1857.] on the Conservation of Force. 355 



the use of the principle, that something remains to be discovered, 

 and to trace in what direction that discovery may lie. 



I will endeavour to illustrate some of the points which have 

 been urged, by reference, in the first instance, to a case of power, 

 which has long had great attractions for me, because of its extreme 

 simplicity, its promising nature, its universal presence, and its 

 invariability under like circumstances ; on which, though I have 

 experimented* and as yet failed, I think experiment would be well 

 bestowed : I mean the force of gravitation. I believe I represent 

 the received idea of the gravitating force aright, in saying, that it is 

 a simple attractive force exerted between any ttooor all the particles 

 or masses of matter, at every sensible distance, but ivith a strength 

 varying inversely as the square of the distance. The usual idea of 

 the force implies direct action at a distance; and such a view 

 appears to present little difficulty except to Newton, and a few, in- 

 cluding myself, who in that respect, may be of like mind with him.f 



This idea of gravity appears to me to ignore entirely the princi- 

 ple of the conservation of force ; and by the terms of its definition, 

 if taken in an absolute sense " varying inversely as the square of 

 the distance " to be in direct opposition to it ; and it becomes my 

 duty, now, to point out where this contradiction occurs, and to use 

 it in illustration of the principle of conservation. Assume two 

 particles of matter A and B, in free space, and a force in each or in 

 both by which they gravitate towards each other, the force being 

 unalterable for an unchanging distance, but varying inversely as the 

 square of the distance when the latter varies. Then, at the distance 

 of 10 the force may be estimated as 1 ; whilst at the distance of 1, 

 i.e. one-tenth of the former, the force will be 100 : and if we sup- 

 pose an elastic spring to be introduced between the two as a 

 measure of the attractive force, the power compressing it will be 

 a hundred times as much in the latter case as in the former. 

 But from whence can this enormous increase of the power come ? 

 If we say that it is the character of this force, and content ourselves 

 with that as a sufficient answer, then it appears to me, we admit a 

 creation of power, and that to an enormous amount ; yet by a 

 change of condition, so small and simple, as to fail in leading the 

 least instructed mind to think that it can be a sufficient cause : — we 

 should admit a result which would equal the highest act our minds 

 can appreciate of the working of infinite power upon matter ; we 

 should let loose the highest law in physical science which our 

 faculties permit us to perceive, namely, the conservation of force. 

 Suppose the two particles A and B removed back to the greater 

 distance of 10, then the force of attraction would be only a 

 hundredth part of that they previously possessed ; this, according 

 to the statement that the force varies inversely as the square of the 

 distance would double the strangeness of the above results; it 



♦ Philosophical Transactions, 1851, p. 1. f See Note, p. 358. 



