REFLECTING TELESCOl'P.. 41 



tides among themselves : so that the coat of pitch, pressed, 

 on each side, between the parallel surfaces of the mirror and 

 polisher, will, by their force, be equally extended laterally in 

 every direction ; by which an equal quantity of motion will 

 be communicated to all its particle : since no particles, except 

 those at the extremities, can move, without protruding others, 

 and these, the rest, successively, as if the mass were a fluid 

 body. 



But, though all parts of the surface of the polisher receive an —but with dif- 

 equal pressure and motion, all do not exert an equal degree of a^^^g^^t'^^i-ff^r- 

 resistance to that pressure : for those parts, that cannot move ent parts of the 

 without displacing and overcoming the resisting tenacity of a surface. 

 greater quantity of the surrounding mass of pitch, than other 

 parts do, must oppose the greater resistance to the mirror, as 

 having that of the other parts superadded to their own. For 

 ascertaining this, the force impressed, and the quantity of 

 pitch, confining any annular tract of the polisher, should b? 

 computed. In the present case, where the coat of pitch is a 

 thin equal statura, of circular form, we need regard only its su- 

 perficial dimension, and consider all parts of it as alike situated 

 in the above respect, which are equidistant from the center, or 

 from the outer edge of the polisher. 



To this purpose, let the surface of the polisher be conceived Deduction of 

 to be composed of an indefinite number of concentrical zones or ^f^^gactio'^^r* 

 annuli. Each of these will sustain an uniform pressure, from pressure. 

 the mirror, proportional to its area, because, the force im- 

 pressed on the mirror, and its attraction to the polisher, is 

 equally diffused on it. The areas of these annuli, taken sepa- 

 rately, are the differences of the two circles, whose periphe- 

 ries inscribe and circumscribe each of them ; and they axe. 

 consequently to each other, as the differences of the squares of 

 their diameters, or as those of their radii ; and the series of 

 them taken, in order, from the center to the extremity, are 

 strictly as a rank of figurate numbers proceeding from unity, 

 viz. the odd number 1, 3, 6, 7, &c. But, since their breadth 

 is supposed to be infinitely small, they may betaken as propor- 

 tional to their mean diameters or radii, i. e. as their distances 

 from the center of the polisher ; which distances will, therefore, 

 represent the pressure on each annulus, and the quantity of 

 motion communicated by that pressure j seeing it mustbc>.a& 



