38 Prof. W. A. Norton on the Fundamental 



ton has shown that if the law of elementary action be that of the 

 inverse squares, the attraction of such a homogeneous sphere for 

 an element exterior to it is the same as if the whole mass were 

 concentrated at the centre, The demonstration involves the 

 supposition that equal portions, however small, of each spherical 

 layer are occupied by equal quantities of matter. The principle 

 demonstrated holds good for every distance of the element at- 

 tracted from the surface — except that at very minute distances, 

 not many times greater than the distance between two contiguous 

 molecules of the earth's mass, it may happen that two lines di- 

 verging from the element in question under a small angle will 

 not actually contain within them any matter on the immediately 

 contiguous portion of the earth's surface, and as a consequence 

 the entire attraction of the first spherical layer would be repre- 

 sented by that of its mass concentrated at a point slightly more 

 remote than the centre. The result would then be that, in the 

 case supposed, the entire attraction exerted by the earth would 

 be slightly less than the Newtonian deduction. It follows, 

 therefore, that if the element at the supposed minute distance 

 (d) from the earth's surface were to approach the surface, the 

 entire attraction it would experience would not be sensibly 

 greater, would in fact be less than at the distance (d); whereas 

 the attraction of adhesion that would actually come into play is 

 immensely greater than the simple force of gravity near the sur- 

 face. We thus demonstrate that the attraction of gravitation can- 

 not be the force of molecular attraction operating at greater dis- 

 tances, either as a whole or in its elements; and accordingly 

 show that the law of inverse squares proved for gravitation can- 

 not be extended inferentially, or by any process of reasoning, to 

 the force of elementary attraction at minute distances. 



The same important conclusion may be reached more directly 

 in another way. The enormous excess of the attraction of adhe- 

 sion or of cohesion at distances a little greater than the distance 

 between contiguous molecules, over the force of gravity at the 

 distance (d) above specified, can only be attributed, from Pro- 

 fessor Bay ma's point of view, to a greatly increased attraction of 

 the molecules lying at or near the earth's surface. Now the 

 number of separate lines that can be drawn from the element 

 attracted through attractive elements so situated is incalculably 

 small, we may say insensibly small,, in comparison with the num- 

 ber that can be drawn through more remote elements which by 

 their united action determine the force of gravity ; and hence the 

 attraction of adhesion should be incalculably small in comparison 

 with the force of gravity. 



It may here be incidentally remarked that, unless the position 

 just taken can be proved to be untenable, it must be admitted 



