In case there is no public school with the proper grades in session within two miles by the shortest public highway of the residence of any child in a school district of the fourth class, or in a township which is a school district of the third class, or in a borough which has a population of less than five hundred (500) inhabitants to the square mile and which is a school district of the third class, such child shall be furnished proper transportation at the expense of the school district to and from a school with the proper grades. When it is not feasible to provide such transportation, the board of school directors may, in lieu thereof with the approval of the Department of Public Instruction,¹ pay for suitable board and lodging for any such child.