Those that are wholly to begin with this Dioptrical Science, cannot do better than to read with Attention a late Treatise of Dioptricks, published by _W. Molineux_, Esq, R. S. S. who has at large shewn the Nature of Optick Glasses, and the Construction and Use of Microscopes and Telescopes; and though some nicely Critical have endeavour'd to spy Faults, and to traduce the Book; yet having long since examin'd it with Care, I affirm, that if I can judge, it hath but two things that with any Colour may be call'd Faults; the one, an over-careful acknowledgment of every Trifle the Author had receiv'd from others; and the other that he labours to make easie this curious Subject, so little understood by most, in a manner perhaps too familiar for the _Learned Critick_, and which demonstrates that it was writ _cum animo docendi_, both which require but very little Friendship or good Nature in the Reader, to pass for Vertues in an Author. [Illustration: _Tab. 5. pag. 359_] But to return to our first Theorem, which accounting for the thickness of the _Lens_, we will here again resume, _viz._ (_mpdrρ - ndρt + nprρt_)/(_mdr + mdρ - mprρ - m - ndt + nrt_) = _f_. And let it be required to find the _Focus_ where a whole Sphere will collect the Beams proceeding from an Object at the distance _d_: Here _t_ is equal to _2r_, and _r_ equal to ρ. And after due Reduction, the Theorem will stand thus, (_mpdr - 2ndr + 2nprr_)/(_2nd + 2nr - mpr_) = _f_; but if _d_ be Infinite, it is contracted to _mpr_/_2n_ - _r_ = ((_2n - m_)/(_2m - 2n_))_r_ = _f_, wherefore a Sphere of Glass collects the Sun-Beams at half the Semi-diameter of the Sphere without it, and a Sphere of Water at a whole Semi-diameter. But if the _Ratio_ of Refraction _m_ to _n_ be as 2 to 1, the _Focus_ falls on the opposite Surface of the Sphere; but if it be of greater Inequality it falls within. Another Example shall be when a Hemisphere is exposed to parallel Rays, that is, _d_ and ρ being infinite, and _t_ = _r_, and after due Reduction the Theorem results (_nn_/(_mm - mn_))_r_ = _f_. That is, in Glass it is at 4/3_r_, in Water at 9/4_r_; but if the Hemisphere were Diamant, it would collect the Beams at 1-4/15 of the _Radius_ beyond the Center.