Temperature and Molecular Attraction. 103 



reference to, the centre of mass, unless the body loses to 

 some third body some of its kinetic energy. This follows 



2e 



because if its total velocity at any point is so great as — 



s i 

 it will, as remarked under 9, necessarily follow a straight 

 line, parabola, or hyperbola, as its path, and will eventually 

 return to the infinite distance at which it started. If, there- 

 fore, the body starts from rest at an infinite distance from the 

 centre of mass, the total velocity gained by the body, due to 

 the action of the attractive force, is given by equation 11, 

 and this equation is equally true for any path (parabola, 

 hyperbola, or straight line) which the body may take in 

 approaching the centre of mass, as can be seen from equation 

 10. The statement already made under section 7 holds good, 

 therefore, under all circumstances, and is quite independent 

 of the paths pursued by the bodies during their approach; 



If two bodies under the action of Newton s law of gravitation 

 start originally at an infinite distance apart, the total amount 

 of potential energy of the ccther which mag be transformed into 

 kinetic energy by the approach of the bodies is, under all 

 circumstances, inversely proportional to the final distance of the 

 bodies from each other, and is given by the equation 



_ km^m 2 

 Fj »-~s~~ (b) 



12. From section 11 it follows that in order that a body, 

 acting under gravitational attraction, should move in a 

 circular, or elliptical, or limited linear orbit, it is necessary 

 that it should part with some of the energy which it would 

 have attained had it assumed its position in the orbit by 

 falling from an infinite distance. Since only mathematically 

 can two bodies with infinite orbits be regarded as forming a 

 stable system, we may further state : 



Any two bodies forming a stable system under the action of 

 gravitational attraction must have lost to some third body a part 

 of the kinetic energy which they obtained from the ccther in 

 assuming that position of equilibrium. 



13. The amount of energy surrendered to a third body 

 may easily be found for any particular orbit from the 

 following considerations : — 



The period of a body is the same whether it moves in a 

 circle, in an ellipse, or in a straight line, and is given by the 

 expression 



27ra 32 



P i>2=^T> ( 13 ) 



