Mr. Barlow on the Refracting Telescope. 3 



duce the entire achromatic correction in a tube one-eighth only 

 of the length of the telescope, and of one eighth of its aperture. 

 In order to illustrate the above view of the subject, let 

 / + S/= the focal length of the red ray. 

 / = ditto mean ray. 



f df = ditto violet ray. 



In any positive lens, let also 



/' + ^/', /',/'-<*'/'. 



represent the same quantities in another lens, having a different 

 index and dispersive power, where S, $ denote the dispersions 

 of the red ray in the two media, and d and d ' those of the 

 violet ray. In most cases we consider = d, and ^ = d' ; it 

 is not so, however, in all cases, and I propose therefore at pre- 

 sent to give this generality to the notation. 



Confining now our investigation to one side oply of the 

 spectrum, as for example the red, and considering the second 

 lens as negative, we have, when the two are in contact, 



-- = reciprocal 



focus of the red ray, and 



i 



-i, _L = 4 - = reciprocal focus of 



/ 



the mean ray. 

 Consequently 



/a + *> -/a + *) /'-/ 



coloured focus ; and this therefore, being divided by the mean 

 focus, gives 



(i + > + y + y)Cr-/) _ 1 = di ion of 



/(I + &')-/(! + S) 



the compound lens, which after reduction, and denoting this 

 dispersion by A, becomes 



f*(i + n -/yg + v = A (1) 



/d + ^O -/(I + 5) 

 And here it is obvious, 



1. if / : / :: i + U' : y + iy 



we get A = 0, and it becomes the common double achromatic 

 object-glass ; in which ^ being very small, the proportion is 

 generally given as 



B 2 



