730 PHILOSOPHICAL TRANSACTIONS, [anNO 17Q6. 



Part 2. Of Rejection. — That bodies reflect light by a repulsive power, ex- 

 tending to some distance from their surfaces, has never been denied since the 

 time of Sir Isaac Newton.* Now this power extends to a distance much greater 

 tlian that of apparent contact, at which an attraction again begins, still at a dis- 

 tance, though less than that at which before there was a repulsion ; as will ap- 

 pear by the following demonstration which occurs to me, and which is general 

 with respect to the theory of Boscovich.-|- In fig. 4, let the body a have for p 

 an attraction, which, at the distance of ap, is proportional to pm ; then let p 

 move towards a so as to come to the situation p', and let the attraction here be 

 p'm' ; as it is continual during the motion of p to p', mm' is a curve line. Now 

 in the case of the attraction of bodies for light, and for each other, pm is less 

 than p'm', and consequently mm' does not ever return into itself, and therefore 

 it must go, ad infinitum, having its arc between ab and ac, to which it approaches 

 as asymptotes ; the abscissa always representing the distance, and the ordinate 

 the attraction at that distance : let p' now continue its motion to p", and m' will 

 move to m", and if p" meets a, or the bodies come into perfect contact, p'^m", 

 will be infinite ; so that the attraction being changed into cohesion, will be infi- 

 nite, and the bodies inseparable, contrary to universal experience ; so that p can 

 never come nearer to a than a given distance. In the case of gravity, pm is in- 

 versely as the square of ap, so that the curve nmm'" is the cubic hyperbola ; but 

 the demonstration holds, whatever be the proportion of the force to the distance. 

 It appears then that flexion, refraction, and reflection, are performed by a force 

 acting at a definite distance ; and it is reasonable to think, even a priori, that as 

 this same force, in other circumstances, is exerted to a different degree on the 

 different parts of light, in refracting, inflecting, and deflecting them, it should 

 also be exercised with the like variations in reflecting them. Let us attend to the 

 proof, which enables us to change conjecture into conviction. 



Obs. 1. The sun shining into the darkened chamber through a small hole ^ 

 of an inch in diameter, I placed a pin of ^l of an inch diameter in the cone of 

 light, 4^ inch from the hole, inclined to the rays at an angle of about 45°, and 

 its shadow was received on a chart parallel to it, at the distance of 2 feet. The 

 shadow was surrounded by the 3 fringes on each side, discovered by Grimaldo ; 

 beyond these there were 2 streaks of white light diverging from the shadow, and 

 mottled witVi bright colours, very irregularly scattered up and down; but on using 

 another pin, whose surface was well polished, and placing it nearer the hole than 

 before, the colours in the streaks became much brighter, and the streaks them- 

 selves narrower, being extended from one side to the other, so that, except in a 

 very few points here and there, no white was now to be seen; and on moving the 

 pin, the colours moved also. But they disappeared if the pin was deprived of its 

 polish, by being held in the flame of a candle, or if a roll of paper was used in- 

 * Optics, book '.!, part 3, prop. 8. -f Nova Tlieoria Philosophise Naturalis. — Orig. 



