Subject to the provisions of Article XIX, the Board of Zoning Appeals shall have the power to grant a variance in the density, bulk, height or area requirements in any district so as to relieve practical difficulties or particular hardships when and where the strict application of each regulation or restriction would result in peculiar and exceptional practical difficulties to or exceptional hardship upon the owner of such property by reason of exceptional narrowness, shallowness, size or shape of a specific piece of property at the time of the enactment of such regulation or restriction or by reason of exceptional topographical conditions or other extraordinary situations or conditions of such piece of property. Such grant or variance shall comply, as nearly as possible in every respect with the spirit, intent and purpose of this chapter. The purpose of this provision is to authorize the granting of a variance only for reasons of demonstrable and exceptional hardship as distinguished from variations sought by applicants for the purpose or reasons of convenience, profit or caprice.