356 MifceUanea Curiofa. 



p d ? r 



equal Spheres, then will be 



d r -+• d f — /> r ? 



/> d r 



reduced to — / • and in cafe d be infi- 



id—p r J 



nite, then it will yet be farther contracted to 



n 



I p r, and p being = ■■ ■ the focal diftance 

 m — • », 



in Glafi will be = r, in Water 1 i r, but in 

 Diamant \ r. 



I am fenfible that thefe Examples are too 

 much for the compleat Analyft, though I fear 

 too little for the lefs Skilful , it being very hard, 

 if poifible, in fuch Matters, fo to write, as to 

 give fatisfa£tion to both ; or to pleafe the one, 

 and inftrucT: the other. But this may fafrice 

 to mew the extent of our Theorem, and how 

 eafie a Reduction adapts any one cafe to all 

 the reft. 



Nor is this only ufeful to difcover the Focus 

 from the other propofed dam, but from the Focm 

 given, we may thereby determine the diftance 

 of the Object ; or from the Focus and Diftance 

 given, we may find of what Sphere it is requi- 

 fite to take another Segment, to make any 

 given Segment of another Sphere caft the 

 Beams from the diftance d to the Focus f. As 

 likewife from the Lens^ Focus , and Diftance 

 given, to find the Ratio of Refraction, or of 

 m to w, requifite to aniwer thofe Data. All 

 which it is obvious , are fully determined 

 from the Equation we have hitherto ufed, 

 p d$r = d rfHr d §f — f r sf 9 for to find d 



fx if 



The Theorem is ■ =s d, the 



r f Hr f f—p %r 

 diftance of the Objeft. For 



