Dr. Roget on a Violation of the Law of Continuity. 119 



The simpler illustrations of this law are obvious, and must 

 readily occur to those who seek for them ; but it is important 

 to familiarize the mind to them, with a view of preparing our- 

 selves for the inquiry to what extent the principle admits of 

 being carried, and whether it be really, as it is pretended, a uni- 

 versal law. It appears to obtain without exception in all those 

 physical changes of situations, qualities, and conditions, which 

 are connected with one another by their mathematical rela- 

 tions. All the forces and powers of nature vary by a con- 

 tinuous gradation from one period of time to another, or un- 

 dergo differences of degree at different parts of space, without 

 suffering any abrupt transition at any one point. Continuity 

 is an attribute common to the law of gravitation, which acts 

 at a distance, as well as to the laws of the corpuscular forces, 

 of which the sphere of operation is limited to insensible di- 

 stances, and which give rise to the phaenomena of cohesion, of 

 elasticity, and of all chemical combinations and decomposi- 

 tions. It belongs equally to the forces concerned in the phae- 

 nomena of electricity and of magnetism. As the law of each 

 of these forces may be expressed by some mathematical func- 

 tion of the distance at which they operate, so the same con- 

 tinuity must continue to pervade and characterize all the ef- 

 fects which can result from them, either when exerted singly, 

 or in combination. The motions of bodies may in every case 

 be regarded as the aggregate of the motions of every one of 

 their particles ; and the motions of any single particle, as well 

 as of an aggregate of par tides, produced by a continuous force, 

 must be itself continuous, not only with regard to augmenta- 

 tions or diminutions of velocity, momentum, mechanical force, 

 &c, but also with regard to the spaces they traverse, and the 

 lines they describe in space. No deflection from a perfectly 

 rectilineous course can take place but by infinitely small de- 

 grees ; or, to express it in geometrical language, the line of 

 motion cannot pass into any curve, of which that line is not 

 the tangent at the point where the change of direction begins; 

 far less, therefore, can a motion in one right line, suddenly 

 pass into a motion in another right line, which forms any angle 

 whatsoever with it. All angular motions are therefore ex- 

 cluded by the law of continuity, according to which abrupt 

 transitions, either of velocity or direction, are physical impos- 

 sibilities. The apparent violations of this law in the effects of 

 the collision of elastic bodies, or their reflection after impinge- 

 ing on hard surfaces, and even the phaenomena of the refrac- 

 tion and reflection of the rays of light, are shown by Bosco- 

 vich to be really all in perfect conformity with the law of con- 

 tinuity. 



Not 



