IN THE DOUBLE ACHROMATIC OBJECT-GLASS. 561 



ill terms of the radii and distances; and then performino- the required 

 differentiation, we find, for ^.tan R,q,3I,, tlie same expression as we have 

 just obtained for ^(D- D'), as we clearly ought to do. 



To enable us to judge of the value of the new correction, it is 

 necessary to apply it to a case which may arise in practice. For this 

 purpose I have chosen the third case in Sir John Herschel's table in 

 tiie paper before referred to; as the dispersive ratio in that case is 

 what he considers the mean value for such glass as is usually obtained 

 in England. I have also considered the radii of the interior surfaces 

 to be the same, tlieir difference being little more than a fiftieth of an 

 inch in three feet, so that we have for our data for a telescope of ten 

 feet focal length, as follows: 



M = 1.524, 

 m' = 1.585; 



h 



whence 7^^, = . 53743, 



;•, = 6.7069 feet, 



r2 = l{3. 0488 + 3. 0640}, 



= 3.0564, 

 r,= - 14.2937. 



If we take, now, the same dimensions, for our example, as tliose 

 of the Northumberland telescope recently put up at the Cambridge Ob- 

 servatory, in which the focal length is 19 feet, the aperture 11^ tnches, 

 the thickness of the double convex crown lens ^ inch at the edge, and 

 that of tlie concave flint lens 1 inch, we must take the radii of the 

 surfaces in proportion to the focal length, and thus have 



r, = 12.74311 feet, 

 r,= 5.80716, 

 /•3= -27.15803, 



