157 



on each annulus, and the quantity of motion communicated 

 by that pressure; seeing it must be, as the number of par- 

 ticles the annulus contains that are moved; i. e. as its area. 



But the resistance to the force impressed on any annulus, 

 being as the quantity of pitch to be put in motion by it, 

 will be diflferent, not only as the annulus is nearer to, or 

 farther from, the margin of the polisher, but difterent, also, 

 as this has either one margin only, or two, i. e. when the 

 poUsher is entirely covered with pitch, or when it has a 

 space left uncoated at the middle; which latter always is, 

 and must be the case, when the great mirror of the Gre- 

 gorian telescope is to be polished, which has a perforation 

 at its center. 



First. When there is no vacant space in the middle:, the 

 resistance to the several annuli Avill be as the circumambient 

 spaces only; because, the pitch not being compressible, it 

 is only into these, and not towards the center, it can, in 

 yielding to the force or weight of the mirror, extend itself, 

 by lateral motion : and the space, surrounding any annulus, 

 is the difference between the circular area of the polisher, 

 and that inscribed in the annulus ; and is, relatively to the 

 rest, measured by the difference of the squares of their 

 radii, viz. of the distances of the edge 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, consequently, the resistance 

 to it, and reaction, exceed that which is impR-ssed: on 



which 



