Major _Holmes_ at his return, hath made a relation concerning the usefulness of _Pendulums_, which surpasseth my expectation: I did not imagine that the Watches of this first Structure would succeed so well, and I had reserved my main hopes for the New ones. But seeing that those have already served so succesfully, and that the other are yet more just and exact, I have the more reason to believe, that the Invention of _Longitudes_ will come to its perfection. In the mean time I shall tell you, that the _States_ did receive my Proposition, when I desired of them a Patent for these new Watches, and the recompense set a-part for the invention in case of success; and that without any difficulty they have granted my request, commanding me to bring one of these Watches into their Assembly, to explicate unto them the Invention, and the application thereof to the _Longitudes_; which I have done to their contentment. I have this week published, that the said Watches shall be exposed to sale, together with an Information necessary to use them at Sea: and thus I have broken the Ice. The same Objection, that hath been made in your parts against the exactness of these _Pendulums_, hath also been made here; to wit, that though they should agree together, they might fail both of them, by reason that the Air at one time might be thicker, than at another. But I have answered, that this difference, if there be any, will not be at all perceived in the _Penduls_, seeing that the continuall Observations, made in Winter from day to day, until Summer, have shewed me that {15} they have alwaies agreed with the Sun. As to the Printing of the _Figure_ of my New Watch, I shall defer that yet a while: but it shall in time appear with all the Demonstrations thereof, together with a _Treatise_ of _Pendulums_, written by me some daies since, which is of a very subtile Speculation. * * * * * _The Character, lately published beyond the Seas, of an Eminent person, not long since dead at _Tholouse_, where he was a Councellor of Parliament._ It is the deservedly famous _Mounsieur de Fermat_, who was, (saith the Author of the Letter) one of the most Excellent Men of this Age, a _Genius_ so universal, and of so vast an extent, that if very knowing and learned Men had not given testimony of his extraordinary merit, what with truth can be said of him, would hardly be believed. He entertained a constant correspondence with many of the most Illustrious Mathematicians of _Europe_, and did excel in all the parts of Mathematical Science: a Testimony whereof he hath left behind him in the following Books. A Method for the Quadrature of _Parabola's_ of all degrees. A Book _De Maximis & Minimis_, which serveth not only for the determination of Problems of _Plains_ and _Solids_, but also for the invention of _Tangents_ and _Curve Lines_, and of the _Centres_ of Gravity in Solids; and likewise for Numerical Questions.