To these great purposes serve the THREE PRINCIPLES, while in conjunction: But now, as in the civil world and the affairs of men, our pleasure, in contemplating the wisdom and goodness of providence, is often viewed and checked by the view of some human perversity or folly which runs across that dispensation; so it is here in the intellectual. This admirable provision for the support of virtue hath been, in great measure, defeated by its pretended advocates; who, in their eternal squabbles about the true foundation of morality, and the obligation to its practice, have sacrilegiously untwisted this THREEFOLD CORD; and each running away with that part he esteemed the strongest hath affixed that to the throne of heaven, as the golden chain that is to unite and draw all unto it.
Siris! The allusion is to the same passage of the Iliad from which Berkeley derives the same image for his philosophical work Siris, used to a different end.
It's also an interesting passage in that Warburton explicitly denies that you can do without any of the three -- the people who try to eliminate any of the three as 'excitements to virtue' do so 'sacrilegiously'. So he has a much more sophisticated view than comes across in Cockburn's response to him, since he explicitly rejects the claim that morality as a whole is a matter entirely of the will of a superior. Nonetheless, Cockburn's summary is quite accurate. While Warburton thinks each of the three is equally necessary for moral motivation, he insists very clearly that the will of a superior is the "true bottom" of morality. This is because he thinks the will of a superior is necessary for moral obligation, which is what Cockburn is explicitly contesting. Thus, the point of dispute is not morality in the broad sense (including all our reasons and motivations for being moral) but morality in the strict sense (what constitutes moral obligation).
In another post I'll give Warburton's argument, in his own words, for the claim that an atheist, as such, can never attain to knowledge of morality in the strict sense.