AN ELECTRON TUBE POTENTIOMETER FOR THE DE- TERMINATION OF pH WITH THE GLASS

ELECTRODE.

BY WILLIAM C. STADIE.

(Prom the John Herr Musser Depurtment of Research Medicine, University of Pennsylvania, Phi+ladelphia.)

(Received for publication, June 14, 1929.)

Recent developments (Clark, 1928) of the glass electrode indi- cate that it might well become the method of choice for the deter- mination of pH in serum, blood, etc. Its usefulness is seriously restricted, however, by the fact that the internal resistance of the glass cell is high (20 to 500 megohms) necessitating the use of a troublesome quadrant eIectrometer in pIace of the customary galvanometer. The elimination of the electrometer would ap preciably enhance the value of the method. This paper de- scribes an easily controlled, sensitive, and stable electron tube potentiometer which will measure an E.M.F. to 0.001 volt or less through resistances up to 600 megohms. No electrostatic effects are present, body and hand capacity effects are negligible, the indicating galvanometer image is extremJy steady, and the sen- sitivity with the Leeds and Northrup galvanometer No. 2420C is 1 to 4 mm. per 0.001 volt. With glass electrodes of 30 to 50 megohms resistance filled with buffers, equilibrium is quickly obtained and maintained constant (~1=0.0005 volt) for 2 to 8 hours.

Several types of electron tube potentiometers have been de- scribed (Clark, 1928), but these have been used exclusively with cells of low internal resistance. Recently, however, two papers have appeared (Elder and Wright, 1928; Partridge, 1929) which describe potentiometers for use with cells of high internal resistance. The method described here is different in principle from those re- ported and possesses certain advantages which will be discussed below.

477

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478 Glass Electrode

Determination of Plate Current-Grid Potential Characteristics of Electron Tubes.

Fig. 1 shows the customary circuit by which the properties of the tube are obtained. The electron tube has three electrodes: filament, grid, and plate. When the filament is heated (by the A battery) current flows in three circuits; viz., filament circuit and (by virtue of the electron emission from the hot filament) the grid and plate circuits. The negative filament terminal (A -) is the point common to the three circuits and all potential differences are referred to it as zero.

+ ZEP

FIG. 1. Circuit to determine grid potential-plate current characteristics of electron tubes.

Let Ep = plate potential (high and positive) ZP = the plate current

Rp = the external plate resistance RL = the internal plate resistance

The plate current is given by the equation

For any given tube the plate current depends on the plate poten- tial, the filament temperature, the external and internal plate resist- ance, the grid potential, and the external grid resistance. We

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W. C. Stadie 479

discuss only the effects of variations of the grid potential (E,) and the external grid resistance (R,) on the plate current, all other factors affecting I, remaining constant. Changing E, from a negative to a positive value decreases the internal plate resistance (R’,) and hence increases IP (Equation 1). The curve of I, plotted against E, is the plate current-grid potential characteristic or briefly the characteristic. Two cases arise: (1) The resistance in the grid circuit (R,) is low. This is the familiar case and is illustrated by the solid line in Fig. 2. Only the straight portion of the curve

FIO. 2. Characteristics of electron tube when external grid resistance is low or high. The characteristic with high external resistance is dis- torted due to residual gas in the tube.

concerns us. Its slope t+ or the amplijication depends on the

tube, plate voltage, etc. Ge may take 0.3 X lo+ ampere per millivolt as an-average value for the electron tubes suitable for

AI use as laboratory potentiometers. -Z is the change of plate

A& current which must be measured to determine an E.M.F. to 0.001 volt. (2) The resistance in the. grid circuit is high (R,) > 2 megohms. The presenoe of small irremovable traces of gas

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480 Glass Electrode

within the tubes produces a distortion of the characteristic when a high resistance is placed in the grid circuit. All tubes tested (Nos. 199, 171, 201A, 222, 300A) gave altered characteristics of the same general nature. A knowledge of the nature of the curves permits the selection of suitable conditions for operating the tube as a voltmeter in measuring the E.M.F. of glass cells. Denote grid potentials on the high resistance curves by E’,. The curve (Fig. 2) is convex to the straight line characteristic between E’, = -8.0 to -1.0 volts but is almost parallel to it between E’, = -3.0 to -1.0 volts. Above - 1.0 volt the curve passes through the low resistance characteristic at a point whose abscissa is always negative. At this point the plate current is the same as that when the grid circuit is open which is equivalent to making R, = co. The curve then becomes asymptotic to a slightly higher value of I,. On higher plate voltages (67.5 to 180 volts) the convexity of the high resistance characteristic is more marked. Moreover the posi- tion of the characteristic varies with the resistance. We further consider the plate current (log) when the grid circuit is opened, i.e. when (R, = m). Its value is not that at 0 grid potential (grid to A- when R, = 0) but less. In other words the open grid acts as if it had a potential negative to A - . Call this apparent potential the open. circuit grid potential (E,,). It varies from -0.2 to -0.8 volts in the tubes tested (- 4 volts in tube No. 202A).

The two curves (high and low grid resistances) intersect at a point whose coordinates are IO, and E,,. E,, is constant for any set of conditions but varies with filament temperature, plate poten- tials, etc. Note that if E, = E’, = E,, the grid may be placed on low, high, or infinite grid resistance without change in plate current. Denote the horizontal distance between the curves by ET. To the left of EoB, E, is negative and small; to the right E, is positive and large. Any selected and constant value of I, inter- sects the curves at points called the operating points (IoP) and the grid potentials Eg and E’, for low and high grid resistances respec- tively at the same I,, are obviously related by

E,I=E,+E,

The terms defined are collected in tabular form for reference.

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W. C. Stadie 481

Symbols.

ZP = plate current in general ZOI, = plate current at any selected operating point I,, = plate current when grid is on open circuit E, = grid potential when external grid resistance is low Ei = grid potential when external grid resistance is high

IS,, = abscissa of point of intersection of characteristics with high and low external grid resistance

E, = horizontal distance between two characteristics E, = E.M.F. of unknown in grid circuit E’ = E.M.F. of compensating potentiometer in grid circuit

Ah - = increment of plate current to increment of grid potential AK,

or amplification R,, RP = external resistance in grid and plate circuits respectively

RL = internal resistance of filament to plate

E.M.F. Measurement by Electron Tubes.

The electron tube may be used in two ways to measure E.M.F. The first is the dejlection method. The plate current-grid potential characteristic is established by calibration with known E.M.F. in the grid circuit. An unknown E.M.F. in the grid circuit may be then read directly from the resulting I, and this curve. The tube characteristic, however, is subject to frequent changes and the variation of I, over a considerable range introduces serious variations in the tube action. Since the characteristic varies with the resistance this method is not suitable for use with glass cells.

The second or null method possesses the advantage that the tube action is maintained constant by keeping I, at some selected oper- ating point. Call this constant plate current I,,. An unknown E.M.F. = E, and the E.M.F. = E’ of a compensating potentiometer in series are placed in the grid circuit. The plate current may be restored to the operating point by adjustment of the potentiom- eter. When the grid resistance under both conditions is low it is clear from Fig. 2 that no extra grid potential is needed so that lop is constant when E, = E’.

When, however, the unknown has a high resistance as in the case of a glass cell an additional negative E.M.F. = E, must be put on the grid to maintain IOp constant. Obviously E, = E, + E’ from which

E, = E, - E’ (2)

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482 Glass Electrode

E, depends on resistance of the glass cell and the operating con- ditions (Fig. 2) of the tube, but its exact value need not be known since it is constant for any given cell if the operating con- ditions are constant. Since all pH measurements with the glass electrode are relative to some known pH, Equation 2 and the familiar Nernst equation give for any two solutions the equation

EzI - Es2 = E; - E; = kg (pH1 -pHz)

from which

PHI = pHz + ST (E; - E;)

pH2 being known, pH1 may be calculated from the difference of the potentiometer readings. The absolute valueof E, can be calculated only if the cellresistance and value of E, at this resistance is known. The need for this in most pH work is rare.

The significance of the characteristics with low and high grid resistances in the measurement of the E.M.F. of glass cells by the null method is brought out by the following remarks. Select some fixed grid potential (E,) by introducing a dry cell into the grid cir- cuit and maintain the filament temperature constant. I,, and E,. are thus fixed. Connect the grid (always through the source of grid potential E,) by a switch (1) directly to A - through low resist- ance or (2) indirectly through the E.M.F. = E, of the glass cell (which includes a high resistance) and the E.M.F. = E’ of a compen- sating potentiometer. In passing from low to high resistance there will be no change of plate current when E, = E, + E’. Fig. 2 makes it clear that by variation of the fixed grid potential (E,) relative to the open grid potential (E,,) three cases arise.

Case 1. Case 2. Cese 3. Eg > Eog Eg=Eog Eg < Eog

E,. . . . . . . . . Positive and Zero. Negative and infinite. small.

Amplification ( )

f$ . . . . . Zero. Small. Large. cl

Grid current. . . . . . . . . . . Large. Zero. Zero.

The schema shows whether and how the current can be restored to the operating point in the three cases. Case 1 is completely

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excluded since it would be impossible to restore the plate current to the operating point. The second use has the advantage that at balance the grid can be connected to A- directly or through the glass cell or be on open circuit without change in plate current. However the difficulty of exactly locating the Eog, the diminished amplification, and the possibility of grid current flowing through the cell if EoB is not exactly located nullify this advantage. Case 3 (E, < E,,) by a simple arrangement yields maximum sensitivity and retains all the stability of Case 2. Eog for tube UX 222 varies from -0.2 to -0.5 volt depending on operating conditions. A fixed bias (E,) of -1.5 volts gives proper working conditions for this tube.

Grid Current.

In the measurement of any reversible E.M.F. it is of course es- sential that no current be drawn from the cell. In galvanometer circuits of high sensitivity this current may be reduced to very low values usually of the order of lo-lo to 1O-8 amperes. A perfect electron tube shouId have no grid current at a bias of 0 volt (grid to A-) but again the presence of gas alters its action so that, in general, tubes uniformly show zero grid circuit at E, = Eog rather than EB = A-. Grid current increases rapidly as E, becomes less negative so that at E, = A- there is appreciable current. At E,, more negative than EoB (-0.5 to -3 volts) no grid current can be demonstrated by a galvanometer whose sensitivity is 2 X 1O-8 amperes per mm. If the grid bias is made highly negative (- 3 to -6 volts) there is a small (about 10-g amperes) grid current in the opposite direction. This is a third gas effect. The working condition of - 1.5 volt for fixed grid bias assures zero current taken from the cell.

Practical Electron Tube Potentiometer Circuits.

Both deflection and null methods require current indicators in the plate circuit with high sensitivity (0.3 X 10V6 amperes to measure 0.001 volt) and considerable range (since I, may be 0.5 to 1.5 milliamperes). These requirements cannot be contained in one instrument. The methods commonly used to overcome this difficulty are of five types:

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484 Glass Electrode

1. Use of High Sensitivity Galvanometer with Shunt (EZder and Wright, 1928).

A resistance is shunted across the galvanometer and is adjusted to retain the galvanometer image on the scale. Since only a portion of the current passes through the galvanometer, part of the amplification factor of the tube is sacrificed.

2. Diminution of Plate Voltage.

This reduces the plate current and lessens the galvanometer deflection at the operating point (Pope and Gowlett, 1927). Again, however, the marked reduction of plate voltage sacrifices amplification.

3. Increase of Negative Grid Potential (Williams and Whitenack, 1927’).

The plate current may be reduced to zero at sufficiently negative grid potential (Fig. 2) at the cost, however, of considerable ampli- fication.

4. Multiple Stage Amplification.

The above methods are difficult in practice and the use of the galvanometer directly in the plate circuit has generally been abandoned. To employ a milliammeter one or two further stages of amplification may be added to the first tube and the amplifi-

cation factor 2 increased say 20-fold. An instrument sensitiv- Q

ity of about 6 X 1O-6 then suffices to measure a change of E.M.F.

in the grid of 0.001 volt so that a milliammeter with range of 1.50 milliamperes for 150 scale divisions may be used (Partridge, 1929; Goode, 1928).

5. Balanced Wheatstone Bridge Circuit.

Multistage circuits designed to increase amplification require large plate voltages with heavy drain on B batteries. The author has found that under these circumstances there is unsteadi- ness of plate current requiring frequent adjustments of the operat- ing point. These difficulties have been fully discussed (Goode, 1928; Bienfait, 1926) and have led the author to abandon the method for a simpler one which completely overcomes all the

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W. C. Stadie 485

difficulties discussed and permits the use of a high sensitivity gal- vanometer indirectly in the plate circuit.

The principle of the circuit is that of a Wheatstone bridge with arms containingfour resistances, two of which are the internal (filament to plate) resistances of the tubes; and two are the external (variable) resistances of the plate circuit. These latter when properly selected balance the bridge. A high sensivitity galvanometer across the bridge measures zero current at balance and if the electron tubes possess approximately the same electri- cal properties, changes of filament and plate batteries affect the internal resistances of both tubes alike so that balance is not dis-

a

d FIG. 3. Schematic balanced Wheatstone bridge circuit adapted to

measure E.M.F. of the glass electrode in one grid circuit.

turbed. By this arrangement great steadiness of tube action is obtained independent of minor fluctuations of the batteries and the advantage of using a sensitive indicating galvanometer working over a narrow range is secured. The Wheatstone bridge principle in electron tube circuits has been employed in a variety of ways notably in the strobodyne method of stabilizing radio frequency amplification and in push-pull audio-frequency amplification. For laboratory purposes Fitch (1927) has successfully used it in measuring impedance at high frequencies and Wynn Williams (1928) has recently described such a circuit suitable for the meas- urement of small ionization currents.

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The sohematic circuit is shown in Fig. 3. (The filament battery is omitted.) The three circuits (grid, plate, and filament) of two electron tubes are connected in parallel and have the usual common C (grid), B (plate), and A (filament) batteries. The grid circuit of one tube (upper) is fitted with a switch .allowing a glass electrode and compensating potentiometer to be inserted in series in the circuit at will. If RI and Rz are the external resistances of the plate circuit (which may be varied) and R’1 and R’z the internal resistances (filament to plate) of the electron tubes since the circuit is obviously a Wheatstone bridge there will be no current in the circuit abed when

RI R: -==1 R2 R2

If the grid potential on the upper tube is changed by inserting the glass cell and potentiometer, E.M.F., E, and E’, and R’1 changes, the bridge is unbalanced and a deflecting current will pass through the circuit abed. This may be reduced to zero by adding E, volts to the grid potential of the upper tube and we may calculate pH as before. This circuit permits a high sensitivity galvanometer to be inserted in abed since at balance only small currents are measured and the circuit used as a null method to measure E.M.F. in the grid circuit. With a Leeds and Northrup galvanometer No. 2420C of 0.025 X low6 ampere per mm. sensitivity a change of E, = 0.001 volt, may be made to give a deflection of 4 mm. when the grid resistance is 30 to 600 megohms.

The circuit gives a convenient null method adaptable to the glass electrode. The construction is simple and except for the potentiometer and galvanometer, which are as a rule standard laboratory equipment, is inexpensive. It obviates the disadvant- age of multistage amplification and the need for relatively inaccu- rate and expensive milli or micro ammeters.

Fig. 4 shows in detail the complete circuit used. A standard Weston cell is included so that the potentiometer may be adjusted from time to time. Fig. 5 shows the assembled apparatus. A list of component parts is given.

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I FIG. 4. Working balanced Wheatstone bridge circuit arranged as a

potentiometer for use with the glass electrode.

FIG. 5. Assembled electron tube potentiometer for the measurement of E.M.F. through high resistance, particularly the glass electrode. The electron tubes are omitted.

487

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Components.

2 cx 222 h’, 4 to 6 volt storage battery E, 1.5 volt flash light cell Ep 22.5 volt radio battery (heavy duty)

Es.,. Weston standard cell RI 5 ohm rheostat (Yaxley) R2 15 ohm fixed resistance (Yaxley)

R3, Es 10,000 ohm fixed resistance (Durham 2.5 watt Powerohm) Rq 400 ohm vernier variable resistance (Yaxley potentiometer)

R,, Es fixed resistance 0.5, 0.1 megohms respectively (Durham, Powerohm)

I’, Leeds and Northrup student potentiometer Rs 6000 ohm potentiometer (Centralab No. P. F.) S, mercury cup “telegraph key” switch, silica insulated S:! double pole-double throw switch (Leeds and Northrup type I<)

l’.K. tapping keys G.C. glass cell and connecting calomel cells

G Leeds and Northrup galvanometer No. 2420C M.A. Weston panel milliammeter (1.5 m. Amp. No. 506)

Selection and Matching of Tubes.

The screen grid D.C. electron tube, UX 222, is superior to any tube tried. The control grid terminal is at the top of the tube and is hence effectively insulated.

A further advantage of the UX 222 tube is the space charge grid which is operated at +22.5 volts. With +22.5 volts on the plate and filament at 1.5 volts (0.20 ampere for 2 tubes) a plate current of 0.45 milliampere and a galvanometer deflection of 3 to 4 mm. per 0.001 volt change of E, is obtained. The low plate voltage and filament temperature give great steadiness of tube action.

The chief object of the bridge circuit is to reduce fluctuations of galvanometer current due to changes in the tubes or batteries. Theoretically, if both tubes have the same electrical properties, changes in either A or B batteries would affect both alike so that no change in galvanometer current. would occur. Practically this is almost accomplished. To insure a stabilized circuit the tubes selected must be matched. The plate current-grid volt character- istics of a batch of tubes are determined and the most closely matching pair selected.

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W. C. Stadie 489

Insulation.

The internal resistance of the glass electrode varies from 20 to 500 megohms. Obviously the insulation of the grid from A or B battery terminals must be of the highest order. To obtain this the following procedures are necessary.

The control grid is insulated by coating the tube with paraffin. The tube sockets are painted with paraffin. The mounting panel and base of the apparatus are of Bakelite. All wire is of covered bus wire and arranged so that the wires of different circuits do not touch. The A and B batteries are placed on paraffin blocks. The C battery (1.5 volt pocket flash light cell) is paraffined.

The make and break switch is a platinum wire dipping into a small cup of glass containing mercury. The cup is supported by a silica rod. The platinum wire is insulated by a silica rod and is raised and lowered by an arrangement similar to a telegraph key. The leads from the key to the electrode and potentiometer carried through the case are supported in silica tubes. The glass electrode and connecting calomel cells are insulated by silica plates or rods. The potentiometer is placed on insulating blocks.

Body Capacity Efects and Shielding.

Without adequate grounding violent body and hand capacity effects may be evident even if insulation is most thorough They can be almost completely eliminated by placing the entire appara- tus on a sheet of galvanized iron which is grounded to a water pipe. In addition a sheet of grounded galvanized iron may be placed under the chair of the operator.

No shielding is necessary as the apparatus is practically free of electrostatic effects.

#witching in the Glass Electrode.

Since Case 3 is selected as the working condition the disadvan- tage of a change of I, on open grid circuit must be overcome. The importance of this lies in the following: If constant current at the operating point be momentarily altered (as by opening the grid circuit) it will not return instantly to its former value but will fluctuate unsteadily for 2 to 3 minutes and may change so that many adjustments may be necessary before a satisfactory read-

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ing can be obtained. To eliminate this difficulty no change should be allowed to take place in the lop and this is accomplished by never allowing the grid to be on open circuit. To do this the un- known is shunted across the switch. The grid circuit is short- circuited on the make and is not influenced by the cell and poten- tiometer but on the break the grid is connected through the unknown and potentiometer with zero time of open circuit. It is possible then to pass freely back and forth from low to balanced high resistance with negligible variations of I.

The disadvantage of short-circuiting the glass cell is slight. Our experience shows that with selected glass cells polarization even with a large E.M.F. difference is quickly recovered from. Polarization is minimized by reducing the time of short-circuit- ing the cell.

Necessity for Constant Plate Current.

Equation 2 requires E, to be constant between successive deter- minations of pH. Now E, increases as I, is increased (e.g. by change of filament temperature or plate voltage). In general the variation of E, with changes of plate current is greatest when filament temperature and plate voltage are high. For example, filament voltage = 4.0 and filament current = 0.3 ampere, screen grid and plate voltage = +45; the change of E, is 0.1 volt when I, changes from 0.90 to 1.10 milliampere or 0.005 volt per 0.01 milli- ampere. With the conditions selected, however, namely 22.5 volts on plate and screen grid, 1.5 volts on filaments and plate current = 0.30 milliampere, the change of E, for change of I, of 0.01 milliampere is < 0.001 volt. Changes in E, are thus easily avoided by keeping the current constant by means of the filament rheostat and the panel milliammeter which reads to 0.01 milliampere.

Technique.

Adjust the filament till I, = 0.30 milliampere and allow 20 min- utes for the tubes to reach a steady state. Adjust the plate resist- ances until the galvanometer registers no deflection. Break the direct grid connection by means of the switch thus putting the glass electrode and potentiometer in series with the C battery and grid of the control tube. Rapidly adjust the pot.entiometer

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until the galvanometer is again balanced. Leave the key open for 1 to 2 minutes, close the key, and adjust to galvanometer zero a second time. Again insert the unknown and adjust the potentiom- eter to zero deflection. Repeat at intervals of a minute until the system attains equilibrium. Always maintain plate current con- stant when the key is closed by filament adjustment. Close the switch when changing the cells for if the grid is left on open circuit for a few minutes the galvanometer zero may shift and may re- quire 3 to 5 minutes to become constant.

Calculation.

The glass cell constant e, is first established. Determine the E.M.F. (E) of five or six buffers of known pH over the desired range. Plot the value of pH against E, draw the best straight line, and obtain the constants of the equation

pH = s (E - eo)

The constants e, and gT allow the calculation of an unknown

pH from its E, and this equation. In general $T is close to

0.058 the theoretical value at room temperature and is very con- stant (&O.OOOl) for any given cell. e, is not quite so constant so it is best to verify its value daily by determination on one or two known solutions.

SUMMARY.

A null method for the measurement of E.M.F. of glass electrodes with an electron tube potentiometer is described. The grid, filament, and plate circuits of two electron tubes (No. UX 222) are connected in parallel. The plate circuits are arranged as a Wheat- stone bridge which may be balanced by variable resistances allowing a high sensitivity galvanometer to be inserted into the plate circuit. The E.M.F. of a glass cell in the grid circuit of one tube may then be measured to 0.001 volt or less. The apparatus is free from electrostatic disturbances and is very steady in its action. In measuring E.M.F. through resistances of 20 to 600 megohms its sensitivity is 1 to 4 mm. of deflection per 0.001 volt.

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BIBLIOGRAPHY.

Bienfait, H., Rec. tram. chim. Pays-Bas, 46, 166 (1926). Clark, W. M., The determination of hydrogen ions, Baltimore, 3rd edition,

328, 433 (1928). Elder, L. W., Jr., and Wright, W. H., Proc. Nat. Acad. SC., 14, 936 (1928). Fitch, A. L., J. Opt. Sac. Am., 14, 348 (1927). Goode, K. H., J. Opt. Sot. Am., 17, 59 (1928). Partridge, H. M., J. Am. Chem. Sot., 61, 1 (1929). Pope, C. G., and Gowlett, F. W., J. SC. Instruments, 4, 380 (1927). Williams, J. W., and Whitenack, T. A., J. Physic. Chem., 31, 519 (1927). Williams, W., Phil. Msg., 6, 324 (1928).

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William C. StadieGLASS ELECTRODE

DETERMINATION OF pH WITH THEPOTENTIOMETER FOR THE

AN ELECTRON TUBE

1929, 83:477-492.J. Biol. Chem. 

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