Mr. W. J. M. Raukine on the Conservation of Energy. 253 



This may be otherwise expressed by saying that the potential 

 energy is the product of the distance between the surfaces of the 

 spheres, ?•, — «, into the mean attraction through that distance, 

 Ymm! 



II. The actual energy ^^^^ ^^,^,^ 



III. The total energy 



and this quantity is conserved, being incapable of change by the 

 attractive force exerted between the two bodies, whatever varia- 

 tions the distance ?•, may undergo. 



This is nothing more than what is demonstrated by Newton 

 in propositions 39 and 40 of the first book of the ' Principia.' 



The quantity above denoted by is well known to ma- 



'*' • 

 thematicians under the name of "potential function.' 



9. Besides energy, there are two mechanical magnitudes 

 which are constant in a system of bodies acted upon by their 

 mutual forces only; viz. the resultant momentum of the system, 

 and its resultant angular momentum: but these quantities are 

 purely mechanical, and their conservation in the mechanical 

 form is absolute under all circumstances, being a necessary con- 

 sequence of the equality of action and reaction ; so that they do 

 not connect mechanics with other branches of physics, as the 

 quantity called energy does*. 



10. The principle which the preceding remarks are intended 

 to illustrate may be summed up by saying that energy, or the 

 quantity which remains constant in all physical actions amongst a 

 system of bodies, is either the product of two factors — a tendency 

 or effort to produce a change, and the change throughout which 

 that effort is capahle of continuing to act, — or is equivalent to 

 such a product ; and that, consequently, no law of conservation 

 is to be looked for when one factor only of that quantity is con- 

 sidered ; such, for example, as the attraction between two bodies 

 statically measured. 



I am. Gentlemen, 



Your most obedient Servant, 

 Glasgow, March 12, 1859. W. J. Macquorn Rankine. 



* In the case of a pair of attracting hodics, the resultant momentum. 

 relatively to their common centre of gravity is always nothing. 1'hcresull- 

 ant anijular mommtum is the sum of the jiroducts made by nuiltijilying 

 each mass into twice the area swept over by its radius-vector in unity of 

 time ; and is constant, according to one of " Kepler's laws," 



