A new apparatus for determining the relationship between wave-lengths of light and the fundamental standards of length has been previously described.* Definitive determinations have now been completed of the lengths of the yard and metre in terms of the wave-length of the cadmium red radiation, both in air and in vacuum, and the present paper gives the results of these determinations. Previous determinations have been made by MICHELSON and BENOÎT, by BENOÎT, FABRY, and PEROT,} and by WATANABE and IMAIZUMI, of the length of the metre in terms of the cadmium red radiation in air, and these results, after adjustment as nearly as possible from the experimental data available to uniform conditions, agree with each other and with that obtained in the present work, within a total range of four parts in ten millions, a range which is not greater than may reasonably be attributed to the experimental errors of determination of the lengths of the different copies of the metre against which the several comparisons have been made. No previous direct measurement has been made of the length of either the yard or the metre in terms of wave-lengths in vacuum. The paper records the first independent determination of these important relationships, and incidentally affords a new direct determination of the refractive index of dry air, free of carbon dioxide, which is in good agreement with that given by PÉRARD, but differs appreciably from that given by MEGGERS and PETERS.