of the Eye-pieces of Telescopes. 21 



7th. A single eye-glass to produce the same effect must have 



'" CC'C'C'" 



a focal length n,n'> n,„ =Mx 2,l6, and, therefore, its smallest value 



of Q would be -^ X ,2896. 



These instances will probably be sufficient, as exemplifying the 

 application of the formulae and as giving results of some practical 

 value. It appears at first somewhat curious that (as in Ex. 3.) the 

 spherical aberration of one lens should correct that of another, 

 when the ray is received on the second before its intersection with 

 the axis of the lens. This may be explained nearly in the same 

 way as the correction of chromatic aberration by the same con- 

 struction (Cambridge Transactions, Vol. II. p. 231.). The ray 

 converging to a point nearer than that to which, without sphe- 

 rical aberration, it would converge, is incident on the second lens 

 at a point where the refracting angle is so small that it emerges 

 in a direction parallel to that which it would have had if there 

 had been no aberration. Of the mutual correction of aberration 

 in the more complicated eye-pieces, a similar explanation may 

 be given. 



Having considered the course of the axis of a pencil of rays, 

 I shall now consider the convergence of the rays in each pencil. 

 In general, the rays of a small pencil diverging from a point, after 

 refraction by a lens do not converge to a point, but pass through 

 two straight lines in different planes. To elucidate this, suppose 

 in Fig. 3, one ray AF of a pencil, diverging from a point in the axis 

 of the lens BC, to be refracted in the direction GE ; then another 

 ray at a very small distance from ^F, in the plane perpendicular 

 to the i>aper, and passing through JF (which we shall call the 

 perpendicular plane), will also converge to E; that is, two rays 

 in the perpendicular plane meet at E. In the same manner, it 



