244 



Rev. J. B. Emmett on the 



[April, 



nates vary inversely as the highest power of the abscissa, will 

 either lie wholly between the other curve and the common axis, 

 or will intersect it in one point. 



Lemma 3. — If the force of attraction vary inversely as any 

 power of the distance, and there be two equal and parallel 

 planes ; when the distance between them is very small, their 

 mutual attraction varies as the same power of the distance 

 inversely, the force belonging to the surface only. 



This follows from lib. 1, Prop. 90, Newt. Princip. by placing 

 instead of a corpuscle at P, a plane parallel to D L, and making 

 the distance A P very small. 



Cor. 1. — If the force of such planes be finite at any finite 

 distance, it will be infinite in contact. 



Cor. 2. — The same applies to spheres of indefinitely small 

 magnitude, the force belonging to the surface only ; in contact 

 it will not be infinite. 



Prop. I. 



When the particles of a solid are separated by the force of 

 heat, they remove to such a distance from each other, that the 

 force of attraction at that distance balances that of repulsion, 

 and the body becomes fluid. 



Let A C be two equal 

 and similar particles of 

 matter; while they are in 

 contact with each other, 

 the force of cohesion ex- 

 ceeds that of repulsion; 

 let the repulsive force of 

 heat be increased until it 

 overcomes the cohesion ; 

 the particles will separate 

 (Lemma 1), but the force of cohesion is indefinitely greater than 

 the attraction of the particles at the least possible distance, and 

 vanishes when contact of the particles ceases ; therefore A and 

 C become repulsive. Join A C, and bisect A C in B ; describe 

 the curve DFH such that its ordinates are as the forces of 

 attraction at the distances represented by their respective 

 abscissa? ; at K erect the perpendicular E K, and D K is the 

 entire force of attraction at K, except cohesion. Take E K to 

 D K, as the force of repulsion in contact is to that of attraction, 

 and describe the curve E F I such, that its ordinates F G are 

 always as the force of repulsion ; that is, as the density of the 

 calorific atmospheres at B ; this curve approaches A C niore 

 rapidly than the former, but E K is by the hypothesis greater 

 than J) K ; therefore (Lemma 2), the corves will intersect each 

 othsr, or the forces will be equal at some given point F ; let fall 

 the perpendicular F G, and the particles will be in equilibrio at 





