426 Mr. ramsden’s Defcription of 
imaginary parabolas, would demonftrate the properties 
of curves for mirrors which, placed in a telefcope, will 
fliew images of objedts perfectly free from aberration; 
or, what will yet be more ufeful in practice, of what 
forms fpecula might be made, that the aberration caufed 
by one mirror may be corrected by that of the other. If 
mathematicians affirm zdata which really exift, they mail 
fee, that when the two fpecula of a refledting telefcope 
are parabolas, they caufe a very confiderable aberration, 
which is negative, that is to fay, the focus of the extreme 
rays is longer than thofe of the middle ones. If the large 
fpeculum is a parabola, the fmall one ought to be an el- 
lipfe ; but when the fmall fpeculum is fpherical, which 
is generally the cafe in practice, if concave, the figure of 
the large fpeculum ought to be an hyperbola ; if convex, 
the large fpeculum ought to be an ellipfe, to free the te- 
lefcope from aberration. 
This will be eafier underftood by attending to the po- 
fitions of the firft and fecond images; when a curve is of 
fuch form that lines drawn from each image, and meet- 
ing in any part of the curve, make equal angles with the 
tangent to the curve at that point, it is evident, that fuch 
curve will be free from aberration. 
This is the property of a circle when the radiant 
and image are in the fame place; but when they recede 
from 
