VOL. XVII.] PHILOSOPHICAL TRANSACTIONS. Sfff 



uses of them ; the one to find the distance whereat an object being placed, it 

 shall by a given lens be represented in a species as large as the object itself, 

 which may be of singular use, in drawing faces, and other things in their true 

 magnitude, by transmitting the species by a glass into a dark, room, which will 

 not only give the true figure and shades, but even the colours themselves, 

 almost as vivid as the life. In this case d is equal toy, and substituting d fory 

 in the equation, we shall h&ve p dr f = ddr -\- dd f — dp fr, and dividing all 



by d, then pr p = dr -{- d f — P ^ ft that is — — -' = d ; but if the two con- 

 vexities be of the same sphere, so as r = p, then will the distance be ^ /> r ; 

 that is, if the lens be glass = 2r ; so that if an object be placed at the diameter 

 of the sphere distant, in this case the focus will be as far within as the object is 

 without, and the species represented will be as large as the life ; but if it were 

 a plano-convex, the same distance will be = 2pr, or in glass equal to 4 times 

 the radius of the convexity. But of this method I may perhaps entertain the 

 curious in some other transaction, and show how to magnify or diminish an 

 object in any proportion assigned, which yet will be obvious enough from what 

 is here delivered, as likewise how to erect the object, which in this method is 

 represented inverted. 



A second use is to find what convexity or concavity is required, to make a 

 vastly distant object be represented at a given focus, after the one surface of the 

 lens is formed ; which is but a corollary of our theorem for finding p, having 



r f 



p, d, r andy given ; for d being infinite, that rule becomes — -— = p, that is 



r f 



in glass — f^^ P5 whence, if y be greater than 1r, f becomes negative, 



2 r ^ J 

 r f 



and 7: — - — is the radius of the concave sought. 



Those who are wholly to begin with this dioptrical sience, cannot do better 

 than to read with attention a late treatise of dioptrics, published by W. 

 Molineaux, Esq. R. S. S. who has at large shown the nature of optic glasses, and 

 the construction and use of microscopes and telescopes ; and though some nicely 

 critical have endeavoured to spy faults, and to traduce the book, yet having 

 long since examined it with care, I affirm, that if I can judge, it has only two 

 things that with any colour may be called faults'; the one an over careful ac- 

 knowledgement of every trifle the author had received from others ; and the 

 other, that he labours to make easy this curious subject, so little understood by 

 most, in a manner perhaps too familiar for the learned critic, and which demon- 

 strates that it was written cum animo docendi, both which require but very little 

 friendship or good nature in the reader, to pass for virtues in an author. 



