120 



Transactions. 



Fig. 1. 



As the rays of light 

 from the heavenly 

 bodies may be practi- 

 cally taken as parallel, 

 it is evident that this 

 is the theoretical 

 figure for the specula 



of reflecting telescopes, for then only can all the rays of light be reflected to 

 one point {F). 



It will be observed that this curve, near its vertex, approaches to, although 

 it cannot perfectly coincide with, the figure of the sphere. 



Now as this curve is a varying one it is clear that no grinding and 

 polishing can mathematically produce the parabolic figure ; but as the curve 

 in a sphere is invariable, therefore the spherical figure is first imparted to the 

 ordinary speculum, and this is then modified empirically so that it sliall 

 approach to the parabolic figure. 



In this manner specula have been constructed whose diameters eqnal one- 

 sixth of their focal length, but as the parabolic curve rapidly departs from the 

 spherical it is evident that reflecting telescopes of large aperture on the 

 ordinary construction must be of great length and cumbrous in their manage- 

 ment. There is also a difficulty in giving them a perfect and durable polish, 

 and then mounting them so that they shall neither be afifected by changes of 

 temperature nor deflection of different parts, from their great weight. 



The telescope here described has been constructed with a view of sur- 

 mounting some of these difficulties ; its speculum may be said to be cast in 

 Nature's mould, as its figure is determined by the action of those " Laws of 

 Motion," the truth of which were enunciated, and their universality demon- 

 strated by Newton. 



Let any liquid be rotated in a vessel, with a given velocity, on an axis 

 which has been adjusted perpendicular to the horizon. After a short time all 

 the forces will be in equilibrium, and the fluid will assume a fixed position. 

 As the surface is free to move, it must, at every point taken upon it, be 

 perpendicular to the resultant of the forces acting upon it at that point. 



Let the curved line (Fig. 2) be a section of the 

 rotating surface made by a plane passing through 

 N V, the axis of rotation. 



Let P be any point taken on it. If P M be drawn 

 at a right angle to the vertical axis N V, it is 

 evident that during the motion of the point P will 

 describe a circle in a horizontal plane whose centre 

 is M. In consequence of this circular motion, a 

 Fig. 2. centrifugal force will be developed, pressing against 



