VOL. LXVII.] PHILOSOPHICAL TRANSACTIONS. iSS 



known by the great equality there is in the feel while you are working, and by 



which an experienced workman will form a pretty certain judgment; having 



proceeded thus far, you may then try your metal, and judge of its figure by this 



more certain manner. Wash the hone-pavement quite clean; then put the 



metal on the centre of it, and give '2 or 3 light strokes round and round only, 



not carrying however the edges of the metal much over the hones; this will take 



out the order of straight strokes: then having again washed the hones, and 



placed the speculum on their centre, with gentle pressure, slide it towards you 



till its edge be brought a little over that of the hones, then carry it quite across 



the diameter as far on the other side, and having given the metal a light stroke 



or two in this direction, take it off the tool. The metal being wiped quite dry, 



place it on a table at a little distance from a window; stand yourself as near the 



window, at some distance from the metal ; and looking obliquely on its surface, 



turn it round its axis, and you will see at every half turn the grain given by the 



last cross strokes flash on your eye at once over the whole face of the metal. 



This is as certain a proof of a true spherical figure as the operose and difficult 



method described in Dr. Smith's Optics; for as there is nothing soft or elastic, 



either in the metal or in the hones, this glare is a certain proof of a perfect 



contact in every part of the two surfaces; which there could not be if the spheres 



were not both perfect and precisely the same. 



Indeed there is one accidental circumstance which necessarily affords its aid in 

 this and every business of the like sort, and that is, that a concave and convex 

 surface ground together, though ever so irregular at first, will (if the working 

 be uniform and proper, consisting, especially at last, of cross strokes in every 

 possible direction across the diameter) be formed into portions of true and equal 

 spheres; had it not been for this lucky necessity, it would have been impossible 

 to have produced that correctness which is essential in the speculum of a good 

 reflecting telescope by any mechanic contrivance whatever. For when it is con- 

 sidered, that the errors in reflection are 4 times as great as in refraction, and 

 that the least defect in figure is magnified by the powers of the instrument, any 

 thing short of perfection in the figure of the speculum would be evidently per- 

 ceived by a want of distinctness in the performance. It must however be 

 observed that both in forming the tools and at last figuring the metal (and indeed 

 the same must be observed in the future process of polishing) that no kind of 

 pressure is used that may endanger the bending or irregularly grinding them; 

 they should therefore be held with a light hand, and loosely between the fingers, 

 and the motion given should be in a horizontal direction, with no more pressure 

 than their own dead weight. 



• The polishing of the speculum is- the most difficult and essential part of the 

 whole process; for every experienced workman knows, to his vexation, that the 



