This investigation owes its origin to a remark by Professor Lennard-Jones that it should be possible to calculate the approximate force between two atomic systems at large distances apart by a fairly direct method. The inter-atomic force is known to be of the form kR−7 at a large distance R, and an attempt to obtain the value of the constant k for two hydrogen atoms was made by Wang. The method suggested to the writer of this paper by Lennard-Jones was used by London and Eisenschitz for this case, and they obtained a value ofk differing from that given by Wang. The value given by London and Eisenschitz has been confirmed by following the method given in this paper, but further applications to the calculation of the inter-atomic force at large distances were postponed as the problem of calculating the polarizability of helium provided, on Lennard-Jones' suggestion, a simpler case on which the method could be tested.