A Bipolar Theory of Living Processes

field of force equal to М Fè. Evidently this electrostatic energy is proportional to C, and to Ё?, say equal to NO, ; consequently we have, if C is the capacity of the suspension in microfarads, Неге N is dependent only on the constants which define the single suspended particle geometrically. We shall now proceed to calculate N for the case of a suspension of spheroids. The electric forces in the suspending liquid are obtained by means of the equations given in Part I using k, = 0. Since the potential inside the corpuscle is constant, the resistance of the inside of the corpuscle having been assumed low as compared with the impedance of the membrane, Vi, of Eq. (6) Part I, represents the potential difference between the two sides of the membrane. The average total static energy at the surface of a spheroid, arbitrarily placed in a homogeneous field of strength unity is consequently

ф being the angle between the direction of the field and one of the axes of the spheroid. Hence ad | zs £ есіне | (when a > ђ) In these equations еу рез уђе (ab); emp je ae n Consequently ($ x ab?n being equal to р), ae 4 k Д e Oa 20 о E ds aam (For the value of M see Part I, p. 348.) and substituting resistances (т, ті) for conductivities (k, ki) we obtain in which 2q represents the major axis of the spheroid. The values of а are given for different values of b/a in Table I. Ап experimental verification of the formula will be presented in the following

The following experiments illustrate the application of the theory which was presented in the preceding paper (p. 353) and confirm it. The capacity, which for a one centimeter cube of normal blood is of the order of a few hundred micromicrofarads in parallel with a resistance of a few hundred ohms, was measured with a specially designed bridge over a range of frequencies from 800 to 4,500,000 cycles. The sensitivity of the bridge is such that such a capacity сап be measured with an accuracy of a few uuf at the lowest frequency. Two arms of the bridge contain a Kohlrausch slidewire which is always used near its middle point; the third arm contains a decade resistance box В, (General Radio Company) with a decade condenser in parallel, and the fourth arm the electrolytic cell with a variable condenser C, (General Radio standard condenser) in parallel. By means of a switch the electrolytie cell can be replaced by a decade resistance box В, similar to Ві. The coils in the resistance boxes are wound by the Ayrton-Perry method and their effective inductances are rather low.

The current to the bridge is delivered by an audion oscillator and the heterodyne method of detection is employed, using three stage amplification. The bridge is connected to generating and heterodyne oscillation and to the detector tube by very loose inductive couplings. The electrolytic cell has the form of an hour-glass with large platinized platinum electrodes sealed into the glass at the ends; it is designed to have the lowest possible amount of polarization at the electrodes. The electrode area is between 10 and 20 cm?; the distance between the electrodes between 5 and 10 cm. The cell constant is about 1. Effective stirring, which is essential, is accomplished by gently blowing through two glass tubes which are sealed to the top of the cell.

The abstract of the protocol, given in Table I, will explain the experimental procedure. The cell filled with the suspension is compared with the resistance box В, ; the difference between the settings of the condenser C,, (C," — 0,’ ), gives an uncorrected value for the capacity of the suspension. This value is first corrected for the inductance of the coils used in the resistance box Б, and for the difference between the inductances of the leads which connect the cell and R, respectively to the bridge; this correction for our case is (L/R,?) farad, when this total inductance L is in henries. A small correction is thereafter introduced for the static capacity of the electrolytic cell, which, when filled with a homogeneous liquid of dielectric constant К, is К/4лс’ em. in which с” is the cell constant equal to the ratio of resistance to specific resistance. For the case of a suspension with a non-conducting disperse phase, like blood, К is the dielectric constant of the suspending liquid (for blood therefore about 81) and с’ is the constant of the electrolytic cell c times r/r,, r and r, being the specific resistances of the suspension and the intracellular liquid. Consequently, the static

The value for the capacity thus obtained is still faulty, due to the difference in static coupling between the electrolytic cell and the other parts of the bridge on one side and on the other side between the resistance box №, and the other parts of the bridge. The corresponding correction is obtained by making once for all a series of measurements with the cell filled with various dilutions of serum covering the total range of resistances used; the measured capacities are corrected as above and the values which vary very slowly with the resistance, are plotted against the resistance. From this curve a “zero value” for the capacity of the cell is found at the resistance observed in the case of blood which comprises the said difference in static coupling. This “zero value” is subtracted from the value for the capacity as obtained above.

The procedure described above would not have given a correct elimination of a polarization at the electrodes of the electrolytic cell if such an effect had been present to any appreciable amount within the experimental range of frequencies. The frequency at which the polarization becomes appreciable is easily determined by measuring the serum at decreasing frequencies; the setting of the standard condenser remains practically constant until the critical frequency is reached, when an abrupt change takes place.

A confirmation of the accuracy of this method was obtained by making measurements on cream, in which case the resulting capacity is zero. The fact that the value of the capacity of a corpuscle suspension is found to be independent of the form of the electrolytic cell and of the frequency serves as a further confirmation. (The capacity is found to be independent of the frequency between 3600 and 87,000 cycles per sec. ; for higher frequencies the capacity decreases due to the fact that the impedance of the static capacity of the corpuscle membrane becomes comparable with the resistance of the corpuscle interior. )’

Tables II and III present the results of two series of measurements, typical of several, on the blood of a dog. They include corpuscle concentrations between 10 and 84 per cent. The stated volume concentrations were derived from the resistances by an earlier formula (a/b = 1/4). The capacity (С) for 100 per cent volume concentration is calculated by formula (21) of the 1H. Fricke and S. Morse, The electric resistance and capacity of blood for frequencies between 800 and 4,500,000 cycles. Jour. Gen. Physiol.,

Capacity of suspensions of red corpuscles of a dog in own serum Defibrinated blood of dog No. 1 was concentrated by centrifugation, and the concentrated suspension was diluted with serum. Resistance r, of - Capacity of suspensions of red corpuscles of a dog in own serum Defibrinated blood of dog No. 1 was diluted with own serum. Resistance preceding paper (p. 353). The values are constant for concentrations up to about 60 per cent; for still higher concentrations, which approach the stage of total packing for which the theoretical foundation for the formula may be doubtful, there may be a slight tendency to an increase. Using the lower concentrations alone, we obtain 380uuf as the average value of Cio. Since the constant of the electrolytic cell is .98 (= resistance/spec. resistance), the specific value of С. (corresponding to a one centimeter cube) is 380 X .98 = 372 uut.

Using a/b = 1/4 as in our earlier paper ? and taking 7.2 (10)-* em for the diameter 2q of the corpuscle, by formula (22) we obtain for the capacity per cm? of the membrane It has been shown elsewhere * that the capacity of blood is independent of the frequency between 3600 and 87,000 cycles per sec. For higher frequencies the capacity decreases; this decrease, however, for the experimental range of frequencies (up to 4,500,000 cycles), is satisfactorily explained as due to the impedance of the inter- and intra-cellular liquids, with which the capacity of the corpuscle membrane is in series, Со itself being independent of the frequency over the above range. We find also that the capacity is not changed when the corpuscles from defibrinated blood are suspended in Ringer's solution or in an isotonic solution of dextrose.

On the ground of our present, although rather incomplete, knowledge of polarization, such a constancy of the capacity would seem hardly possible if it were due to a polarization at the surface of the red corpuscle. Furthermore,* there is much evidence that the resistance of the membrane which surrounds the corpuscle is high as compared with the impedance of the capacity C, over our whole experimental range of frequencies; therefore, even with a constant polarization capacity at the surface of the corpuscle, the observed capacity should have decreased as the frequency increased. (The resistance of the membrane may, for instance, be estimated from known data for the diffusion of electrolytes from the serum into the corpuscle.) At present, therefore, it seems probable that the observed capacity is due to the static capacity of the corpuscle membrane. The order of magnitude of the thickness of this mem-

brane, which may be derived on this assumption, is suggestive. By using a value of 3 as the dielectric constant of the membrane (a value which of course is rather uncertain, the more 80, since the membrane appears to be monomolecular), we obtain a thickness of 3.8 X 107 cm. This value corresponds to a chain of from 20 to 30 carbon atoms. Thus, we evidently arrive at the conclusion that the membrane of the corpuscle is monomolecular.’ Abderhalden, Emil. Lehrbuch der physiologischen Chemie. Berlin.

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