Otto Julius Zobel - Thermal Conduction

Thermal Conduction

Zobel's early work on heat conduction was not pursued in his later career. There are, however, some interesting connections. Lord Kelvin in his early work on the transmission line derived the properties of the electric line by analogy with heat conduction. This is based on Fourier's law and the Fourier conduction equation. Ingersoll and Zobel describe the work of Kelvin and Fourier in their book and Kelvin's approach to the representation of transmission functions would consequently have been very familiar to Zobel. It is therefore no surprise that in Zobel's paper on the electric wave filter a very similar representation is found for the transmission function of filters.

Solutions to the Fourier equation can be provided by Fourier series. Ingersoll and Zobel state that in many cases the calculation involved makes the solution "well-nigh impossible" by analytical means. With modern technology such a calculation is trivially easy, but Ingersoll and Zobel recommend the use of harmonic analysers, which are the mechanical counterpart of today's spectrum analysers. These machines add together mechanical oscillations of various frequencies, phases and amplitudes by combining them through a set of pulleys or springs; one for each oscillator. The reverse process is also possible, driving the machine with the function and measuring the Fourier components as output.