PRINCIPLE OP THE CONSERVATION OF ENERGY. 591 



To record these results in a convenient manner, the following 

 symbols may be employed. The distance between A and £ being r, 

 and that between C and D being x, let the negative energy of the 

 system, when the particles are at G and I) in their descending course, 

 be JY (r, x) ; and the positive, P (r, x). Then, according to the 

 explanations given, 



]V (r, x) = N (r, r) — -| {mv'^ -\- nv?), 

 P (r, x) = P (r, -r) -\- | [mv^ -\- nu^). 

 And, by addition, 



JSJ- (r, x) -^ P (r, x) = N (r, r) -\~ P (r, r) = q; 

 •where N' (r, r) -\- P (r, r), which we represent by q, expresses the 

 total amount of energy conserved ; while N (r, x) and P (r, x) are 

 the parts, whose variations at every instant neutralize one another. 



3. — How THE Dependence of the Accelerations of P and Q on the Relative 

 Quantities oi^ the Two Energies is to be Conceived. 



We might, if we pleased, conceive each of the two kinds of energy 

 as operating effectively at every instant in producing its appropriate 

 result. In this case equal quantities of the two energies would neu- 

 tralize one another ; and the resultant effective energy would be the 

 ■difference between iV (r, x) and P (r, x). 



According to another mode of conceiving the subject, one of the 

 two energies alone would be effective at a particular instant, the other 

 lying in the meantime latent. Thus, in the career of P and Q which 

 we have traced, the negative energy alone would be conceived as effec- 

 tive, the positive being in a state of latency, from which, however, it 

 is destined in due season to come forth into effectiveness. 



I adopt the latter of these two modes of conception. It will be 

 understood, then, that effective and latent energy are distinguished 

 from one another, the negative being effective when the positive is 

 latent, and' the positive effective when the negative is latent ; neither 

 energy ever rising beyond q, the maximum effective energy of the 

 system. 



4. — Negative and Positive Jars. 



By way of figure, we may represent to ourselves the negative and 

 positive energies as contained, apart from one another, in two jars. 

 A certain part of the energy may flow from the negative into the 

 positive jar, or from the positive into the negative ; but the entire 

 quantity in the two jars always remains the same. 



