Whenever the money in the treasury of any county shall be insufficient to meet the demands upon the same, the treasurer, upon the order of the commissioners with the approval of the executive committee of the county convention, and such approval shall not be given until the treasurer has appeared in person before the committee to testify in support of any such request, may borrow such sum as they shall deem necessary for the purpose, and give the note of the county therefor; provided, however, that if the sum to be borrowed, together with the collected taxes of the same fiscal year, shall exceed by 10 percent the total appropriations made for that year by the county convention, the approval of the county convention for such excess borrowing must be secured, unless the convention has not acted upon the appropriations for the ensuing year. Nothing in this section shall be deemed or construed as authority to exceed appropriations made by the county convention.