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We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K.T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of 1 (M, x) can be expressed via these new integrals. The ring of exponential iterated integrals contains the coordinate rings for a class of universal representations, called the relative solvable completions of 1 (M, x). We consider exponential iterated integrals in the particular case of fibered knot complements, where the fundamental group always has a faithful relative solvable completion. ᭧

Polarization capacity and phase angle of electrolytic cell having gold electrodes and potassium bromide as electrolyte.-Using symmetrical condensers in which the separation of the plates could be varied from .002 cm to .3 cm, the series resistance and the capacity for small current density were measured by means of an alternating current bridge. Within the errors of the experiment, the "initial" capacity was independent of the separation of the plates, and the resistance was a linear function of the separation, approaching, however, a definite surface resistance as the distance between the plates was reduced. For concentrations greater than hundredth normal it was possible to work with such small separations that the resistance of the electrolyte could be neglected in comparison with the surface resistance. Direct measurements were, therefore, possible of capacity, resistance, and phase angle (tan _1 o>CR). Using clean gold electrodes as soon as possible after immersion in the electrolyte, a study was made of the variation of these constants with concentration, and for a few frequencies from 570 to 3500 cycles. The capacity varied very nearly directly and the resistance inversely as the one-fourth power of the concentration, the product CR being nearly constant. The phase angle was very nearly constant for variations both of concentration and of frequency, showing only a slight decrease with increasing concentration, and a slight increase with increasing frequency. It was about 65°. POLARIZATION CAPACITYAND PHASE ANGLE 625

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