thing harder; as Intereft fimple and compound, Annuities, c. in which, it is incredible, how much the ordinary Rules and Tables influence the difpatch of business. Arithmetick is not only the great Inftrument of private Commerce, but by it are (or ought to be) kept the publick Accounts of a Nation: I mean thofe that regard the whole State of a Commonwealth, as to the number, fructification of its people, increase of Stock, improvement of Lands and Manufactures, Balance of Trade, Publick Revenues, Coinage, Military power by Sea and Land, &c. Thofe that would judge or reafon truly about the State of any Nation, must go that way to work, fubjecting all the fore-mentioned particulars to Calculation; this is the true Political knowledge. In this refpect the affairs of a Commonwealth differ from thofe of a private Family, only in the greatnefs and multitude of particulars that make up the Accounts. Machiavel goes this way to work in his account of different Eftates. What Sir William Petty and feveral others of our Countrymen have wrote in Political Arithmetick, does abundantly fhew the Pleafure and Ufefulness of fuch Speculations. It is true, for want of good information, their Calculations fometimes proceed upon erroneous fuppofitions; but that is not the fault of the Art. But what is it the Government could not perform in this way, who have the command of al publick Records? Laftly, Numbers are applicable even to fuch things as feem to be governed by no rule, I mean fuch as depend on Chance: the quantity of probability and proportion of it in any two proposed cases being fubject to Calculation as much as any thing elfe. Upon this depend the principles of Game. We find Sharpers know enough of this to cheat fome men that would take it very ill to be thought Bub Bubbles; and one Gamefter exceeds another, as he has a greater fagacity and readiness in Calculating his probability to win or lofe in any propofed cafe. To underftand the Theory of Chance thoroughly requires a great knowledge of Numbers, and a pretty competent one of Algebra. The feveral ufes of Geometry are not much fewer than those of Arithmetick. It is neceffary for afcertaining of property both in Planes and Solids, or in Surveying and Gauging. By it Land is fold by the measure as well as Cloth: Workmen are paid the due price of their labour, according to fuperficial or folid measure of their work and the quantity of liquors determined for a due regulation of their price and duty. All which do wonderfully conduce to the eafy difpatch of business, and the preventing of frauds and controverfies. I need not mention the Measuring distances, laying down of Plans, and Maps of Countries, in which we have daily Experience of its ufefulness. Thefe are fome familiar inftances of things to which Geometry is ordinarily applied of its ufe in Civil, Military, and Naval Architecture we shall speak afterwards. From Aftronomy we have the regular difpofition of our time, in a due fucceffion of years, which are kept within their limits as to the return of the Seafons, and the motion of the Sun. This is no fmal advantage for the due repetition of the fame work, Labour, and Actions. For many of our Publick, Private, Military, and the Country Affairs. Appointments, &c. depending on the products of the Ground, and they on the Seafons, it is neceffary, that the returns of them be adjusted pretty near to the motion of the Sun: and we fhould quickly find the inconveniency of a vague undetermined year, if we ufed that of the Mahumetans, whose beginning and every month wanders through all the days of ours or or the Solar year, which fhews the Seafons. Befide, the adjusting 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 whatever fome people may think of an Almanack where all these are set 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 fingle fheet. Befides, without a regular Chronology there can be no certain Hiftory; which appears by the confufion amongst Hiftorians before the right difpofition of the year, and at present 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 Emperor, to whom we owe our prefent Kalendar; who was himfelf 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 vocavi. The Mechanicks have produced fo many useful Engines, fubfervient to conveniency, that it would be a talk too great to relate the feveral forts of them : fome of them keep Life itself from being a burden. If we confider fuch as are invented for raifing weights, and are employed 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, kind, where they have no other way to be fupplied readily with that neceffary Element; or fuch as, by making Wind and Water work for us, fave Animal force and great charges, and perform thofe Actions which require a vaft 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 contrived to measure time? We fhould 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 completed 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 exactest Numbers and true Syitem, was made by the fame M. Hugens: to which we may very juftly apply Claudian's noble Verfes upon that of Archimedes. Jupiter in parvo cum cerneret Ethera vitro, Jamque Jamque fuum volvens audax induftria mundum 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 (cap. ult. Lib. vii.) tells us, the Romans made ufe of an erroneous Sun-dial for ninety-nine years, till 2 Martius Philippus their Cenfor set 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. These are fuch useful and neceffary things, that alone may recommend the Art by which they are made for by these we are able in our Clofet to judge of the Celestial motions, and to vifit the most distant places of the Earth, without the fatigue and danger of Voyages; to determine concerning their Diftance, 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 thefe I might add thofe 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 ufeful 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 diftance, nor the minutenefs of the Object are any more impediments to it. The Telescope is of so vast ufe, that befides the delightful and useful purposes it is |