174 - PHILOSOPHICAL TRANSACTIONS. [aNNO 1777. 



is supposed to be perfect, and therefore unemployed. There must be 2 other 

 circular pieces of card-paper cut out, of such sizes, that one may cover the 

 centre of the metal by completely filling the hole in the last described annular 

 piece ; and the other, such a round piece as shall exactly fit into the tube, and 

 so broad as that the inner edge may just touch tlie outer circumference of the 

 middle annular piece. It would be convenient to have these last 2 pieces so 

 fixed to an axis that they may be put in their places, or removed so easily as not 

 to displace or shake the instrument. All these pieces therefore together will 

 completely shut up the mouth of the telescope. 



Let the round piece which covers the centre of the metal, or that which has 

 no hole in it, be removed ; and, by a nice adjustment of the screw, let the 

 image, which is now formed by the centre of the mirror, be made as sharp and 

 distinct as possible. Then, every thing else remaining at rest, replace the 

 central piece, and remove the outside annular one, by which means the circum- 

 ference only of the speculum will be exposed, and the image now formed will be 

 from the rays reflr-?ted from the outside of the metal. If there be no occasion 

 to move the screw and small metal, and the 2 images formed by these 2 portions 

 of the metal be perfectly sharp and equally distinct, the speculum is perfect, 

 and of the true parabolic curve ; or at least the errors of the great and little 

 speculum, if there be any, are corrected by each other. If, on the contrary, 

 under the last circumstance, the image from the outside of the metal should 

 not be distinct, and it should become necessary, in order to make it so, that 

 the little speculum be brought nearer, it is plain that the metal is not yet brought 

 to the parabolic figure ; but if, on the other hand, in order to procure distinct- 

 ness, you be obliged to move the little speculum fartlier ofT, then the figure of 

 the great speculum has been carried beyond the parabolic, and has assumed an 

 hyperbolic form. When the latter is the case, the circular figure of the metal 

 must be recovered, after having fixed on the handle with soft pitch, by bold 

 cross strokes on the polisher, finishing it again in the manner above described. 

 If the speculum be not yet brought to the parabolic form, it must cautiously 

 have a few more round strokes on the polisher ; indeed a very few of them in 

 the manner before described make in effect a greater difference in the speculum 

 than would be at first imagined. If a metal of a true spherical figure were to 

 be tried in the abovcmentioned manner in the telescope, which I have frequently 

 done, the difference of the foci of the 2 segments of the metal would be so con- 

 siderable, as to require 2 or 3 turns of the screw to adjust them ; so very great 

 is the aberration of a spherical figure of the speculum, and so improper to pro- 

 cure that sharpness and precision so necessary to a good reflecting telescope. 



This is by no means the case with the object glasses of refractors ; for besides 

 that they are in fact never so distinct as well finishetl reflectors, the ai)ertures of 



