From the intimate connexion of the present subject with the improvement of the Achromatic Telescope, it must be admitted to be one of the most important in Optics; while, from the minuteness of the effects which are to be observed and compared, it is unquestionably one of the most difficult. From this cause very little progress has been made in the investigation. The irrationality of the coloured spaces, in prismatic spectra, formed by different substances, has not even been mentioned in any of our elementary treatises on Natural Philosophy, and there are some philosophers who have scrupled to receive it as a truth established in Physics.