7G2 



BOSC'OVICH'S THEORY. 



Boscovich's 

 theory of 

 N-'urai 



l'i.l.OSO 



phy. 



Fiff 9. 



Continuity 



in reflec- 

 tion 



PlATt 



l.XV. 

 >> 10. 



and rcfraC' 

 tion. 



VlATI 



l.XV. 



rig. n. 



LQ=1, and which it communicates, by direct con- 

 course, to the ball R. Wherefore, say they, with 

 that force which it had with the velocity 2, it has 

 communicated to four balls equal to it, forces which 

 being each si, make a total of 4; and since the ori- 

 ginal velocity was 2, the forces are not as the simple 

 velocities into the masses, but as the squares of the 

 velocities. But in the theory of Boscovich this ar- 

 gument has no force. The ball A does not commu- 

 nicate a part of its velocity AB resolved into DB, 

 TB, to the ball C, and with it a part of its force. 

 There acts upon the balls a new and mutual force in 

 opposite directions, which impresses upon the one 

 the velocity CE, and BD on the other. The velo- 

 city of the former ball, expressed by BF, equal and 

 in the same direction with AB, is compounded with 

 the new acquired velocity BD, and there arises the 

 velocity BG, less than BF from. the obliquity of the 

 composition. In like manner, a new mutual force 

 acts on the balls at G and I, L and O, Q and R, and 

 the new velocities of the first ball GL, LQ, zero, 

 compose the velocities GH and GN, LM and LS, 

 LQ and QL, without either any actual resolution or 

 translation of vis viva. 



In the collision of bodies and reflected motion, it 

 may be observed, that since, by this theory, there are 

 no continuous globes, no continuous planes ; the 

 most part of the phenomena above mentioned take 

 place only perceptibly, and not with a strict ac- 

 curacy. The change of direction in impact is not 

 made in one point, but by a continued curve, since 

 the forces act at a distance, something in the way of 

 AB and DM, Fig. 10. if the forces act only by re- 

 pulsion. If there be alternate attractions and repul- 

 sions, the body will proceed by a winding course. 

 But it is still evident, that if the forces be equal, at 

 equal distances, the two halves ABQ and QDM are 

 tqual and similar. If the plane CO be rough, as 

 must be the case in nature, and as we have exhibited 

 in the Figure, this equality of forces will not take 

 place ; but if the inequalities be very small in respect 

 of the distance, the irregularity, from this cause, will 

 u!so be small; and it must be observed, that all the 

 points within the segment RTS will be in action, 

 which will render the inequality so much the more 

 imperceptible. 



In this manner one may observe, that light will 

 be reflected at equal angles, from glass sufficiently 

 polished, although the polishing matter has left some 

 small inequalities. But from surfaces, which are sen- 

 sibly rough, it must be dispersed irregularly and in 

 all directions. 



To apply the theory to the refraction of light, let 

 there be two parallel surfaces AB, CD, Fig. 11, and 

 a moveable point without them. At some distance 

 it is not acted on by any force, but, within that, is 

 urged by forces which, however, are always perpen- 

 dicular to the plane. Let it approach either of them 

 in the direction GE, with the velocity HE. Let 

 this be expressed, or, as it is usually called, resolved 

 into the two HS, and SE. After ingress, between 

 the planes, its motion will be iucurvated by these 

 forces, in such a manner, however, as not to alter its 

 velocity parallel to the planes ; but its perpendicular 

 velocity will be materially chauged. There are three 

 cases- 1st, The velocity ES may be extinguished 



somewhere in X, and then the body being reflected 

 back by the same forces, will pass oft' in XIMK ; 

 and we have the same phenomena as in Fig. 10. 

 2d, The body may pass on to CD, with a diminished 

 velocity as at O, where, taking PN=HS, but OP 

 less than SE, the angle DON is less than the angle 

 GEA of incidence. 3d, If the velocity be increa- 

 sed, then op being greater than SE, the angle Don 

 will be greater. And it will be easy to demonstrate, 

 that the sine of the angle NES of incidence, is in 

 a constant ratio to the sine of the angle of refrac- 

 tion PON. 



We shall now consider the mutual action of three 

 masses, being a more general application of the sys- 

 tem of three points. Let the three masses, of which 

 the centres of gravity are A, B, and C, act on each 

 other, with forces directed towards the centres of 

 gravity ; and first let us consider the directions of 

 the forces. The force of the point C, when attrac- 

 tive on either side, as CV, Cd, will be C e ; if repul- 

 sive, as CY, C a, it wilU>e CZ ; and the direction, in 

 cither case, will pass through the triangle, at least 

 when produced to the opposite parts, cutting in the 

 one case the interior angle ACB, and in the other, the 

 one vertically opposite. With the attractive force C V 

 towards B, and repulsive CY from A, the resulting 

 force is CX. The opposite supposition gives Cb, 

 each of which keeps without the triangle, and cuts 

 the external angle. To the first, C c, the attractions 

 BP and AG correspond, and these, with the attrac- 

 tions AE and BN, would produce the forces AFand 

 BO ; but with the repulsions AI and BR, they would, 

 produce AH and BQ. In either case the forces he to- 

 wards the same side of the line AB, and either both 

 enter the triangle tending towards it, or both of them 

 go away from it, and tend in a direction opposite te 

 that of the force Ce in respect of AB. To the se- 

 cond, CZ must correspond the repulsions BT and 

 AL, which, with the repulsions AI, BR, constitute 

 AK, BS; but with the attractions AE, BN, they 

 form AD and BM. Of these, the first pair, as well 

 as the last, lie towards the same side of AB, and the 

 directions of both, when produced backwards, enter 

 the triangle, but with contrary directions to CZ ; or 

 they go away without the triangle in opposite direc- 

 tions from CZ. Thirdly, if CX be got, which would 

 beproducedbyCV,CY,then BPand AL correspond 

 to it, and, if the first be conjoined with BN, we shall 

 have BO entering the triangle ; but if with BR, then 

 indeed BQ falls without the triangle as well as CX ; but 

 the corresponding forces AL and AI produce AK, 

 which, at least, enters the triangle when produced 

 back : wherefore there is, in every case, some one of 

 the directions which passes through the triangle; and 

 then what was said in the casos of C e and CZ, re- 

 turns respecting the other two. We have therefore 

 the following theorem : If three masses act on each 

 other, with forces directed to their centres of gravity, 

 the compound force, acting on one at least, has a di- 

 rection, which, at least, when produced towards the 

 opposite parts, will cut the internal angle of the tri- 

 angle, and enter it : The remaining tww both enter, 

 or they both avoid the triangle, and always proceed 

 towards the same parts, in respect of the line joining 

 the centres of the masses : And, in the first case, all 

 the three forces tend towards the interior of the tri- 



Boscovich'e 

 theory of 

 Natural 



Philoso- 

 phy- 



Three 



misses. 



Plate 

 l.XV. 



l'ig. 12. 



Their mu- 

 tual force*. 



