In the present paper experiments are reported which throw new light on the problem of the intermediate stages of oxidation of carbohydrate; in conjunction with the work of Szent‐Györgyi 20), Stare and Baumann 19) and Martius and Knoop 13,14) the new experiments allow us to outline the principal steps of the oxidation of sugar in animal tissues.

IN this paper experiments are described which show that ketonic acids can react in animal tissues according to the general scheme R. CO.COOH + R'. CO. COOH + H20-R. COOH + C02 + R'. CH(OH). COOH ...... (1) oa-ketonic a-ketonic carboxylic a-hydroxy-acid acid I acid II acid or R. CO. COOH + R'. CO. CH2. COOH + H20-R. COOH + CO2 + R'. CH(OH) .C0. COOH ....(2). ae-ketonic fl-ketonic acid carboxylic ,-hydroxy-acid acid acid Examples are given in which oc-ketonic acid I as well as a-ketonic acid II in (1) are represented by pyruvic acid. In other cases the oc-ketonic acid in (2) is pyruvic acid or a-ketoglutaric acid and the ,B-ketonic acid in (2) acetoacetic or oxaloacetic acid. The reactions 1 and 2 elucidate a mechanism by which ac-ketonic acids are broken down in the animal body. Although it has long been known, from the work of Embden, that oc-ketonic acids undergo oxidation to the fatty acids which are shorter by one carbon atom, the question of the mechanism of this oxidation remained open. According to (1) and (2) the oxidation of a-ketonic acids is not brought about by molecular oxygen, but by a dismutation, that is to say by an intermolecular oxido-reduction. The oxidizing agent for the ketonic acid is a second molecule of ketonic acid which is reduced to the corresponding hydroxy-acid. The reactions (1) and (2) appear to play a role in the course of the normal oxidative breakdown of carbohydrates, of fats and of the carbon skeleton of amino-acids. This will be discussed in full in subsequent papers. I. GENERAL EXPERIMENTAL METHODS 1. Determination of cx-ketonic acids (a) Carboxylase method. Pyruvic acid was usually determined by the carboxylase method [Warburg et al. 1930; Westerkamp, 1933]. Freshly pressed top yeast obtained from a local brewery was spread over filter-paper and dried at room temperature with the aid of a fan. The dried yeast, treated according to the directions of Westerkamp, yielded a powerful carboxylase. The addition of 1/5 vol. of 90 % glycerol stabilized the enzyme for about one week at 0°[see von Schoenebeck, 1935]. It is essential that the yeast used should be fresh and quickly dried [Wiilfert, 1936]. (b) Ceric sulphate method. An alternative method applicable to other oc-ketonic acids is based on the reaction R. CO. COOH + 2Ce +H20-R. COOH + CO2 + 2Ce" + 2R

Abstract-TheEwald method is applied to accelerate the evaluation of the Green's function of an infinite periodic phased array of line sources. The Ewald representation for a cylindrical wave is obtained from the known representation for the spherical wave, and a systematic general procedure is applied to extend previous results. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. Singularities and convergence rates are analyzed, and a recipe for selecting the Ewald splitting parameter is given to handle both low and high frequency ranges. Indeed, it is shown analytically that the choice of the standard optimal splitting parameter 0 will cause overflow errors at high frequencies. Numerical examples illustrate the results and the sensitivity of the Ewald representation to the splitting parameter .

The Ewald method is applied to accelerate the evaluation of the Green's function (GF) of an infinite equispaced linear array of point sources with linear phasing. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. It is shown analytically that the choice of the standard ''optimal'' Ewald splitting parameter E 0 causes overflow errors at high frequencies (period large compared to the wavelength), and convergence rates are analyzed. A recipe for selecting the Ewald splitting parameter is provided.

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FROM experiments reported in a previous paper [Krebs & Johnson, 1937] we concluded that carbohydrate is oxidized in animal tissues through the following series of reactions: Oxaloacetic acid + carbohydrate derivative / \ (pyruvic acid?) l-Malic acid Citric acid t Fumaric acid a-Ketoglutaric acid Succinic acid Greville [1936] and Weil-Malherbe [1937] have recently suggested that succinic dehydrogenase may be protected from malonate in the structurally intact tissue. Our experiments show, however, an inhibition of succinic dehydrogenase in the intact body.Maleic acid causes an increased citric acid excretion in Orten & Smith's and our experiments (Table II). It is probable that maleic acid, too, is an enzyme poison, but we cannot exclude the possibility that it acts as a precursor like fumaric acid. Thunberg [1920] and Laki [1935] reported that maleic acid is metabolized in animal tissues. SUMMARY 1. Citric and a-ketoglutaric acids appear in the urine of rabbits and rats after injection of succinic, fumaric, 1(-)-malic or oxaloacetic acids. This is considered to be evidence in support of the "citric acid cycle".

This paper presents models and measurements of linear antenna input impedance in resonant cavities at high frequencies. Results are presented for both the case where the cavity is undermoded (modes with separate and discrete spectra) as well as the overmoded case (modes with overlapping spectra). A modal series is constructed and analyzed to determine the impedance statistical distribution. Both electrically small as well as electrically longer resonant and wall mounted antennas are analyzed. Measurements in a large mode stirred chamber cavity are compared with calculations. Finally a method based on power arguments is given, yielding simple formulas for the impedance distribution.

In the present paper experiments are reported which throw new light on the problem of the intermediate stages of oxidation of carbohydrate; in conjunction with the work of Szent‐Györgyi 20), Stare and Baumann 19) and Martius and Knoop 13,14) the new experiments allow us to outline the principal steps of the oxidation of sugar in animal tissues.