or the Solar year, which fhews the Seafons. Befide, the adjufting of the Moon's motion to the Sun's is required for the decent Obfervation and Celebration of the Church-Feafts and Fafts according to the Ancient Custom and Primitive Inftitution; and likewife for the knowing of the Ebbing and Flowing of the Tides, the Spring and Neap Tides, Currents, &c. So that what ever fome people may think of an Almanack where all these are fet down, it is fometimes the most useful paper that is published the fame year with it: Nay, the Nation could better fpare all the Voluminous Authors in the Term-Catalogue, than that single fheet. Befides, without a regular Chronology, there can be no certain Hiftory; which appears by the confusion amongst Hiftorians before the right difpofition of the year, and at prefent among the Turks, who have the fame confufion in their History as in their Kalendar. Therefore a Matter of fuch importance might well deferve the care of the Great Emperour, to whom we owe our prefent Kalendar; who was himself a great proficient in Aftronomy. Pliny has quoted feveral things from his Books of the Rifing and Setting of the Stars. Lib. XVIII. cap. 25, 26, &c. and Lucan makes him fay, -Media inter prælia femper Stellarum, Calique plagis, fuperifque vacavi. The Mechanicks have produced fo many ufeful Engines, fubfervient to conveniency, that it would be a task too great to relate the several forts of them: fome of them keep Life it felf from being a burden. If we confider fuch, as are invented for raifing weights, and are employ'd in Building and other great works, in which no impediment is too great for them; or Hydraulick Engines for raifing of Water, ferving for great ufe and comfort to Man kind, where they have no other way to be fupply'd readily with that neceffary Element; or fuch as, by making Wind and Water work for us, fave Animal force and great charges, and perform those Actions, which require a vast multitude of hands, and without which every Man's time would be too little to prepare his own Aliment and other neceffaries; or thofe Machines, that have been invented by Mankind for delight and curiofity, imitating the motions of Animals, or other works of Nature; we shall have reason to admire and extol fo excellent an Art. What shall we fay of the feveral Inftruments, which are contriv'd to measure time? We should quickly find the value of them, if we were reduced to the condition of those barbarous Nations, that want them. The Pendulum-Clock invented and compleated by that famous Mathematician Monfieur Hugens is an useful invention. Is there any thing more wonderful than feveral Planetary Machines which have been invented to fhew the motions of the Heavenly Bodies, and their places at any time? Of which the moft Ingenious, according to the exacteft Numbers and true Syftem, was made by the fame M. Hugens: to which we may very juftly apply Claudian's noble Verses upon that of Archimedes. Jupiter in parvo cum cerneret Æthera vitro, Rifit, & ad fuperos talia dicta dedit : Huccine mortalis progreffa potentia curæ ? Jam meus in fragili luditur orbe labor. Jura poli, rerumque fidem, legefque Deorum Ecce Syracufius tranftulit arte fenex. Inclufus variis famulatur fpiritus aftris, Et vivum certis motibus urget opus. Percurrit proprium mentitus fignifer annum, Et fimulata nove Cynthia menfe redit. Famq; Gaudet, & humana fidera mente regit. Here I ought to mention the Sciatherical Inftruments, for want of which there was a time, when the Grecians themselves were forced to measure the Shadow, in order to know the Hour; and as Pliny fcap. ult. Lib. VII.) tells us, the Romans made ufe of an erroneous Sun-dial for ninety nine years, till 2 Martius Philippus their Cenfor fet up a better; which no doubt at that time was thought a Jewel. And at laft, that famous Pyramid was fet up in the Campus Martius, to ferve for a Gnomon to a Dial marked on the street. To this fort of Engines ought to be referred Spheres, Globes, Aftrolabes, Projections of the Sphere, &c. Thefe are fuch ufeful and neceffary things, that alone may recommend the Art, by which they are made. For by thefe we are able in our Clofet to judge of the Celestial motions, and to vifit the most diftant places of the Earth, without the fatigue and danger of Voyages; to determine concerning their Distance, Situation, Climate, Nature of the Seafons, length of their days, and their relation to the Celestial Bodies, as much as if we were Inhabitants. To all these I might add those Inftruments, which the Mathematicians have invented to execute their own precepts, for making Obfervations either at Sea or Land, Surveying, Gauging, &c. The Catoptricks and Dioptricks furnish us with variety of useful inventions, both for the promoting of knowledge, and the conveniencies of Life; whereby Sight, the great Inftrument of our perception, is fo much improved, that neither the dif tance, nor the minutenefs of the Object are any more impediments to it. The Telescope is of fo vast afe, that befides the delightful and useful purposes it is applied to here below, as the descrying Ships and Men, and Armies at a distance, we have by its means discovered new parts of the Creation, fresh inftances. of the furprizing Wisdom of the Adorable Creator. We have by it discovered the Satellites of Jupiter, the Satellites and Ring of Saturn, the Rotation of the Planets about their own Axes; befides other appearances, whereby the Syftem of the World is made plain to fenfe, as was before to reafon. The Telescope has alfo improved the manner of Astronomical Obfervations, and made them much more accurate, than it was poffible for them to be before. And these improvements in Aftronomy, have brought along with them (as ever) correfpondent improvements in Geography. From the Obfervation of Jupiter's Satellites, we have a ready way to determine the Longitude of places on the Earth. On the other hand, the Microscope has not been less useful in helping us to the fight of fuch Objects, as by their minuteness efcape our naked eye. By it Men have pursued Nature into its moft retired receffes; fo that now it can hardly any more hide its greatest Myfteries from How much have we learned by the help of the Microfcope of the contrivance and ftructure of Animal and Vegetable Bodies, and the compofition of Fluids and Solids? But if thefe Sciences had never gone further, than by their fingle Specula and Lentes to give thofe furprizing appearances of Objects and their Images, and to produce heat unimita ble by our hotteft Furnaces, and to furnish infallible, eafy, cheap, and fafe remedies for the decay of our Sight arifing commonly from old Age, and for purblindness, they had merited the greatest esteem, and invited to the clofeft ftudy: efpecially if we confider, that fuch as naturally are almoft blind, and either know not their nearest acquaintance at the distance of a room'sbreadth, or cannot read in order to pass the time us. time pleasantly, are by Glaffes adapted to the defect of their Eyes fet on a level again with those that enjoy their Eye-fight beft, and that without danger, pain or charge. Again, Mathematicks are highly serviceable to a Nation in Military Affairs. I believe this will be readily acknowledged by every body. The Affairs of War take in Number, Space, Force, Diftance, Time, &c. (things of Mathematical confideration) in all its parts, in Tacticks, Caftrametation, Fortifying, Attacquing, and Defending. The Ancients had more occafion for Mechanicks in the Art of War than we have: Gun-powder readily producing a force far exceeding all the Engines, they had contrived for Battery. And this I reckon has loft us a good occafion of improving our Mechanicks: the cunning of Mankind never exerting it felf fo much, as in their Arts of deftroying one another. But, as Gunpowder has made Mechanicks lefs ferviceable to War; it has made Geometry more neceffary: There being a force or refiftance in the due measures and proportions of the Lines and Angles of a Fortification, which contribute much toward its ftrength. This Art of Fortification has been much study'd of late, but I dare not affirm, that it has attain'd its utmoft perfection. And tho' where the ground is regular, it admits but of fmall variety, the measures being pretty well determined by Geometry and Experience, yet where the ground is made up of natural Strengths and Weakneles, it affords fome fcope for thinking and contrivance. But there is another much harder piece of Geometry, which Gun-powder has given us occafion to improve, and that is the doctrine of Projectiles; whereon the Art of Gunnery is founded. Here the Geometers have invented a beautiful Theory, and Rules and Inftruments, which have reduced the cafting of Bombs to great exactnefs. As for |