5'90 SSLAflON OP ¥fi@ LAW of GRAVlTAflOisr TO ¥ltg 



kmount of work Would be done, involving tlie expenditure of att 

 indefinitely great amount of energy : which, on the principle of the 

 Conservation of Energy, is impossible. Consequently, either that 

 principle must be abandoned, or the law of gravitation must, when a 

 certain limit is reached, undergo transformation. 



2. ^Positive ahd Negative Energy. 



I shall limit myself to the consideration of the simple system 

 described in the last paragraph — ^namely, a system, of two particles, 

 Pand Q, whose masses are m and n, and which fall towards one 

 another u.nder the influence of their mutual attraction from positions 

 of rest A and £. To these positions we may suppose them first to 

 have ascended (their centre of gravity remaining stationary) from 

 positions C and D, where they had the velocities v and u. I speak 

 of the particles as in their ascending course when they are moving 

 apart from one another, and as in their descending course when 

 they are falling towards one another. After reaching A and JB, where 

 their velocities have been reduced to zero, P and Q fall back to C 

 and D, 



The velocities v and u, Which P and Q have in the positions C 

 and D, are reduced to zero when the particles have ascended to A. 

 and £. The work done, or energy expended, in the reduction of 

 these velocities from v and u to zero is represented by ^ {mv^ -f~ nu^). 

 The energy so expended may be called negative, because the expen- 

 diture of it tends to lessen the distance between the particles. In 

 ascending, then, from C and D to A and B, the negative energy 

 of the system, available for lessening the distance between the 

 particles, has been diminished by |- (mw^ -)- nu^) ; that is to say, it 

 has been converted into energy in some other form, which we may 

 Gall positive energy. 



The particles, having ascended to A and B, immediately fall back 

 to C and • D. How has the negative energy of the system been 

 affected by this 1 To produce the fall, the same expenditure of . 

 negative energy was required as took place in the ascent from C and 

 D to A and B. In both cases the negative energy was operating in 

 the way of lessening the distance between the moving particles- 

 Hence, when P and Q have arrived at C and D in their descent, 

 the negative energy of the system has been still further diminished, 

 find the positive energy increased, by ^ (mv"^ -j- nu'^)^ 



