  The expansion history of the Universe is calculated using a simple model in
which the entire rest mass energy of a massive particle is distributed
throughout the set of Machian strings connecting it to all the other particles
in the observable Universe. With the assumption that the energy in a Machian
string has the form of positive Newtonian potential energy, the deceleration
rates in the radiation and matter eras are exactly the same as in the
conventional $\Lambda$CDM model. The transition from deceleration to
acceleration at the present time is obtained by making the simplest possible
modification of the Newtonian potential energy to represent the effect of the
cosmological expansion. The effective dark matter and dark energy densities are
calculated in terms of the speed of the Hubble flow at the radius of the
observable Universe.
