40 Mr. W. R. Browne on Central Forces 



Lastly, the laws of the forces of cohesion, whether in the 

 interior of a molecule or between one molecule and another, 

 are unknown. 



In such circumstances, can it be held impossible that there 

 should be laws of distribution of force such that in small 

 bodies like crystals the difference in density at the centre and 

 surface should be insensible ? Lame does not attempt to give 

 any rigid proof that the uniform density of crystals (even if 

 accurately true) is really incompatible with the theory of 

 central forces. It is therefore merely a presumption, and a 

 presumption which seems seriously weakened by the fore- 

 going considerations ; it cannot therefore be allowed to have 

 any weight as against actual evidence. 



3. An objection, due to Prof. Tait, is that we have no right 

 to assume that force has any objective existence at all, or is 

 any thing more than the rate of change of motion — and that 

 in fact it cannot have an objective existence, because it can be 

 affected with a positive or negative sign. But, w r ith regard 

 to the first part of this objection, a force is defined in Mecha- 

 nics simply as a cause of motion ; and therefore the remark is 

 a mere denial of the general principle of causation. This is 

 not the place to discuss the truth of that principle; but it 

 may be observed that it is perhaps almost the only principle 

 which may claim to have been accepted by all thinkers of all 

 schools and in all ages. With regard to the second part of 

 the objection, the circumstance that a force, or rather the 

 symbol of a force, may be affected, for purposes of calculation, 

 with a + or — sign is simply due to the fact that a force 

 has a definite sense, or direction ; and that direction is one of 

 the properties of things to which the conception of positive and 

 negative may properly be applied. For the same reason lines 

 may be represented as + or — , as in algebraical geome- 

 try ; but they are not therefore regarded as non-existent. 

 Nor is direction the only fact to which the conception applies; 

 e. g. in treatises on algebra it is often pointed out that capital 

 may be taken as positive and debt as negative. Will it there- 

 fore be argued that money has no real existence ? 



4. In some quarters an objection appears to be felt to the 

 theory of central forces, on the ground that it involves the 

 conception of action at a distance, which is supposed to be 

 " unthinkable." I am not aware that the term " unthinkable," 

 which is a new one, has ever been defined. Until it has been, 

 it is impossible to say whether action at a distance is un- 

 thinkable, or whether the fact of a conception being unthink- 

 able is sufficient reason, or any reason, for holding it to be 

 untrue. 



