from the base of the prism, which would be coloured if the prism was not an isosceles one. This suggestion seems to have enlightened the Dutch philosophers. Mr. Gascoigne, having no conveniences for making the experiments pointed out by Newton, requested Mr. Lucas of Liege to perform them in his own house. This ingenious individual, whose paper gave great satisfaction to Newton, and deserves the highest praise, confirmed the leading results of the English philosopher; but though the refracting angle of his prism was 60° and the refractions equal, he never could obtain a spectrum whose length was more than from _three_ to _three and a half_ times its breadth, while Newton found the length to be _five_ times its breadth. In our author’s reply, he directs his attention principally to this point of difference. He repeated his measures with each of the three angles of _three_ different prisms, and he affirmed that Mr. Lucas might _make sure to find the image as long or longer than he had yet done_, by taking a prism with plain surfaces, and with an angle of 66° or 67°. He admitted that the smallness of the angle in Mr. Lucas’s prism, viz. 60°, did not account for the shortness of the spectrum which he obtained with it; and he observed in one of his own prisms that the length of the image was greater in proportion to the refracting angle than it should have been; an effect which he ascribes to its having a greater refractive power. There is every reason to believe that the prism of Lucas had actually a less dispersive power than that of Newton; and had the Dutch philosopher measured its refractive power instead of guessing it, or had Newton been less confident than he was[14] that all other prisms must give a spectrum of the same length as his in relation to its refracting angle and its index of refraction, the invention of the achromatic telescope would have been the necessary result. The objections of Lucas drove our author to experiments which he had never before made,—to measure accurately the lengths of the spectra with different prisms of different angles and different refractive powers; and had the Dutch philosopher maintained his position with more obstinacy, he would have conferred a distinguished favour upon science, and would have rewarded Newton for all the vexation which had sprung from the minute discussion of his optical experiments. Such was the termination of his disputes with the Dutch philosophers, and it can scarcely be doubted that it cost him more trouble to detect the origin of his adversaries’ blunders, than to establish the great truths which they had attempted to overturn.