42 REFLECTING TELESCOPE. 



the number oi" parlicles the annulus contains that are moved ; 

 i. e. as its area. 

 This resistance But the resistance to the force impressed on any annulus, 

 may be raised, being as the quantity of pilch to be put in motion by it, will be 

 different, not only as the annulus is nearer to, or farther from, 

 the margin of the polisher, but different, also, as this has either 

 one margin only, or two, i. e. when the polisher is entirely co- 

 vered with pitch, or when it has a space left uncoated at the 

 middle ; '^^hich latter always is, and must be the case, when 

 the great mirror of the Gregorian telescope is to be pohshed, 

 which has a perforation at its center. 

 —by talcing First, When there is no vacant space in the middle :' the 



The'^Jurface of resistance to the several annuli will be as the circumambient 

 tjie pitch at spaces only; because, the pitch not being compressible, it is 

 proper places. Q^Iy into these, and not towards the center, it can, in yielding 

 (o the force or v/eight of the mirror, extend itself, by lateral 

 motion: and the space, surrounding any annulus, is the diffe- 

 rence between the circular area of the polisher, and that in- 

 scribed in the annulus : and is, relatively to the rest, measured 

 by the difference of th.e squares of their radii, viz. of the dist- 

 ances of the edg6 of the polisher, and that of the annulus, from 

 the center. But since, in this case, the bodies (of pitch) are 

 unelastic, there can be no augmentation of motion ; nor can 

 the quantity of motion and action communicated, and, conse- 

 quently, the resistance to it, and reaction, exceed that which is 

 impressed : on which account, I imagine, that the resistance to 

 the several annuli is to be taken as proportional to the pres- 

 sures they sustain, and measured by them, i. e. by their magni- 

 tudes or areas, or the number of particles in them, to which a 

 motion is imparted ; which were stated to be as their respec- 

 tive radii or distances from the center : and, consequently, I 

 suppose the resistance to be the inverse of this, or as the 

 distances of the anntili from the outer edge of the polisher; 

 which distances measure the direct resistance, or the quantity 

 of pitch, to which equal motion, with that in the respective 

 annuli, is communicated. 

 KfTcct of a cen- -^nd from hence it follows, that, if a mirror, previously 

 tral hole, ground to a spherical figure, were to be polished on such a 



polisher as this : the resistance and friction of the pitch, being 

 greatest, and increasing to a maximum at the center, and 

 diminishing towards the extremity, would wear down and 



