70 Royal Astronomical Society. 



some degree, however small, its figure. A pressure, certainly far 

 less than that which a wooden polisher will exert, is capable of pro- 

 ducing this injurious effect. 



" It is, then, to be expected, that when a speculum has been re- 

 ceiving its final figure under any pressure, there will be some, 

 however slight, recession from that figure when the pressure is re- 

 moved ; and if so, the remedy obviously is to diminish successively , 

 by counterpoises, the weight of the polisher as the figure and polish 

 are advancing, till it ultimately moves, in giving the last finishing 

 strokes, without any more pressure than the cohesion between the 

 polished and sliding surfaces affords. It may also be expected that 

 the lustre and perfection of the polish itself will be enhanced, inas- 

 much as the size of the abraded atoms will then be at their minimum, 

 since they diminish in a direct ratio with the diminution of pressure 

 by the abrading surface. 



" In the machine to which these observations refer, the pulley 

 which drives one excentric rod is made to differ slightly in diameter 

 from its fellow, with which it is connected by the endless band, 

 which gives motion to the other excentric rod ; so that the centre of 

 the polisher, by their joint action, is constrained to describe curves, 

 varying from nearly a straight line to ellipsoids having a minor axis 

 equal to twice the thrust of the shorter excentric ; and the parabolic 

 figure is attained by the maintenance of a certain proportion, found 

 experimentally, between the throws of these two excentrics. This 

 proportion, for a speculum having an aperture of one inch for each 

 foot of focal length, and under the action of a polisher of the same 

 dimensions as the speculum, is one-third of the diameter of the spe- 

 culum for the longer, and one-seventh for the shorter thrust ; the 

 figure of the speculum receding towards a spherical figure if that 

 shorter thrust be diminished, or advancing to the hyperbolic curva- 

 ture if it be increased. 



" The counterpoises, then, it is suggested, should be added suc- 

 cessively, and at those periods in the action of the machine when it 

 may be considered that its tendency to give a parabolic figure is at 

 its maximum ; that is, when, by the combined action of the excentric 

 pins, the centre of the polisher is describing the widest ellipsoids on 

 the speculum. A bent wire is so placed, as an index, on the excen- 

 tric rod, that its point, traversing a scale fixed in any convenient 

 position, shows the exact moment when these widest ellipsoids are 

 being described : at those intervals the counterpoise-weights are 

 successively added, so that the polisher may be considered to pass 

 through complete cycles of its action under each alteration and dimi- 

 nution of pressure. 



" Attention to these conditions has, in specula finished by the 

 machine, apparently been entirely successful, both hi obtaining an 

 exceeding fine polish, and a figure which does not sensibly deviate 

 from the parabolic. 



" A nice attention to the quantity and purity of the water used in 

 the polishing is also of much importance. A very convenient method, 

 which, being self-acting, requires no particular care during the pro- 

 cess, is to fix a small vessel on the excentric rod, with a thread de- 



