140 



hollowed into a different and irregular curvature, in the 

 intermediate tract. 



For these inconveniences, however, arising from the un- 

 equal friction of the polisher, there are the following easy 

 and adequate remedies; which will, in the sequel, be 

 more fully explained, and applied as in practice, to effect 

 the decree of curvature, or any correction of the same, 

 which may be requisite. 



First. Since the curvature of the mirror ought to be 

 gradually reduced towards its edges, which can only be 

 effected by an increase of friction in the corresponding 

 part of the polisher; and that this latter effect is to be 

 produced in any part of it, by enlarging the surrounding 

 coat of pitch; it follows, that, for this purpose, the breadth 

 of the polisher must be enlarged above that of the mir- 

 ror; and this in the same degree, as the curvature of the 

 mirror is to be diminished; so. that the polisher is to be 

 of greatest breadth, for a mirror of an hyperbolic, and 

 least, for one of a spherical figure. This, however, is to 

 be done, under the limitations hereafter mentioned. 



Secondly. To preserve the regular gradation of cur- 

 vature towards the middle of the mirror, the uncoated 

 space, at the center of the polisher, should be contracted 

 to a certain limit, which will be defined; though, for the 

 reasons above-mentioned, it can never be filled up alto- 

 gether. 



Thirdly. Vvhere the resistance and friction of the 

 pitch, in anj tract on the face of the polisher, is com- 

 puted 



