These facts and dates cannot be reconciled with those in Huygens’s manuscript. It appears from that document, that, so late as May, 1694, Newton had only so far recovered his health as _to begin to again understand the Principia_. His supposed malady, therefore, was in force from the 3d of January, 1692, till the month of May, 1694,—a period of more than two years. Now, it is a most important circumstance, which M. Biot ought to have known, that in _the very middle of this period_, Newton wrote his four celebrated letters to Dr. Bentley on the Existence of a Deity,—letters which evince a power of thought and a serenity of mind absolutely incompatible even with the slightest obscuration of his faculties. No man can peruse these letters without the conviction that their author then possessed the full vigour of his reason, and was capable of understanding the most profound parts of his writings. The first of these letters was written on the 10th December, 1692, the second on the 17th January, 1693, the third on the 25th February, and the 4th on the 11th[76] February, 1693. His mind was, therefore, strong and vigorous on these four occasions; and as the letters were written at the express request of Dr. Bentley, who had been appointed to deliver the lecture founded by Mr. Boyle for vindicating the fundamental principles of natural and revealed religion, we must consider such a request as showing his opinion of the strength and freshness of his friend’s mental powers. In 1692, Newton, at the request of Dr. Wallis, transmitted to him the first proposition of his book on quadratures, with examples of it in first, second, and third fluxions.[77] These examples were written in consequence of an application from his friend; and the author of the review of the Commercium Epistolicum, in which this fact is quoted, draws the conclusion, that he had not at that time forgotten his method of second fluxions. It appears, also, from the second book of the Optics,[78] that in the month of June, 1692, he had been occupied with the subject of haloes, and had made accurate observations both on the colours and the diameters of the rings in a halo which he had then seen around the sun. But though these facts stand in direct contradiction to the statement recorded by Huygens, the reader will be naturally anxious to know the real nature and extent of the indisposition to which it refers. The following letters,[79] written by Newton himself, Mr. Pepys, Secretary to the Admiralty, and Mr. Millington of Magdalene College, Cambridge, will throw much light upon the subject. Newton, as will be presently seen, had fallen into a bad state of health some time in 1692, in consequence of which both his sleep and his appetite were greatly affected. About the middle of September, 1693, he had been kept awake for five nights by this nervous disorder, and in this condition he wrote the following letter to Mr. Pepys: _Sept. 13, 1693._ “SIR,