William Whiston (1667-1752) was an important English scientist, a disciple of Sir Isaac Newton, and successor of that great man as Lucasian Professor of Mathematics at the University of Cambridge. Unfortunately, his reputation is now overshadowed by his controversial theological studies which led to him being dismissed from that post, and prejudiced his election to the Royal Society.
Whiston's first eclipse map is a prediction of the course of the eclipse across the face of the globe (without any underlying geographical features), marking 'The Path of the Moons Center' with a dotted line. While it gives a broad sense of the surmised route of the eclipse, it is not as useful as Halley's work on the same subject, constructed more as a memento than a scientific treatise. Furthermore, whereas Halley looked on the eclipse as a purely scientific phenomenon, by the end of his life Whiston believed that the 1715 eclipse was a "Divine signal". It is, however, equally as rare as Halley's map.
The map was first advertised, almost as an aside, at the end of a Senex advertisement for Halley's first eclipse map, in the London Gazette (issue 5317) for 2nd - 5th April 1715, followed by a fuller announcement in the Post Man (issue 11050 [sic]) for 7th - 9th April 1715, thus:
"This Day is published, Mr. Whiston's second Account of the great Eclipse; containing, 1. Directions for its easier Observation. 2. The principal Things to be observed 3. A Cælestial Map of the principal Stars and Planets, and of the Sun's milky way, which may then be visible. 4. An exact Calculation of the Eclipse, from Sir Isaac Newton's last Improvement to his Theory of the Moon; with several curious Remarks. Sold by the Author in Crossstreet Hatton Garden, and by Mr Senex in Salisbury Court near Fleetstreet, price 1s. Note, Mr Whiston intends to have one of his Balls of Fire thrown up from Hampstead Heath, just at the middle of the Eclipse, for a Signal to all the remote Observers, and a Specimen how far that Light may be seen at a time of so great Observation."
The curious note regarding the ball of fire was Whiston's attempt to use the publicity surrounding the eclipse to further his own work on longitude. He ran a series of experiments where rockets or fireballs were launched into the air and observers were asked via public advertisements to record everything from the height they reached to their angle from the meridian. This rather unconventional method was mocked by William Hogarth in 'The Rake's Progress': in 'Bedlam', the final plate, Whiston appears in Bedlam Asylum amongst other 'lunaticks'.