(534 PHILOSOPHICAL TRANSACTIONS. [aNNO 1 67 1 . 



A brief summary of these optical lectures the author himself delivers in an 

 epistle to a friend, when he says, that in them he endeavours to promote that 

 part of optics which he undertakes to treat upon, first by explaining and esta- 

 blishing its principles ; then by deriving from them some useful consectaries, 

 serving to the explication of the phaenomena : in the mean while attempt- 

 ing to correct some common errors, and to supply some principal defects 

 therein. 



Towards these ends, he first examines the received hypotheses of this 

 science, showing how they should be understood, and how far admitted. Hav- 

 ing settled the hypotheses, he first draws from them some general corol- 

 laries, partly before acknowledged by others, and partly observed by himself; 

 all confirmed by his own demonstrations. Then proceeding to more special 

 matters, he prosecutes distinctly catoptrics and dioptrics, both plain and sphe- 

 rical. And slightly passing over plain catoptrics, he more largely insists on 

 spherical catoptrics, propounding such theorems, whereby the intersections 

 and the limits of reflected rays are declared, and also the appearing places, 

 or images of points radiating both from a great (and as it were immense) dis- 

 tance, and from a distance sensibly near, are determined, both in respect of an 

 eye placed in the axis of the radiation, and in respect to one placed without 

 that axis any where ; which particulars he had not observed to be truly and 

 diligently handled in any book extant. 



Then he raises a theory concerning both plain and spherical dioptrics, as- 

 suming for a ground that rule concerning the measure of refractions men- 

 tioned by M. Descartes, and which now most writers do admit, and which 

 he judges agreeable to truth, which yet he knows not that any writers have ap- 

 plied to this purpose, so as to have raised any competent superstructure there- 

 on. And here orderly, first in respect to plain, then to spherical surfaces, 

 considering points radiating from a distance so great that their rays may be 

 su[)posed to fall parallel to one another on the refracting surface, he propounds 

 some theorems, from which the chief symptoms of refracted rays do result, 

 their interjections and limits are easily discernible ; the appearing places or 

 images of such points are defined, both in regard to an eye situated in the axis 

 of the radiation, and in regard to one placed elsewhere. Then he prosecutes 

 in like manner the same things in respect to points radiating from a distance 

 sensibly finite or near hand. And that the use of these things may be more 

 ready, and serviceable to practise, he subjoins distinctly and particularly the 



self. After his death appeared the tliree following, Mathematicae Lectiones habitae in scholis acade- 

 miae Cantab, and Lectio in qua tlieoremata Archimedis de sphaera et cylindro, &c. also Isaac! Barrow 

 opuscula, viz. Determinationes, Condones ad clerum, Orationes^ Poemata, &c. 



