The velocity of neutrons reflected almost directly backwards from a crystal is close to h/2dm, where h is Planck's constant, d the lattice spacing and m the mass of the neutron. The velocity can be determined accurately by measuring a time of flight over a known distance, without any very accurate determination of the angle of reflection, and such a measurement may therefore provide an accurate determination of d (or h/dm). The proposed experimental arrangement involves two parallel identical crystals in the form of thin disks, placed some metres apart, the first in an intense neutron beam, and the second reflecting into a detector. They are first adjusted for Bragg reflection, and then set in synchronous sinusoidal vibration. The vibration modulates the velocity of neutrons reflected by the first crystal and the velocity accepted for reflection by the second. The intensity of twice-reflected neutrons is a maximum whenever the velocity wave for neutrons arriving at the second crystal is in phase with the vibration of the second crystal. At a given vibration frequency, plots of intensity against the position of the second crystal would exhibit sharp peaks. Measurement of the positions of two such peaks about 10 m apart to within about 0·01 mm would provide a determination of d to within about 1 p.p.m. Aspects of the proposed experiment such as crystal material and size, the frequency and amplitude of oscillations, intensity, and background are discussed, and it is concluded that it is feasible.