Rhumb tales
In November 1681, the folio records that ‘Mr. Hooke Produced A new sort of Instrument for Describing the Rhombs or spirall lines vpon the Planisphericall projection on the pole of the world and shewed how the same would easily Describe all manner of Proportionall spiralls whether Greater or Lesse whether wider or narrower. And mentioned also what vse it might be for nauigation and sea charts.’ A few months later, Hooke produced a globe about a foot in diameter fitted with this instrument, and claimed that he could ‘thereby both Geometrically and mechanically Draw all the Rhumb lines vpon it most exactly’. A ‘rhumb line’, although sometimes used to indicate a straight line between two points on a Mercator chart, seems here to have its modern meaning of a curve that crosses each meridian at the same angle and the spirals Hooke refers to describe the way in which a rhumb spirals towards one of the poles.
The instrument designed by Hooke apparently had numerous applications: this is probably what he used in June that year to demonstrate the truth of Archimedes’ ancient theory on spirals, namely that ‘If a straight line drawn in a plane revolves uniformly any number of times about a fixed extremity until it returns to its original position, and if, at the same time as the line revolves, a point moves uniformly along the straight line beginning at the fixed extremity, the point will describe a spiral in the plane.’
Hooke later used the instrument in other ways, attaching it to a compass in order to describe a parabola. This apparently met with some opposition: at a meeting of 15 February 1682, it was noted that Flamstead had ‘cavilled against’ Hooke’s method, ‘affirming it to be fals’. On the repeated demonstration of the working of the instrument, however, the Society agreed that it was ‘true and certain and the best way yet known of describing that curve’. The final reference is in March 1682 and refers to the use of the instrument to describe an ellipse. By this entry Waller has noted ‘Quere Mr Hunt what this was and how performed’. Apparently, then the instrument and its method of use had been lost by the time Waller acquired Hooke’s papers in 1708. Richard Waller, a strong supporter of Hooke’s claims to priority had also made annotations against Hooke’s manuscripts about clocks or watches in Trinity College Cambridge – perhaps believing that they contained the solution to the long-term problem of longitude. He may, therefore, have also believed that this lost instrument was a significant piece of equipment in Hooke’s claim to have invented a new method of planispherical projection to be used in mapping.
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