170 Mr. Lubbock on the Double Achromatic Object Glass. 



a, = ir?ii;*H2?- a/)} 



_ (2m+l) , , ct „ 



• 7l to + 2 J * J] "*" w + 2- 72 



m 1 * («-!)« (A, + /.)« ff 1 L-WJL _ I_\' 



" r 'y 2 ('«+2)»!(m-l)*A/\W»'A3 Aj+^Aas A 2 + * 3 ' 



+ (i 4 -iA 3 )(4 4 -x ) ) 2 } = - 



Supposing / 3 = *04, or about half an inch, — - = — -1. 



*^4 



I find — = / 3 = --24389 L = /« = -'034.94; 



and after the numerical substitutions the equation for deter- 

 mining / becomes 



f* - -28015/, = --012113, 



which equation gives 



/ = - -05348, instead of — -051265, which was the value 

 when the interval between the lenses was neglected. 

 With this value of/, I find 



r, aa 6-429 and r 2 = 3-2268, 

 instead of r, = 6*7069 and r 2 = 3-0488. See p. 168. 



It appears to result, therefore, from calculation, that the in- 

 terval between the lenses influences materially the perform- 

 ance of the telescope, which indeed is well known to be the 

 case practically. In consequence it would, I think, be desirable 

 to possess a table similar to Sir John HerschePs Table 4. 

 Phil. Trans. 1821, p. 261, calculated for some given interval 

 between the lenses, as half an inch, for instance; such a table, 

 combined with that which Sir John Herschel has given, would 

 afford the means of interpolating for any interval likely to 

 occur in practice, and hence of obtaining in any case accurate 

 values of the curvatures which ought to be given to the four 

 surfaces of the lenses which compose the object glass. 



In p. 163, I have left the term multiplied by ?/ 4 , with a view 

 to facilitate the appreciation of the magnitude of this quantity 

 in the amount of aberration. In order to ascertain what aper- 

 ture a telescope will bear before this term introduces confu- 

 sion into the image, it would be necessary previously to know 

 what variation in the focal length (or aberration) the eye 



