War went on for four years; the successes gained by Russia were outweighed by Austria's various reverses, terminating by the defeat of Wallis at Krotzka, and the peace concluded at Belgrade was a triumph for Turkish diplomacy.
John Wallis and Lord Brounker jointly obtained a tedious solution which was published in 1658, and afterwards in 1668 by John Pell in his Algebra.
John Wallis utilized the intersections of this curve with a right line to solve cubic equations, and Edmund Halley solved sextic equations with the aid of a circle.
The artifice was successful, and no sooner had Wallis publicly refuted the solution than Hobbes claimed the credit of it, and went more wonderfully than ever astray in its defence.
Passing through the Straits of Magellan, he visited the Tuamotu archipelago, and Tahiti, where the English navigator Wallis had touched eight months before.
Dr Wallis Budge visited several of the far southern sites and made some tentative excavations, but no extensive explorations were undertaken until an unexpected event produced a sudden outburst of activity.
He made experiments, simultaneously with Wallis and Wren, on the collision of hard spherical bodies, and his statement of the results (1669) included a clear enunciation of the conservation of linear momentum, as demonstrated for these cases of collision, and apparently correct in certain other cases, mass being estimated by weight.
The thrusts were easily and nimbly parried by Wallis in a reply (Hobbiani puncti dispunctio, 1657) occupied mainly with the verbal questions.
All voyagers agree that for varied beauty of form and colour the Society Islands are unsurpassed in the Pacific. Innumerable rills gather in lovely streams, and, after heavy rains, torrents precipitate themselves in grand cascades from the mountain cliffs - a feature so striking as to have attracted the attention of all voyagers, from Wallis downwards.
Of New Caledonia; the Huon Islands, a practically barren group; the Wallis Archipelago; and Futuna and Alofa, S.