When in its judgment the public convenience and welfare will be substantially served or the appropriate use of neighboring property will not be substantially or permanently injured, or when there are practical difficulties or unnecessary hardship in the carrying out the strict letter of the zoning provisions of this Code, the Board of Adjustment may, in specific cases, after public notice and hearing and subject to appropriate conditions and safeguards, determine and vary the application of the regulations established in Title 11, Zoning, of this Code in harmony with their general purpose and intent. (Ord. 388, 6-20-1960)