The problem is considered as to whether, in accordance with Newtonian theory, energy can be transferred from one system to another across empty space by gravitational interaction alone. Familiar examples of apparent energy transfer by this means do not give an unambiguous answer since they involve some net change of gravitational potential energy and this is not localized in the theory. Two examples are given here of systems in which the potential energy is the same at the beginning and end of an operation that does produce a resultant energy transfer. The establishment of this result is significant as a preliminary to the discussion of energy transfer according to general relativity theory. The appendix gives a particular illustration of one of the examples that admits exact mathematical treatment.