Indigent children resident anywhere within the state shall be received into the school and asylum, maintained and educated gratuitously, so far as the funds of the institution will admit: Provided, That where more children shall be offered for the benefit of this institution than can be received at any one time, the president and directors shall so apportion their number among the several counties of this commonwealth, according to their representation (when application shall be made), that every county may equally receive the benefits of the same.