The sole purpose of a variance shall be to insure that no property, because of special circumstances applicable to it, shall be deprived of privileges commonly enjoyed by other properties in the same vicinity and zone. No variance shall be granted which would have the effect of granting a special privilege not shared by other properties in the same vicinity and zone. However, the Planning Commission shall have the authority to grant a variance to permit the exploration for, drilling for and production of oil and gas in accordance with the provisions of this chapter.
('64 Code, § 70.01)