Historical Hyperbolae

Abstract

At a first glance, one of the two accompanying diagrams might be taken to represent a three-station Decca or Loran chain, while the other offers familiar instruction on how to interpolate between the lattice lines and plot the fix. In fact, these are illustrations in a German Army handbook entitled An Introduction to Sound Ranging and the Work of the Sound Ranging Section, published in July 1918.

Hyperbolic Origins

“…Bull's recording technique was used, in wfyich the vibrations of six 'string' (fine wire) galvanometers, linked to the respective microphones, were photographed on a moving film which ajso carried 1 o ms timemarks generated by a toothed wheel interrupting the incident light. 4 The grid shown in Fig. 1, the time differences were read directly off the film, which took only a few seconds to develop and fix; they were converted into bearings, and thence into a fix, on a plotting board.…”

“…Eventually, however, they introduced a three-station hyperbolic layout which was strikingly prophetic of the radio-navigational aids of a later era. 4 The grid shown in Fig. 2, reproduced from an army handbook of 1918, 5 was marked directly in time-differences and is self-explanatory; it is useful today as a non-technical introduction to the principle of hyperbolic position-fixing.…”