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Gassmann's method (Jahresbericht des Schweltzerischen Erdbebendlensts, 1925) for determining focal depth from the areas enclosed within the various isoseismal lines, leads (after correcting a misprint in the original paper) to the formula in which J is the maximum intensity, Rj is the radius of the area enclosed within isoseismal j, h is the depth of the focus below the surface of the ground, p is an empirical absorption‐coefficient, and M is the logarithmic modulus log10 e. This formula has been tried on the two strong earthquakes at Helena, Montana, on October 18 and 31, 1935. The fit is not good; the exponential variation of the energy with distance appears to be too strong.

It has long been known that deep earthquakes are felt more widely, for a given epicentral intensity, than shallow. Several attempts have been made to express this tendency in precise form for the estimation of focal depth. The purpose of this paper is to discuss the shortcomings of the formulas that have been tried and certain ways in which they may be improved. It is noteworthy that while the inverse square of the distance of the observer from the earthquake focus is insufficient to account for the falling off of the intensity, the introduction of an absorption coefficient is not a satisfactory method of dealing with the lack.

A fundamental problem of symbolic logic is to define logical calculi sufficient to comprise important parts of mathematics, and to develop systematic methods of calculation therein.The possibility of progress in this direction has been severely limited by Gödel's proof that a consistent system sufficient to comprise arithmetic must contain propositions whose truth-value cannot be decided within the system, and by Church's extension of Gödel's method to the result that even in the first order logical function calculus the general decision problem cannot be solved.