240 How to find the -Focus of a Sphere. [Book lit. 



The points Qjmd q will be on the oppofite fides of 

 their refpeftive foci. The greater QF is, the lefs will 

 be qf, and vice verfa ; and the apparent places of ob- 

 jects viewed through thefe glaffes will be found in the 

 fame manner as with fingle furfaces. It will be fuffi- 

 cicnt therefore only to refer the reader to Plates XIX. 

 XX. Fig. 36, 37. which he will eafily undcrftand with- 

 out farther explanation. 



The principal focus of a fphere is found with the 

 fame facility as that of a 'lens. Let M (Plate XX. 

 Fig. 38.) be the principal focus of rays incident on the 

 convex fufface A O, then bifed M D in I, and I will 

 be the principal focus of the fphere. For let the my 

 G A be refracted by the convex furface to B, and at. 

 B by the concave fufface to I, and let IB,- G A pro- 

 duced meet each other in K. Now iuppofe that the 

 ray A B within the fphere emerged at both places A 

 slnd B, then fihce the 4 angles of incidence C AB, C B A 

 are equal, the angles of refraction, and the difference 

 between the angles of incidence and refraction, will 

 be equal; therefore KAB is equal to KB A, and K A 

 equal to K B ; but the triangle BIM is fimilar to the 

 triangle K B A, therefore I B is equal to I M j and as 

 B approaches to D, the nearer will I B be equal to ID,- 

 that is, I D to I M, and confequently the principal fo- 

 cus will bifedt D M* or the leaft diftance of the princi- 

 pal focus of rays refracted by the convex furface from 

 the fphere. 



Having thus found the principal focus of the fphere, 

 I mail leave the reader to find the apparent places of 

 objects feen through it, as the mode to be purfned has 

 already been fufHciently dcfcribcd, and the proportion 

 is fimiiar to that difcovered in the confidenmon of 

 Jenfes. 



