560 PHILOSOPHICAL TRANSACTIONS. [aNNO 1779. 



to 100, and the index i shows the motion of the screw with the wheel round its 

 axis, while the number of revolutions of the screw is shown by the divisions on 

 the same index. The steel screw r may be turned by a key, and serves to incline 

 the small mirror at right angles to the direction of its motion. By turning the 

 finger head of a screw, the eye tube is brought nearer to or farther from the 

 small mirror, to adjust the telescope to distinct vision; and the telescope itself 

 has a motion round its axis, for the conveniency of measuring the diameter of 

 a planet in any direction. The inclination of the diameter measured with the 

 horizon, is shown in degrees and minutes, by a level and vernier on a graduated 

 circle, at tlie breech of the telescope. 



The method of adjusting and using the catoptric micrometer is too obvious to 

 require any explanation: it is only necessary to observe that, besides the table 

 for reducing the revolutions and parts of the screw to minutes, seconds. Sec. it 

 may require a table for correcting a very small error which arises from the eccen- 

 tric motion of the half mirrors. By this motion their centres of curvature will, 

 when the angle to be measured is large, approach a little towards the large 

 mirror; the equation for this purpose in small angles is insensible, but when 

 angles to be measured exceed 10 minutes, it should not be neglected. Or, the 

 angle measured may be corrected by diminishing it in the proportion the versed 

 sine of the angle measured, supposing the eccentricity radius, bears to the focal 

 length of the small mirror. 



The telescope to which the catoptric micrometer is applied, is of the Casse- 

 grain construction. The great speculum is about 11 inches focus, and bears an 

 aperture of b\ inches, which is considerably larger than those of the same focal 

 length are generally made: indeed the apparent utility of this micrometer makes 

 me wish to see the reflecting telescope meet with further improvements. I believe 

 it would tend more to the advancement of the art of working mirrors, if writers 

 on this subject, instead of giving us their methods of working imaginary parabolas, 

 would demonstrate the properties of curves for mirrors which, placed in a 

 telescope, will show images of objects perfectly free from aberration; or, what 

 will be still more useful in practice, of what forms specula might be made, that 

 the aberration caused by one mirror may be corrected by that of the other. If 

 mathematicians assume data which really exist, they must see, that when the 2 

 specula of a reflecting telescope are parabolas, they cause a very considerable 

 aberration, which is negative, that is, the focus of the extreme rays is longer 

 than those of the middle ones. If the large speculum is a parabola, the small 

 one ought to be an ellipse; but when the small speculum is spherical, which is 

 generally the case in practice, if concave, the figure of the large speculum ought 

 to be an hyperbola; if convex, the large speculum ought to be an ellipse, to 

 free the telescope from aberration. 



