## Bullard et al.’s (1965) fit of the continents around the Atlantic

Bullard et al.’s (1965) fit (Fig. 2) was arrived at using “modern” numerical methods. The data came from the contours on maps of the world provided by the U.S. Hydrographic service (1961). The maps provided 100 , 500- and 1000 fathom contours. Thus, the fits were tested using these as the depths of continental shelf. The numerical method was based on the application of Euler’s Theorem to the movement of points on a line across a sphere. In this case, Bullard et al. utilised this method to define the displacement of a contour line (or continent) as a rigid rotation. The best fit was arrived at by choosing a point, Pn, on the contour of the western continent, and finding a corresponding point, P'n, on the eastern continent at the same distance from the centre of rotation. After a rotation, the misfit was described by the square of the difference in longitude between such points, summed over all points on the eastern contour. The best fit rotation minimised this sum (i.e. a "least squares method").

The best fit was found to occur when the 500-fathom (914.4 m) contour was used as the continental boundaries with the rotation listed in Table 1. This process resulted in a root-mean-square misfit of about 130km for South America to Africa. The reconstruction technique was seen as providing a first-step approach for which correlation of various geological features across the region was still required. The two areas of greatest misfit, the Niger delta and the Walvis Ridge, were taken to correspond to areas of post break-up features: The Niger delta was taken to be a Tertiary feature, and the Walvis Ridge as being related to the Tertiary Mid-Atlantic Ridge.

**Table 1. Euler rotations for continental South America relative to Africa from early proposed fits.**

Mobile plate: S. America | Age (Ma) | Lat | Lon | Angle | Relative to |
---|---|---|---|---|---|

Du Toit (1937) (est’d.) | Jurassic | 49 | -28 | 46 | Africa |

Bullard et al. (1965) | U. Jurrasic | 42.9 | -30.1 | 57.1 | Africa |

Smith and Hallam (1970) | U. Jurrasic – L. Cretaceous | 44 | -30.6 | 57 | Africa |