fwo new Micrometers. 427 
from each other, of an ellipfe, of fuch form that the 
radiant and image are in the two foci, till one diftance 
becoming infinite the ellipfe changes into a parabola, 
and to an hyperbola when the focus is negative ; that is 
to fay, when reflected rays diverge, and the focus is on 
the oppofite fide of the mirror. 
Thefe principles made me prefer Cassegrain’s con- 
ftruCtion of the reflecting telefcope to either the Grego- 
rian or Newtonian. In the former, errors caufed by one 
fpeculum are diminilhed by thofe in the other. 
From a property of the reflecting telefcope (which 
has not been attended to) that the apertures of the two 
fpecula are to each other very nearly in the proportion 
of their focal lengths, it follows, that their aberrations will 
be to each other in the fame proportion, and thefe aber- 
rations are in the fame direction, if the two fpecula are 
both concave ; or in contrary directions, if one fpeculum 
is concave, and the other convex. 
In the Gregorian conftruCtion, both fpecula being con- 
cave, the aberration at the fecond image will be the fum 
of the aberrations of the two mirrors; but in the Casse- 
grain conftruCtion, one mirror being concave, and the 
other convex, the aberration at the fecond image will 
be the difference between their aberrations. By afluming 
fuch proportions for the foci of the fpecula as are gene- 
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