232 Mr. Arry on Achromatic Eye-pieces of Telescopes, 
much less refracted, as to emerge parallel to the red rays; and 
the object is now seen without any tinge of colour.. In a way 
nearly similar it may be shewn, that any number of eye-glasses 
may be combined so as to form an achromatic eye-piece. 
The investigations of Clairaut and D’Alembert do not relate 
to the achromatic eye-piece properly so called. These writers 
have shewn, that in certain cases a fault of the object-glass 
may be corrected by the eye-piece, and that all the rays of any 
one colour may be made to emerge parallel to each other. But 
the intention of the achromatic eye-piece is, not to make the 
rays of each colour emerge parallel to each other, (a small 
deviation from which is quite insensible to the eye), but to make 
the axes of the differently coloured pencils emerge parallel. 
Euler in the Turin Memoirs has considered at great length 
the properties of eye-pieces. But he has paid most attention 
to the correction of spherical aberration, and his formula for the 
correction of chromatic aberration is not demonstrated. The 
greater part too of his work is occupied with the consideration 
of eye-pieces of five and six lenses; which now are seldom or 
perhaps never employed. In fact, little information can be 
gathered from this paper, that is either interesting to the theo- 
rist, or useful to the workman. 
In his large work on Dioptrics he has treated the subject 
far more completely. His method (to which that which I have 
employed is in some degree similar) is this; he investigates the 
position and magnitude of every image: from the position 
and magnitude of the last image, and the position of the eye, 
he finds the visual angle; he then differentiates this, supposing 
the focal lengths of the lenses to vary in consequence of the 
variation of the refractive index for differently coloured rays, and 
he makes this variation=0. He then makes the position of 
the eye that which gives the greatest field of view, and eli- 
