1820.] Mathematical Principles of Ckemical Philosophy. 185 



Prop. 5. — If equal cylinders be formed of particles of equally- 

 attractive matter, their cohesive force will be reciprocally as the 

 diameters of these particles. 



For by prop. 2, the cohesion will be as the diameters of these 

 particles, and since in a given area the number of equal circles 

 that can be described is reciprocally as the squares of their 

 diameter, the number of points of contact in equal sections of 

 these equal cylinders will also be reciprocally as the squares of 

 the diameters of the particles ; and by compounding these 

 ratios, we obtain that of the inverse diameter of the particles. 



Cor. 1. — If the centripetal force vary, the cohesion of the 

 equal masses will be as the centripetal force directly, and the 

 diameter of the particles inversely. 



Cor. 2. — All that has been proved of spheres will equally apply 

 to any other solids, which are formed by the revolution of any 

 curves of finite curvature, and which return into themselves upon 

 their axes. 



ScholiiDii. 



Since the assumption of spherical atoms may be objected to 

 ty some, I have thought it proper to demonstrate generally that 

 ail sohds, as spheroids, &.c. excepting those that have plane 

 surfaces, will present the same phenomena ; yet the sphere is 

 that which seems most properly adapted to all cases. We have 

 a good example of the operation of magnetical attraction in pro- 

 ducing an effect precisely similar to cohesion in the following 

 experiment ; present an iron sphere to one pole of a magnet, it 

 will adhere with such force as will enable it to sustain a consi- 

 derable weight ; cover the pole with goldbeater's skin, or other 

 exceedingly thin lamina of matter : the tendency of the sphere 

 to the magnet will be considerable, but w'ill be verv little 

 increased, by being brought into contact with the film, when it 

 will be found to sustain much less weight than before. In this 

 experiment we observe that when the lamina is interposed, the 

 tendency of the whole sphere will be very little diminished, 

 since its thickness is almost insensible, compared with the dis- 

 tance between the centre of the sphere and the centre of attrac- 

 tion of the magnet ; the difference between the forces with 

 which the sphere adheres to the magnet before and after the 

 interposition of the lamina can arise only from the attraction of 

 the points of contact when in contact, being in one case added 

 to the whole tendency of the sphere, but being removed in the 

 other ; and magnetical attraction is reciprocally as the square of 

 the distance. 



It has been demonstrated, prop. 4, that the effects of cohesion 

 will result, according to whatever inverse power or root of the 

 distance the centripetal force be supposed to vary ; and in prop, 

 1, it has been particularly demonstrated, when the force is sup- 



