1820.] Mathematical Principles of Chemical Philosophy. 187 



substances are highly insoluble, the only use of the water is to 

 keep them in some measure separated, by which means they will 

 have freedom of motion, and can arrange themselves in that 

 order in which their mutual attraction has a tendency to place 

 them. 



Also by pressure coarsely powdered sulphur cannot be made 

 to cohere into a mass, but when finely pulverized, or sublimed, 

 the impalpable powder, by moderate pressure, will form a mass, 

 having considerable hardness. By carefully examining these 

 experiments, we find that by diminishing the diameter of the 

 small masses or parts of which any mass of matter is composed, 

 the cohesive force of the whole mass is increased, which it 

 should be by prop. 5, but the cohesion of any two particles is 

 diminished, which coincides with prop. 2, since however hard 

 it may be a very moderate degree of friction will be found to 

 remove some particles from its surface. We also find that the 

 cohesive force vanishes when the particles are removed to the 

 least possible distance from contact, as is proved by breaking 

 the mass, which will not cohere again by being joined : this 

 coincides with prop. 1 and 4. 



Since some may yet suppose that some other force besides 

 that which varies reciprocally as the square of the distance is 

 concerned in producing the phenomena of cohesion, it may not 

 be improper to show that a force which varies inversely as a 

 higher power of the distance will not answer the conditions. 

 Suppose it to vary reciprocally as the cube of the distance, and 

 the force of the whole sphere or particle to be finite, at a finite 

 distance from contact, then, Princip. lib. 1 . prop. 81, Example 2, 

 when the corpuscle P is placed in contact with A (see fig. 7, 

 prop. 4), the whole force becomes infinite, which does not 

 coincide with the observed phenomena, and in this case its 

 influence must be observed in its eftects upon the planetary 

 motions. Let the force be such that at any finite distance from 

 A the attraction of the whole sphere is insensible, or indefinitely 

 small, in which case the attraction of any finite part of the 

 sphere is but finite, when P is placed in contact with it, suppos- 

 ing the particle P to coincide with a finite part of the spherical 

 surface ; but when the corpuscle is in contact with the sphere, 

 by lemma 1, the points of contact will be indefinitely less than 

 any finite magnitude ; consequently the force is indefinitely 

 small ; and since the attraction of the whole sphere = 0, when 

 P A has a finite ratio to A B, by the hypothesis, the attraction 

 of each of the figures E^j m p, which is not in contact with P, 

 and consequently of their sum, or the whole sphere, excepting 

 the point A, is = ; therefore, upon this supposition the cor- 

 puscle is attracted only by the point A, which has been proved 

 to attract it with a force which is less than any finite force. 

 The same may be demonstrated, if the force be supposed to vary 



