Ruling on the pubic law appeal brought by

S.________ Corporation, represented by Mr Bernard Vischer, Attorney-at-law, Geneva bar,

against the decision rendered on 2 September 1999 by the 1st Section of the Court of Justice of the Canton of Geneva in the case of the appellant against B.________ SA, represented by Mr Alain Lévy, Attorney-at-law,

Geneva bar,

(definitive dismissal of the objection to pay a debt)

Given the exhibits, which reveal the following facts:

A.- In a partial award of 15 August 1997, a London arbitral tribunal ordered B.________ SA to pay S.________ Corporation US$ 1,146,663.58, subject to interest and costs (set at £ 6,005). Relying on that award, S.________ Corporation requested that the London High Court of Justice wind up the debtor, which was granted on 2 February 1998. However, the London Court of Appeal set aside this decision on 31 July 1998.

B.- On 15 March 1999, S.________ Corporation notified B.________ SA that an order to pay amounts of CHF 1,685,486.60 and CHF 14,021.68, with interest of 7.5% per annum as of 16 August 1997, to which the latter objected. By a decision of 10 June 1999, the Tribunal of First Instance of Geneva granted exequatur to the arbitral award as well the definitive dismissal of the objection to the payment of the debt; the respondent seized the Geneva Canton Court of Justice on 2 September 1999, which set aside the decision and dismissed the request for the definitive dismissal of the objection to the debt’s payment.

C. In its public law appeal before the Federal Tribunal, S.________ Corporation, concludes on the merits that the decision be set aside and that the objection to the payment of the debt be definitively dismissed. The respondent argues for the dismissal of the action and the confirmation of the challenged decision.