The axes or cores of extensive air showers have been selected by observing in a cloud chamber cascade showers produced by a single high-energy (>5 x lo9 ev) electron or photon, and an upper limit of 5 m for the spread of such particles has been found. By placing trays of hodoscoped counters at various distances from this core selector it has been possible to determine the relation between density of ionizing particles and distance from the axis for showers of approximately 1 04-105 particles. T h e experimental arrangement and method of analysis used have certain advantages over those employed by other workers. I t is concluded that although the results of the present experiment and those of other workers are consistent with the Molikre structure function, not too much weight should be placed on this agreement.
By virtue of the well-known concept of Fisher information in the theory of statistical inference, we obtain an inequality chain which generalizes and refines the conventional Heisenberg uncertainty relations.
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