172 PHILOSOPHICAL TRANSACTIONS. [aNNO 1777. 



After this has been done some time, tlie metal will begin to move stiffly as the 

 friction now increases, and the specnlum polishes very beautifully and fast ; and 

 the whole surface of the polishing tool will be equally covered over with a fine 

 metallic bronze. The tool even now must not be suffered to become dry ; a 

 single round stroke in each of your stations and turnings of the metal will be suf- 

 ficient, and the rest must all be cross ones, for we are completing a circular 

 figure. You must now be very diligent, for the polisher drying, and the friction 

 increasing very fast, the business of the spherical figure is nearly at an end. As 

 the metal wears much, its surface must be now and then cleaned, with a piece of 

 shammy leather, from the black, stuff" which collects on it ; and the polisher 

 likewise from the same matter, with a soft piece of wet sponge. You will now 

 be able to judge of the perfect spherical figure of the metal and tool, when there 

 is a perfect correspondence between the surfaces, by the fine equable feel there is 

 in working, which is totally free from all jerks and inequalities. Having pro- 

 ceeded thus far, you m^y put the last finishing to this figure of the metal by 

 bold cross strokes, only 3 or 4 in the directions of each of the 8 diameters, turn- 

 ing the metal at the same time : this must be done quickly, for it ought, in this 

 part of the process particularly, to be remembered, that if you permit the tool 

 to get quite dry, you will never be able, with all your force, to separate that and 

 the metal, without destroying the polisher by heat. The metal has now a beau- 

 tiful polish and a true spherical figure, but will by no means make a sharp distinct 

 image in the telescope : for the speculum (if it be tried in the manner hereafter 

 recommended) will not be found to make parallel rays converge without great 

 aberration ; indeed the deviation will be so great, as to be very sensibly per- 

 ceived by a great indistinctness in the image. 



Hoiv to give the parabolic figure to the metal. — In order then to give the 

 speculum the last and finishing figure, which is done by a few strokes, it must be 

 particularly remarked, that by working the metal round and round, the sphere 

 of the polisher by this means becoming less, it wears fastest in the middle : and 

 as a segment of a sphere may become parabolic, by opening the extremes 

 gradually from within outwards, so it may be equally well done by increasing the 

 curvature in the middle, in a certain ratio, from without inwards. Supposing 

 then the metal to be now truly spherical, stop the hole in the polisher by forcing 

 a cork into it underneath, about an inch, so that it do not reach quite to the sur- 

 face ; and having washed oft' any mud that may be on the surface of the tool 

 with a wet soft piece of sponge, while its surface is a little moist, place the centre 

 of the metal on the middle of the polisher ; then having, with the wet brush, 

 lodged as much water round the edge of the metal as the projecting edge will 

 hold, fill the hole of the metal and its handle with water, to prevent the evapo- 

 ration of the moisture, and the consequent adhesion between the speculum and 



