162 Mr. Lubbock on the Double Achromatic Object Glass. 



that these data might be compared with the results given by 

 theory *. Unfortunately no such measures have yet been 

 published, as far as I am aware, except those in Sir David 

 Brewster's Encyclopaedia, under the article Achromatic Tele- 

 scopes ; but certain data are there wanting to render them 

 complete. I am informed that the universal practice in this 

 country and in France has been to make the flint lens double 

 concave, and not concavo-convex as theory indicates, which 

 circumstance seems to me very extraordinary. I am told that 

 Fraunhofer employed the latter construction; but it would seem 

 from the representation of an object glass incidentally given 

 in a plate which accompanies his paper on the lines in the 

 spectrum, that he did not do so invariably. 



LetEAorER = r AQ = A Aq = A' RP=# 



Q R is the incident ray meeting the axis A E in Q, R q the 

 refracted ray, the direction of which cuts the axis in q, 

 E the centre of the surface of which RA is a section. R P 

 is drawn perpendicular to A E. The notation employed is 

 that of Mr. Coddington's Elementary Treatise on Optics, 2nd 

 edit., p. 54. 



- sinERQsinREg = EQ .Rg __ (A— rW{(A'— AP)«+W 

 w ~" 8 inREQsinER? RQ.Eq (A'-r)V{(A-AP)*+^} 



m being the index of refraction for the substance of which the 

 lens is formed, which is bounded by the sphere of which E 

 is the centre. 



A P = cT^rxy A P = -£(l + -fA nearly 

 2r— A P tr \ kr l ) *, 



(A'- AP)» = A*-^(l + |p) +.$i'iY 



* The curvatures of the surfaces can be ascertained very correctly by 

 the Spherometer, an instrument described by M. Biot. (Traitc de Physique, 

 vol. iv. p. 343.) 



