364 PROCEEDINGS OF THE AMERICAN ACADEMY § 3 



Hence no force can explain the laws of cohesion which is 

 not capable of varying, inversely, as a power of the dis- 

 tance which is greater in some cases than four at least, 

 and less in others than 2^. It would therefore appear that 

 the law of universal gravitation, which requires a variation 

 at great distances according to the inverse square, cannot 

 explain the phenomena of cohesion; neither can an}' force 

 which disappears completely in the state of vapor. 



We have seen the conditions required by the considera- 

 tions of the preceding sections. The only forces known 

 to physics which can by any possibility satisfy them are 

 those involving both attraction and repulsion, that is, po- 

 larity in some form.* 



There is, however, a possibility of error in the result of 

 any reasoning, no matter how many facts may have been 

 gathered to support it; and in most minds there will be 

 found an unwillingness to limit in any way the application 

 of such a general truth as the law of universal gravitation, 

 the beauty of which, if it could be adapted to the explana- 

 tion of the laws of cohesion, would be admitted by all. It 

 is to answer this objection, and to prove, once for all, that 

 the law of universal gravitation can never explain the 

 phenomena in question, that the following proof is added 

 of a proposition which might be considered self-evident. 



Let us suppose that the attraction between different par- 

 ticles varies inversely as the A^th power of the distance; 

 then the potential will vary inverse!}' as the x — i^^ The 

 potential at the common centre of a series of nearly spheri- 



* It is true that, in one sense, the law governing all forces, properly so called, is fundamentally 

 the same, being reducible to elements attracting or repelling inversely as the square of the 

 distance ; nevertheless, in effect, forces are essentially different. 



Two small systems of electrified points, neither being charged as a whole, will in general 

 attract each other inversely as the fourth power of the distance. Small circular currents or 

 electric vortices will do the same; and this is also the law for small magnets under certain 

 conditions. (See Maxwell, Volume II., ^ 388.) Arranged in different ways, two particles of 

 magnetized matter may attract inversely as the square, the fourth power, or again 

 inversely as the seventh power of the distance; and the probable resultant of an indefinite 

 number of such particles will be found to vary inversely as some power between the fourth 

 and fifth of the average distance bet^veen them. 



