The bulletin of mathematical biophysics

, Volume 3, Issue 2, pp 39–55 | Cite as

Weber's theory of the kernleiter

  • Alvin M. Weinberg
Article

Abstract

The potential distribution about a kernleiter is determined according to Weber's method. It is shown that the distribution reduces to the solution of a telegrapher's equation when the volume of the external medium is small. The velocity of propagation as a function of the external volume is determined approximately. This involves the solution of the equation
$$\frac{{\left[ {Y_0 (k\xi )} \right]^\prime }}{{\left[ {J_0 (k\xi )} \right]^\prime }} = \frac{{\left[ {\xi ^{ - a} Y_0 (\xi )} \right]^\prime }}{{\left[ {\xi ^{ - a} J_0 (\xi )} \right]^\prime }}$$
whereY 0 andJ 0 are bessel functions, and roots of this equation are tabulated. The velocities thus found reduce to Lillie's values determined experimentally on the iron wire when the conducting medium is small. Deviations from these values are predicted for larger volumes.

Keywords

Potential Distribution External Medium External Resistance Mathematical Biophysics Order Root 

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Copyright information

© The University of Chicago Press 1941

Authors and Affiliations

  • Alvin M. Weinberg
    • 1
  1. 1.The University of ChicagoChicagoUSA

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