M.S.thesis, West Virginia Pniversity, 1951.
E'orman, J.. atid Crisp, D., Tmiih. F'arndrzy SOC.,42A, 186 (1946). Glasgow, H . S . , "Principles of Radio Engineering," pp. 349--99, Xes. York, RlcQraw-Hill Book Co., 1946. Hall. J. I>.,and Gibson, J. .L,Jr., . I S ~ LCHEM., . 23, 966 (19.51). Jeusen, F. W., and I'airack, .I.I,., Tsn. ESG.CHEM..~NAI.. ED., 1 8 , 5 9 5 (1946).
Jensen, F. JV., )Vatson, G . 11.. iiiid Beckhnni, ,J, 1 3 , . .ix.ii.. C H K Y .23,1770 , (1951).
.Jetisen, F. IT.,Watson. G. A i . . :\rid Vela, I,. Cr,,Ihid., 23, 1327 (1951) .
Massachuseth Institute of Technology. Electrical Engineering Staff, "Applied Elrcvoiiics." pp. 5 9 g - 8 0 5 , S e n I'ork, John Wley & Sons, 1943. hlonaghan, P. H., Moseleq-,P. U.. Burkhaltrr, T. R., and Sance, , ANAI..CHEY.,24, 193 (1952)). Kance, 0. A., Rurkh:rltri.. 1' 8..niid l\lutiaghan, 1'. 11.. Ibid., 2 4 , 2 1 4 (1952).
Richards, W.T., atiri I ~ o i n i s .i. . I... Proc. S u t l . .Icnd.
'Sr.;.,
1 5 , 5 8 7 (1929). Sargeiit, E. H.. and Co.. S c i o ~ t i . / ?Appm(ftur ~ and Mitirods. 5 , 4 (winter 1951). Sinclair, D. B., Proc. I a ~ t Radio . E'ngrru., 28, 310 (1940). Terman, F . E., "Radio Engiricexiiip," pp. .?4R-SR. Ken- 1-ork. McGraw-Hill Book Co., 1937. )Vest, P. W.. Burkhcilter. T. arid Hloussard. I... ASAI..C'HE:M., 2 2 , 4 6 9 (1950). t+.,
Theory of Chemical Analysis by High-Frequency Methods W. J. BLAEDEL, H. V. MALMSTADT', D. L. PETITJEAN,
AND
W. K. ANDERSON*
ChemistryrDepartrnent, University of T'iseonsin, Madison, T i s .
The work-was undertaken to explain semiqualltitatitely the nature of the response of high-frequency instruments for chemical analysis. Different instruments show two types of curves of response versus concentration for electrolyte solutions. The dependence of these response curves upon the properties of the solution and the oscillator is explained by assuming that the solution acts like a resistor and capacitor in parallel in the oscillator circuit. Some experimental support of the theory is given. The shapes of titration curves obtained by other workers may be explained. A n understanding of the nature of the response o f these high-frequency instruments should aid in elucidating their limitations, and should allow- more effective application of these instruments.
T
0 DATE there have been developed several different kinds of instruinents (6) using high-frequency oscillatom, which
provide a means of measuring solution composition without' mat,erial contact of any sort Kith the solution. The solution in a coiit'ainer is placed in the tank circuit of the oscillator. -4change in composition of t,he container contents then produces changes in t,hc plate and grid currents and voltages and also changes in fre-
' Present address, Chemi4try Department, 111.
University of Illinois, Urbana,
* Present address. Naval Reactor Division, Argonne National Laboratory, Chicago 50,Ill.
quencx. Various instrument5 differ according t'o which of these changes is observed and taken RE a nieasure of the change in cornposition. l f a n y of these instruments have been used to follow the course of titrations (6). The titmtion vemel is placed in the oscillator circuit and thc oficillator characterirtie-Le., current, voltage, or frequencx-is measured a t various times during the titration. 4 plot of the characteristic mearured versus volume of titrant added results in a curve with a break at the end point, resembling the type of curve obtained from a conductometric titration. Potentiall>., such an instrument could be 1ride1~useful wherever
1241
V O L U M E 24, NO. 8, A U G U S T 1 9 5 2 a measure of solution concentration is desired. lTariousinvestigat,ors have applied high-frequency instruments to measurement of the composition of simple organic systems (12) and to chromatography ( I I ) , and have suggested their use in the measurement of reaction rates ( 8 ) . So farj attention has been centered primarily upon inst,rumentation, and litt,le syst,ematic work has been performed on the nature of the response of these instrument,s. How the response is related to the properties of solutions has only been speculated upon by most investigators (1-3, 6 , 8). This paper describes the nature of the response of these highfrequency instruments and s h o w upon n-hat properties of the solution the response depends. TYPES O F HIGH-FREQUENCY INSTRLAIESTS
>fort instruments so far described may be placed in one of two clnases, dependent upon thc nature of the response curve-Le., us concentration of the electrolyte solution: th(, current- or voltage-measuring type, whose response curve is hump-shaped, and the frequency-measuring type, n-hose response curve is S-shaped. The two types of response curves are shoii-n in Figure 1, both having been obtained at a frequency of ahout 30 3Ic. per second. Plotting response curves on a semilogarithniir basis has no theoretical significance, but is done only to accommodate the wide range over n-hich the instruments respond to concentration changes.
LOG HCI OR NoCI M O L A R I T Y . Figure 1. Response of 30-Megacycle High-Frequent? Instruments as a Function of Concentration of Electrolyte Curves 1 and 2 are for frequency-measuring instrument: one ordinate scale unit equals a beat frequency of 20 kilocycles per second. Curves 3 and 4 are for grid-dip instrument: one ordinate scale unit equals 50 fia.
The S-shaped response curves (1 and 2, Figure 1) were obtained with the frequency-measuring instrument of Blaedel and Malmstadt (3). I n this instrument a change in composition of the electrolyte solution causes a change in frequency of the oscillator loaded with this solution. This frequency is measured by beating it against the frequency of an identical, unloaded oscillator and reading the beat frequency directly on a frequency meter. The hump-shaped curves (3 and 4, Figure 1) were obtained with the grid-dip instrument of Anderson et al. (1). This instrument may be operated a t several frequencies between 5 and 40 J I c . per second by the insertion of different coils in the tank circuit. A change in electrolyte concentration causes a change in grid current, which is measured A ith a wall-type galvanometer. A study of the curves of Figure 1 shows that the sensitivity of high frequency instruments is high only in certain concentration regions-that is, the response changes rapidly with concentration and may be used as a good measure of concentration only in certain regions of concentration. This limitation is much less severe for the grid-dip instrument than for the frequency-measur-
The frequency-measuring i n s t r u m e n t s h o w only one region of high sensitivity, corresponding to a salt concentration of 0.003 to 0.03 X (curvz 2). In this region the sensitivity and stahilit!. are such that a 0 . 0 5 9 change in concentrAtion may be tlctccteil (3). In the c s e that the elec-
h?!
r- -
- - - - - - -R- / -1
I II
L
_ _ _ _ _ _ _ _ _ _J SOLUTION
ANALYTICAL CHEMISTRY
1242 I n Figure 2, L is the inductance of the coil used in constructing the oscillator, and is independent of the properties of the solution. CI is also independent of the solution, being the total capacitance in series with the solution. C1 is primarily dependent upon the capacitance through the walls of the titration vessel, from the electrodes on the outer walls of the vessel to the solution in contact with the inner walls. Cz is the capacitance of the solution, and R is its resistance. CZis dependent upon the geometry of the titration vessel and the dielectric constant of the solution, which does not change greatly with concentration ( 4 ) . As the concentration of the solution changes, the conductance changes almost proportionately and the resistance, R, varies almost inversely.
0 CALCULATED
RESISTORCAPACITOR DATA
0 0 z
“t
/
2 21.6 w U
LL
21.41
21.2’
4
I
3
L O G SPECIFIC RESISTANCE
1 2
Figure 3. Response of Frequency-Measuring Instrument as a Function of Resistance
The response curve of the grid-dip oscillator may be explained qualitatively by the equivalent circuit of Figure 2 in the same way that Hare and H a w s explained the hump-shaped response curve for their instrument. At very low values of R (as in concentrated solutions), R offers little resistance to the flow of current; therefore, the amount of radio-frequency energy dissipated in R is low. S s R increases, the amount of energy dissipated in R increases, and the plate current of the oscillator increases to supply this energy to the tank circuit. This increase in plate current is brought about by an instantaneous readjustment of the oscillator to new operating conditions, including the flow of less rid current and therefore a lower grid bias. As R increases furtter, so that its impedance becomes much greater than that of CZ (as in very dilute solutions), Ct passes the major proportion of the current; only a small proportion of the current is passed by R, so that little energy may be dissipated in R. Thus, the plate current of the oscillator passes through a maximum and the grid current passes through a minimum as the resistance of the solution changes from high to low, or as the concentration of the solution changes from low t o high. This is in agreement with the experimental hump-shaped response curves of Figure 1, in which the changes in galvanometer current plotted are opposite in sign to changes in grid current ( I ) . For the frequency-measuring instrument, when R approaches zero (as in very concentrated solutions), Cz is effectively shorted out of the circuit, and the o z l l a t o r frequency is determined bv L and C1-i.e., fo = l / d L C 1 . When R approaches very large values (as in very dilute solutions), it is effectively out of the circuit. This leaves C1 and C* in series, and the oscillator frequency is f m = l / ~ d L C I C t / ( C l Ct): For intermediate values of R, the corresponding frequencies lie intermediate between these two asymptotic values.
+
SEMIQUANTITATIVE SUPPORT O F EQUIVALENT CIRCUIT FOR FREQUENCY-MEASURING INSTRUMENT
Theoretical analysis (9) of the circuit of Figure 2 gives
This is a theoretical relation betweenf and R, and if it is possible to fit this equation to an experimentally determined curve o f f against R for electrolyte solutions, this may be taken as evidence of the correctness of the equivalent circuit of Figure 2. To do this, a response curve was measured for sodium chloride solutions of known concentrations. Absolute frequencies were measured with a Gertsch Model FBI-1 frequency meter with a guaranteed accuracy of 0.005%. Specific resistances of the solut.ions used were obtained from the literature (IO). The experimental plot, of frequency versus log specific resistance, P , is shown by the smooth curve in Figure 3. (The experimentaI points from which the smooth curve was drawn are omitted to avoid confusion.) The agreement between calculated and experimental values is very good, indicating that the Blnedel-Malmstadt instrumeiit ( 3 ) can be approximately represented bj- the circuit of Figure 2 . Perfect agreement cannot be expected, since the simple equivalent circuit does not take into consideration such factors as stray capacitance, lead capacitance and inductance, and other circuit inductances and capacitances. For instruments which have an additional capacitor connected in parallel with L, the response curves still exhibit the same form of dependence upon concentration, but the oscillator characteristics are affected less by concentration changes, and the sensitivity is reduced. To fit the theoretical Equation 1 to the experimental curve, it is necessary to evaluate the parameters L , C,, and C2. Because of stray capacitance and lead capacitance and inductance, it is not possible t,o measure the values of these circuit components directly with sufficient accuracy. Instead, the theoretical Equation l is fit,ted to the experimental curve by making the theoretical equation coincide with the experimental curve a t three points on the latter. Two of the points chosen are the asymptot,ic limits, (pa,-fo) and ( p m , f , ) . T h e third point is an intermediate one, (j,f ) , where j = .\/fofm. The theoretical equation fitted to the experimental curve then becomes
Using the fitted theoretical Equation 2, values of pare calculated for various values o f f between the three points chosen for fitting. These calculated points are the unshaded circles shown in Figure 3.
I
o NaCl
z
W
3 0
21.6
W
a LL
21.4 21.2
L O G SPECIFIC RESISTANCE Figure 4. Response of Frequency-Measuring Instrument as a Function of Specific Resistance of Solution Loading Oscillator
Further support of the correctness of the equivalent circuit of Figure 2 was obtained by removing the titration vessel from its holder and substituting a variable resistor and two capacitors in its place to form the arrangement of C1, Cp, and R of Figure 2. This substitution was accompanied by a special modification of the titration vessel holder, made in such a way that reactance
V O L U M E 24, NO. 8, A U G U S T 1 9 5 2
1243
contributions of the holder to the circuit were unaltered in replacing the titration vessel by the resistor-capacitor combination. After the proper adjustment of the two capacitors to duplicate the two frequency limits obtained for sodium chloride solutions in the titration vessel, frequency measurements were obtained for settings of the variable resistor from 0 to 5000 ohms. For purposes of comparison, these resistance values were all multiplied by a constant factor of 5.83 to make the sensitivity curve obtained by the resistor-capacitor combination coincide exactly a t 21.800 hlc. per second with the sodium chloride sensitivity curve, This amounted to assuming a value for the geometrical factor of the titration vewel used in obtaining the sensitivity curve for sodium chloride solutions, since only specific resistance values (and not total resistance) of the solution can be accurately determined. The data are represented graphically by the shaded circles in Figure 3.
1
1
I
I
I
0.4 0.6 0.8 C U R V E 0.2 4.0 6.0 8.0 C U R V E 2.0 S P E C I F I C CONDUCTANCE, OHM-' X IO3
1
B A
Figure 5. Response of Frequency-Rleasuring Instrument as a Function of Specific Conductance of Solution Loading Oscillator
The resistor-capacitor combination gives an S-shaped curve, and the agreement with the curve of frequency versus log specific resistance for sodium chloride solutions is good but not perfect. This lack of perfect agreement is probably due in part to a small amount of lead inductance in the resistor-capacitor combination, for which complete compensation could be obtained only a t the frequency limits. The disagreement between the above-mentioned points and the smooth response curve for sodium chloride solutions may also be due in part to neglect of the Debye-Falkenhagen effect. HOKever, the slight variations of C, with concentration and of solution resistance with frequency ( 4 ) have only a second-order effect on the response; therefore, these phenomena are neglected in this semiquantitative explanation of the nature of the response. The relative importance of the Debye-Falkenhagen effect in explaining the response of high frequency instruments is the subject of a future paper. EXPLANATION OF TITRATION CURVES
According to the equivalent circuit theory (Equation 1), the response of a high-frequency instrument is dependent only upon the specific resistance of the solution loading the oscillator, and independent of electrolyte type. This fact has been verified with the frequency-measuring instrument by comparing data obtained with three different types of electrolytes, sodium chloride, barium chloride, and potassium ferrocyanide, using reliable conductance data from the literature (IO). The experimental data obtained are represented graphically in Figure 4. Therefore, a single response curve of frequency versus specific
resistance applies to all electrolytes, and it is unnecessary to determine response curves for more than one electrolyte. In order to have a means of determining beforehand how the frequency will change during a titration, it is convenient to have a plot of frequency versus specific conductance, since conductance changes are almost linearly proportional to changes in concentration. To graph nearly the entire region of high sensitivity, the plot has been divided into two portions, as shown in Figure 5. Curve A covers the range of frequencies from the lower frequency limit up to 21.7 hIc. per second, while curve B covers the range from about 21.9 to 22.3 hIc. per second. How the shape of a titration curve is affected by the concentration a t which the titration is carried out may be predicted from Figure 5.
If 75 ml. of a solution containing 15 ml. of 0.01 N hydrochloric acid is titrated with 0.01 N sodium hydroxide, the frequency changes that occur due to changing conductance may be traced on curve B. The initial conditions are indicated by point a on the graph. As the end point (indicated by point b ) is approached, hydrochloric acid is replaced with sodium chloride, the conductance of the solution decreases, and the frequency increases almost linearly. As the end point is passed, the conductance of the solution again increases, owing to addition of excess sodium hydroxide, and the frequency decreases almost linearly. After 20 ml. of sodium hydroxide have been added, the oscillator frequency and specific conductance of the solution are given by point c. The titration curve thus has the appearance of curve B in Figure 6. If the titration is carried out a t tenfold-higher concentrations, the conductance changes occur in a region where the rate of change of frequency with conductance is not constant, and the resulting titration curve is not linear. The conditions corresponding to 0,15, and 20 ml. of 0.1 N sodium hydroxide are represented by points d, e, and f, respectively, on curve A of Figure 5 , A41thoughthe shape of this titration curve is not a t all linear, the end point is still very sharp, as shown by curve A of Figure 6. If solutions one tenth as Concentrated as those giving curve B of Figure 6 are considered, a sharp break is not obtained at the end point, as the end point occurs in a region of very low sensitivity. Ot
; J '
0
VOLUME
OF NaOH, ML.
Figure 6. Titration Curves for Titration of HydrochloricAcid with Sodium Hydroxide, Plotted from Figure 5
Titration curves more complicated than A of Figure 6 may be obtained with the current-measuring type of instrument ( 1 ) if the titration occurs in a concentration range where the initial and end point conductances are on opposite sides of the hump. I n this case, the grid current decreases a t the beginning of the titration, and until the hump is passed, after which the current increases again as the end point is approached. After the end point is passed, the grid current again decreases, and if a large enough excess of titrant is added t o pass over the hump, the current eventually increases again. The resulting titration curve has the pip-shaped appearance described by previous workers (1).
ANALYTICAL CHEMISTRY
1244
I n the use of instruments operating a t different frequencies, care must be used in selecting the proper frequency for a titration, as these regions of linear response and high sensitivity are dependent upon frequency (S). ACKNOWLEDGMENT
This iTork was supported in part by a grant-in-aid from E. I. du Pont de Kemours & Co., Inc., and in part by a grant from the Kisconsin Alumni Research Foundation. LITERATURE CITED (1) Anderson,
W. K., Bettis, E. S., and Revinson, D., ANAL.
CHEW,22, 743 (1950). (2) Bever, R. J., Crouthamel, C. E., and Diehl, H., Iowa State C022. J . Sci., 23, 289 (1949). (3) Blaedel, W.J., and Malmstadt, H. V., ANAL. CHEM.,22, 734 (1950).
(4) Falkenhagen, H., “Electrolytes,” London, Oxford University Press, 1934. (5) Forman, J., and Crisp, D., Trans. Faraday SOC.,42A, 186 (1946). (6) Hall, J. L., and Gibson, J. A . , Jr., AXAL.CHEM.,2 3 , 966 (1951). (7) Hare, G., and Hawes, R. C., private communication from Beckman Instruments Co., Pasadena, Calif., May 26, 1950. (8) Jensen, F. K., and Parrack, A. L., IND.ENG. CHEW,ANAL. ED.,18, 595 (1946). (9) Tang, K. T.,“Alternating-Current Circuits,” Scranton, Pa., International Textbook Co., 1940. (10) Weissberger, A , “Technique of Organic Chemistry,” Vol. I, Part 11. Xew York, Interscience Publishers, 1949. unpublished work from Coates Chemical Labora(11) JTest, P. W.,
tories, Louisiana State University. W,,Burkhalter, T. S., and Broussard, L., ASAL. CHEM.,22, 469 (1950).
(12) West, P.
RECEIVED for review November 30, 1951
Accepted April 14, 1952.
Practical High-Frequency Titration Apparatus for General laboratory Use JAMES L. HALL West Virginia University, Morgantown, W. Va. An instrument has been constructed to meet the need for a reliable low-cost high-frequency titration apparatus which will respond to both effective overall capacitance and effective over-all conductance changes of a titration cell. This instrument is based on a simple crystal oscillator circuit and a commercially obtained vacuum-tube voltmeter. The oscillator operates at 2 Mc. It is easily constructed and is simple in operation. The cost is low enough and its performance is reliable enough to permit the introduction of the high-frequency method into student analytical laboratories. The effective capacitance changes of a titration cell are significant only in working with solutions of 0.1 N or less, but effective conductance differences are significant for many reactions at much higher concentrations.
S
0 MAKY circuits have been described for use in high-fre-
quency titration that the presentation of a new one requires justification. The apparatus described here has a number of advantages for routine laboratory use. The cost is low. The instrument is stable in operation, and the tuning adjustments are easily reproduced to a high degree of precision. Its construction requires no great knowledge of electronics and no techniques are required beyond the ability to use a soldering iron. This circuit, for the first time in a simple apparatus, provides direct indication of both effective over-all conductance and effective over-all capacitance changes of a titration cell. These are read from a calibrated capacitor dial or from an auxiliary vacuumtube voltmeter. A coupling arrangement is included in the circuit t o allow its use with a variety of cells. The low cost and simple design of this instrument make it possible t o introduce the high-frequency method into the undergraduate and graduate student analytical laboratories. The instrument described here is not intended to take the place of the highly versatile impedance-measuring circuit described by Hall and Gibson ( 6 ) , but i t has been found very satisfactory for a large variety of determinations. The circuit used for this instrument is, with only slight modi-
fication, the crystal oscillator circuit described by Alexander ( 1) and also used by Bender ( 2 ) and by Fischer ( 4 ) for the deterniination of dielectric constant. An auxiliary vacuum-tube voltmeter is required for follon ing effective over-all conductance changes of the cell. The principle of operation is simple. If the tuning capacitor of a crystal oscillator is set a t a value too great for oscillation to take place, and then the capacitance is gradually decreased, a point is reached a t which oscillation abruptly starts. This point may be precisely reproduced. This feature enables one to follow accurately the over-all capacitance changes of a high-frequency titration cell. If the tuning capacitor of a crystal oscillator is adjusted until maximum resonant voltage is attained, the grid bias voltage is a t a maximum. The maximum grid bias voltage at each point of a titration provides an excellent indication of effective conductance changes of the cell. The grid bias voltage may be measured by a vacuum-tube voltmeter of suitable range. Large changes of grid bias voltage are not directly proportional to conductance changes, but this does not interfere Rith the accuracy of end-point determinations. CIRCUIT
The complete circuit diagram is shown in Figure 1. The 250-volt power supply is not shown, as i t was exactly as described by Bender ( 2 ) . Any poaer supply delivering 6.3 volts alternating current and 250 volts direct current would be satisfactory. The 20 volts direct current was obtained from a separate power supply or from a 22.5-volt B battery. The vacuumtube voltmeter was a Silver Vomax Model 900 meter or an RCri Model WV-97A Volt Ohmyst. Any good vacuum-tube meter having direct current ranges up to 30 volts could be used. The oscillator was built into a 10 X 7 X 8 inch steel cabinet. 4 photograph of the instrument including cell and voltmeter is shown in Figure 2. The capacitors, C, and CA,were made by removing some of the plates from capacitors obtained from surplus navy GP-7 radio equipment, I n the S a v y equipment, these were fitted with geared drives, and M-ith scales dividing the 180 degrees of rotation into 800 divisions; these were retained in the present apparatus. Equivalent capacitors and suitable vernier scales may be obtained from radio supply houses. A shunt feed for the plate supply voltage to the tube was used, in order that both the rotors and the stators of the tuning ca-
