various refrangibility, was the following:--Let a tin plate painted with the prismatic colours in stripes be placed in an empty cubical vessel, so that from the spectator's point of view the colours may be just hidden by the rim. On pouring water into this vessel, all the colours become visible in the same degree; whereas, it was contended, if the Newtonian doctrine were true, some colours would be apparent before others.--Historischer Theil, p. 434. Such are the arguments and experiments adduced by Goethe on this subject; they have all probably been answered. In his analysis of Newton's celebrated _Experimentum Crucis_, he shows again that by reversing the prismatic colours (refracting a dark instead of a light object), the colours that are the most refrangible in Newton's experiment become the least so, and _vice versâ_. Without reference to this objection, it is now admitted that "the difference of colour is not a test of difference of refrangibility, and the conclusion deduced by Newton is no longer admissible as a general truth, that to the same degree of refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of refrangibility."--Brewster's Optics, p. 72. NOTE Q--Par. 387. With the exception of two very inconclusive letters to Sulpice Boisserée, and some incidental observations in the conclusion of the historical portion under the head of entoptic colours, Goethe never returned to the rainbow. Among the plates he gave the diagram of Antonius de Dominis. An interesting chapter on halos, parhelia, and paraselenæ, will be found in Brewster's Optics, p. 270. NOTE R.--Par. 478. The most complete exhibition of the colouring or mantling of metals was attained by the late Cav. Nobili, professor of physical science in Florence. The general mode in which these colours are produced is thus explained by him:[1]-- "A point of platinum is placed vertically at the distance of about half a line above a lamina of the same metal laid horizontally at the bottom of a vessel of glass or porcelain. Into this vessel a solution of acetate of lead is poured so as to cover not only the lamina of platinum, but two or three lines of the point as well. Lastly, the point is put in communication with the negative pole of a battery, and the lamina with the positive pole. At the moment in which the circuit is completed a series of coloured rings is produced on the lamina under the point similar to those observed by Newton in lenses pressed together." The scale of colours thus produced corresponds very nearly with that observed by Newton and others in thin plates and films, but it is fuller, for it extends to forty-four tints. The following list, as given by Nobili, is divided by him into four series to agree with those of Newton: the numbers in brackets are those of Newton's scale. The Italian terms are untranslated, because the colours in some cases present very delicate transitions.[2] _First Series._