The first attempt to penetrate by way of the river Plate and its affluents inland, with a view to effecting settlements in the interior, was made in 1526 by Sebastian Cabot.
He did not, however, confine himself to the consideration of forms involving only three indeterminates, but succeeded in establishing the principles on which the extension to the general case of n indeterminates depends, and obtained the general formulae, thus effecting what is probably the greatest advance made in the subject since the publication of Gauss's Disquisitiones arithmeticae.
In May he defeated a greatly superior royalist force at Grantham, proceeding afterwards to Nottingham in accordance with Essex's plan of penetrating into Yorkshire to relieve the Fairfaxes; where, however, difficulties, arising from jealousies between the officers, and the treachery of John Hotham, whose arrest Cromwell was instrumental in effecting, obliged him to retire again to the association, leaving the Fairfaxes to be defeated at Adwalton Moor.
But the cost of effecting a repair still remains a very uncertain quantity, success being dependent on quiet conditions of sea and weather.
The grappling of the cable and raising it to the surface from a depth of 2000 fathoms seldom occupy less than twenty-four hours, and since any extra strain due to the pitching of the vessel must be avoided, it is clear that the state of the sea and weather is the predominating factor in the time necessary for effecting the long series of operations which, in the most favourable circumstances, are required for a repair.
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