points that had not been fufficiently explained by former writers, was the principal motive with me to take them more particularly into confideration.

BUT as our acquaintance grew by degrees into a fettled friendship, I became defirous of giving you fome publick teftimony of the refpect and affection I had for you; to which end I began to collect together and revise my scattered papers, and to think of preparing them for the Prefs. And fo follicitous was I to produce fomething not unworthy of the Patronage you were then pleased to grant me, that I attended too little to the good old rule, Quid valeant humeri, and projected a design much too large for the health and leisure I had to profecute it.

By the want of these, the work has been retarded for fo many years, that in the more active and confpicuous scene of life you have fince entered upon, wherein you appear with so much honour to yourself and fo much pleasure to your friends, when your former thoughts upon this fubject must neceffarily have been long fince discontinued and laid afide, I am fenfible you can hardly have time to look into, or think of

what

what in the days of your Academical leisure would have been no difagreeable entertainment.

To you however I must beg leave to address it, because, of how little ufe or pleasure foever it may now be to you, to you the Present of right belongs. 'Twas you that fet me first to work 'twas you that procured me leifure in time to finish it; 'twas my affection for you and that alone, that gave me ftrength and spirit to go through with it.

FOR in the weak and unsettled ftate of health I have been in for many years, the common motives to fuch undertakings, as the importunity of acquaintance, the hopes of fame, or even the defire of promoting useful knowledge, could never have been strong enough to carry me through fo large and difficult a Work, had I not been animated by a warmer affection arising from the amiable qualities of the best of Friends, improved by a long experience and obfervation of them, and still farther heightened by a train of favours and honours received from his hand and heart.

THESE

I

THESE effects of your Friendship for me are fo much to my reputation, that you must pardon my vanity in taking this publick notice of them. Were the Treatife I prefent you with at all answerable to my ambition, it should be a lafting Monument of the Gratitude of,

ر

SIR,

Your most affectionate Friend,

and bumble Servant,

ROBERT SMITH.

PREFACE.

TH

HE first of the four Books, or the Popular Treatife, though partly intended as an Introduction to the reft, is chiefly defigned for the use of those who would know fomething of Opticks, but want the preparatory learning that is necessary for a thorough acquaintance with that Science. With this view I have here avoided all Geometrical Demonftrations, and inftead thereof have substituted that more entertaining and loofer fort of proof, that may be drawn from experiment only; and the experiments I have contrived for that end, are not only easy to be understood, but may, if the Reader pleases, be tryed with very little trouble or apparatus

By this means one who uses a little application, may find himself mafter of no inconfiderable part of the doctrine of Opticks, which is here explained in fuch a manner, as I hope may be eafy to all, and yet not tedious to more Skilful Readers, who perhaps may find here and there fomething not unworthy of their notice.

Another advantage defigned for the Readers above-mentioned is, that this Popular Treatife well understood, will be abundantly fufficient to conduct them 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 some of the firft and eafieft principles of Aftronomy.

In the third Book, befides fome curious collections belonging to the art of grinding Glaffes, drawn up and communicated by the late Hon. Samuel Molyneux Efq; I have given a full defcription of a compleat Set of Optical and Aftronomical Inftruments, according to the latest and best improvements; together with particular explanations of their several uses, when applyed to the purposes of Aftronomy, Geography, Navigation, Levelling, and other useful Arts.

And in the fourth Book I have given a compleat history and collection of Telescopical Discoveries in the heavens, felected from a great variety of books, memoirs, and obfervations of the best Aftronomers. To which I intended to have added a like collection of Microfcopical Difcoveries, but found my Work was grown too large without it.

Thus I have endeavoured to lay open a large field of Knowledge, even to perfons very moderately prepared for this fort of Learning.

Those that are better versed in Euclid's Elements, after reading the four first chapters of my fecond Book, which contain the Geometrical Elements of the whole Work, demonftrated in a short and eafy manner, may then proceed to fuch parts of it as they are most inclined to. For I have endeavoured to make all the Chapters in the four Books, and the pieces in the Remarks, as much independent on one another as I could; chufing rather to repeat a few matters in the order and form in which they occafionally presented themselves, than to trouble my readers to recur to them elsewhere in a different dress: not to mention that different views of the fame truths are seldom disagreeable to men of taste, and are equally useful to beginners with the writings of different authors upon the fame fubject.

As I generally demonftrate every thing from the first principles, the Remarks are feldom explanatory of any thing in the four Books, but are chiefly additions to them; as containing the Hiftory of Inventions and their improvements, differtations on different opinions in difficult points, confutations of errors, collections of hints, obfervations and queries, subjects enlarged upon or reconfidered in a different manner, both phyfical and mathematical, as curious and valuable as any in the four Books: and as fome of thefe pieces are pretty long, I should have printed them with a letter fomewhat larger, had the prefs been furnished with it.

As the general contents of the whole Work will fufficiently appear by the Table of the Chapters, and the particulars by the Index, I might bere conclude; but as the Reader may expect fome account of what is to be found in this Work, either of new discovery, or of improvement upon what has been delivered by other writers, I fhall here mention fome of the principal mat

ters.

1. The determination of the Focus of a pencil of reflected rays, after falling directly or obliquely on any number of plane or spherical furfaces, or of refracted rays, after passing directly or obliquely through any number of lens's of any thickness, or through different mediums having plane or spherical furfaces, is made more general and easy; by reducing it in all these cafes to the like fimple proportion, that determines the focus of a pencil after falling directly upon a single furface: and even in the Popular Treatife, I have given a plainer and fuller idea of the pofitions and relative motions of conjugate focus's along the axis of the glaffes, than what I could meet with in Books of Opticks.

2. The