*

himself has turned very much to the Advantage of the Publick, by producing a Syftem the most comprehenfive and inftructing that has ever appeared upon this noble Subject.

The first of the four Books, or the popular Treatife, (to follow the Account our Author has himfelf given us in his Preface) tho' partly intended as an Introduction to the reft, is chiefly defigned for the Ufe of those who would know fomething of Opticks, but want the preparatory Learning that is neceffary for a thorough Acquaintance with that Science. With this View he has there avoided all Geometrical Demonftrations, and inftead thereof has fubftituted that more loofe and entertaining Sort of Proof that may be drawn from Experiment only; and the Experiments he has contrived for that End, are not only eafy to be understood, but may be tried with very little Trouble or Apparatus. By this Means, with a moderate Application, confiderable Attainments may be made in this delightful Branch of Knowledge, which the Doctor has explained in fuch a Manner, as he hopes may be eafy to all, and yet not tedious to more skilful Readers, who may find therein fomething not unworthy their Notice. But further, this popular Treatife well understood, will be, as he adds, abundantly fufficient to conduct the above-mentioned Readers through many curious Pieces contained in the Remarks, and even through the whole third and fourth Books; especially if their Heads be a little turned towards mechanical Matters, and be furnished with fome of the first and eafieft Principles of Aftronomy.

This Books confifts of eight Chapters. In the firft the Properties of Light are difplay'd, and the Laws of its Refraction and Reflection are delivered. In the fecond are fhewn the feveral Effects of its Refraction and Reflection by Glaffes,

either concave, convex, plain, or prifmatick: The fundamental Principles and Theory of Catoptricks and Dioptricks are here exhibited, illuftrated, and exemplified in a great Variety of Cafes. The third Chapter defcribes the Construction, and affigns the general Dimenfions of the human Eye; the Modus of Vifion is explained, and the Affections of that wonderful Organ are diftinctly specified. In the fourth Chapter our Author has confidered Vifion with refracting and reflecting Glaffes, both fingle and combined, accounting for the Phenomena of the feveral Sorts of Microfcopes and Telescopes, into the Compofition of which they enter. The Subject of the fifth Chapter is very curious, Concerning our Ideas acquired by Sight. The former Part of it is a Tranfcript from the Philofophical Tranfactions, No. 402, in which is Mr. Chiffelden's Account of the Sentiments and Behaviour of a young Gentleman, whom he had brought to Sight, which he had never till then enjoyed, by Couching. Nothing could be a properer Introduction to the Doctrine of this Chapter, which includes many fine Speculations and Theorems relating to the Modus of Vifion. The fixth Chapter, Concerning the Origin and Caufe of Colours, comprifes very many of Sir Ifaac Newton's Obfervations and Experiments, whereby he inveftigated and proved one of the nobleft Difcoveries that ever was made, and of which he was most eminently the Inventor. The seventh and eighth (which are the two last) Chapters of this Book, are likewife in a great Meafure borrowed from the Opticks of that prodigious Genius; fetting forth The Caufe of Refraction, Reflection, Inflection, and Emiffion of Light; and of The Transparency, Opacity, and Colours of Bodies.

The four firit Chapters of the fecond Book (which is the Mathematical Treatife) contain the Geometrical Elements of the whole Work, demon

N

ftrated,

ftrated, Dr. Smith says, in a short and easy Manner. The nine fubfequent Chapters of it comprehend a great Variety of Problematical Propofitions. Those of the fourth Chapter are for determining the apparent Distance, Magnitude, Situation, Degree of Difinetnefs and Brightness, greatest Angle of Vision and vifible Area, of an Object feen by Rays fucceffively reflected from any Number of plane or Spherical Surfaces; or fucceffively refracted through any Number of Lenfes of any Sort, or through any Number of different Mediums, whofe Surfaces are plane or Spherical: With an Application to Telescopes and MicroScopes. Thofe of the fixth Chapter are for determining the Aberrations of Rays, from the Geometrical Focus, caufed by their unequal Refrangibility, and also by the Sphericalness of the Figure of reflecting and refracting Surfaces. The Propofitions of the feventh Chapter are fubfervient to the Solution of this Problem: A refracting or reflecting Telescope being given, whofe Aperture and Eye-Glass are adjusted by Experience, to determine the Length, Aperture and Eye-glafs of another Telescope, through which another Object shall appear as bright and distinct as the given one, and magnified as much as shall be required. The eighth Chapter contains general Properties of Focufes and Images, belonging to the Eye and to any Number of Mediums; with general Conftructions, fhewing the Variations of the apparent, Distance of an Object, and of the real Distance of its laft Image, from the Eye, caufed by a direct Motion of the Eye, Object, or Mediums. The Propofitions of the ninth Chapter are for the Determination of Focufes of Rays falling with any Degrees of Obliquity upon any Number of reflecting and refracting Surfaces of any Sort, and alfo of the Properties of Caufticks. The tenth and eleventh Chapters are altogether employed in the Solution of divers Meteorological Appearances; as the Rainbow, Corona's,

and

and Parbelia, commonly called Halo's and MockSuns.

In the Beginning of the tenth Chapter our Author premises fuch Mathematical Principles as are neceffary for an exact Computation of the apparent Diameters and Breadths of Rainbows, and then fubjoins Sir Ifaac Newton's entire Explication of the Colours of the Bows, and the Manner in which they are formed; taking the Liberty here and there of making a few Additions to it, for the Sake of fuch Readers as may not be fo skilful as those to whom that great Man generally wrote. In the eleventh Chapter the Doctor has tranflated Hugenius's Differtation on the two laft of the forementioned Phenomena. That noble Writer did not carry on this Differtation fo far as he originally intended. He defigned to demonftrate the more difficult Parts of his Subject at the Conclufion; but leaving this undone, and the Editors of his pofthumous Works fupplying the Defect but in a few Words, our Author has done the fame more at large in an Appendix to this Chapter, which comprises alfo fuch Obfervations as are referred to in the Differtation, and a Demonftration of the Conftruction of the Tables therein used, and of fome other Mathematical Propofitions relating thereto. The twelfth Chapter is employed in determining the apparent Shapes, Pofitions, Magnitudes, and Diftances of large Objects, feen by Rays that fall upon reflecting or refracting Surfaces, perpendicularly, almost perpendicularly, and with any Degrees of Obliquity. In the last Chapter The Aberrations of Rays is refumed and carried further, in order to discover the Limits of the Perfection of reflecting and refracting Microfcopes.

In the third Book, which is the Mechanical Treatife, befides fome curious Collections belonging to the Art of grinding Glaffes, drawn up and communicated by the late Honourable Samuel Moly

neux, Efq; our Author has given a full Defcription of a complete Set of Optical and Aftronomical Inftruments, according to the latest and best Improvements; together with particular Explanations of their feveral Uses, when applied to the Purposes of Aftronomy, Geography, Navigation, Levelling, and other beneficial Arts. Mr. Molyneux's Collections, which fill up the first Chapter of this Part of the Work, are extracted from Mr. Huygens and other Writers. I had, myfelf, fome little Acquaintance with Mr. Molyneux. when he was a very young Man, and know he had even then a mighty Tafte for Mechanicks, and for no Branch of them more than that which is the Subject of this Chapter. And Dr. Smith tells us, That out of his great Regard for the Improvement of Aftronomy, by perfecting the Methods of making Telescopes, both by Refraction and Reflection, he did not only collect and confider what had been written and practifed by others, but alfo made feveral new Experiments of his own contriving, after he had procured a moft complete Apparatus of all Sorts of Inftruments for that Purpose. The Papers here published were left by him imperfect. He was, after he had wrote what we here fee of them, appointed a Lord Commiffioner of the Admiralty, which engaged him fo far in the publick Affairs, that he had no Leifure to purfue the Intention of them. Then it was he gave them to Dr. Smith, inviting him to make use of his House and Inftruments, in order to finish what his Employment in the Business of the State would not permit him to proceed in. But his Death quickly following, deprived the Doctor of that Opportunity, and a moft worthy Friend. Having therefore feen nothing of the Practice of grinding Glaffes, he durft not venture, he tells us, to add any Thing of his own relating to it; but has fupplied from Mr. Huy

gens