If any corporation formed under this chapter has accidentally or inadvertently failed to comply with the requirements hereof in its organization, such omission or defect may be corrected by filing an amendment as provided in this section. The certificate of incorporation of any corporation formed under this chapter may also at any time and from time to time be amended so as to make any changes therein and add any provisions thereto which might have been included in the certificate of incorporation in the first instance. Any amendment shall be effected in the following manner: The members of the board of directors of the corporation shall file with the governing body of the county an application in writing seeking permission to amend the certificate of incorporation, specifying in such application the amendment proposed to be made. Such governing body shall consider such application and, if it shall by appropriate resolution duly find and determine that it is wise, expedient, necessary, and advisable that the proposed amendment be made, and if an additional project or projects are proposed, that there is a public need therefor, and shall approve the form of the proposed amendment and shall authorize the amendment to be made, then the persons making such application shall execute an instrument embodying the amendment specified in such application and shall file the same with the judge of probate of the county. The proposed amendment shall be subscribed and acknowledged by each member of the board of directors before an officer authorized by the laws of Alabama to take acknowledgments to deeds. Such judge of probate shall thereupon examine the proposed amendment and, if he finds that the requirements of this section have been complied with and the proposed amendment is within the scope of what might be included in an original certificate of incorporation, he shall approve the amendment and record it in an appropriate book in his office. When such amendment has been so made, filed and approved, it shall thereupon become effective, and the certificate of incorporation shall thereupon be amended to the extent provided in the amendment. No certificate of incorporation shall be amended except in the manner provided in this section.