NATUEAL PHILOSOPHY. 187 



considered as a force which disappears at any appreciable distance 

 from its centre of action, and it has this character, whether we admit 

 with Newton an interruption of continuity, or prefer to have re- 

 course with Laplace to the remarkable hypothesis of forces whose 



sphere of activity does not extend to sensible distances 



Laplace thus expresses himself on this subject : After having calcu- 

 lated the pressure in a gaseous mass, bounded by a spherical envelope, 

 in accordance with the hypothesis of a repulsive force with an indefi- 

 nite sphere of activity, he shows that the law of repulsion adopted 

 by Newton is far from representing the conditions which this con- 

 stant pressure exhibits, and he then remarks : " This great geometer 

 does indeed assign to this law of repulsion an insensible sphere of 

 activity ; but the manner in which he explains its wants of continu- 

 ity is little satisfactory. We must, without doubt, admit a repulsive 

 force between the molecules of the air, which is only operative at 

 imperceptible distances. The difficulty consists in deducing from it 

 the laws of elastic fluids, and this can only be done by the following 

 considerations." These considerations take for their point of depart- 

 ure the formulas by which the mutual attraction of spherical bodies 

 is determined, and a simple change of sign enables us to pass from a 

 case of attraction to one of repulsion. 



No one will deny the necessity for this narrow limitation of the 

 sphere of activity assigned to molecular force, but must we therefore 

 conclude with Laplace that it is a special force, distinct from the 

 great forces of nature, which operates at all distances ? No. It is 

 easy to see that the repulsion due to heat, and defined by its astro- 

 nomical characters, exhibits precisely the phenomena of forces with 

 an insensible sphere of activity, although in free space it operates at 

 all distances. That which conceals the true explanation is, that our 

 minds, for a long time habituated to speculations on Newtonian 

 attraction, experience a difficulty in considering forces of a totally 

 different nature, and if we speak of repulsion we conceive of it only 

 as an attraction with a change of sign, and philosophers like Bessel 

 only see a negative attraction in the repulsion so visibly exerted by 

 the sun. But it is not so. Solar repulsion, as exhibited in the move- 

 ments and figures of comets, differs widely from a negative attrac- 

 tion, first by its successive propagation, and, secondly, that it does 

 not pass through matter as the attractive force does. It is in 

 this last characteristic that we find the key of the difficulty, and it is 

 in harmony with all the evidence collected in niy researches, and on 

 which I have had to insist so often during the last three years. For 

 if we consider the essential character of the repulsive force, we shall 

 easily perceive that it assumes in all bodies the conditions of a force 

 with an insensible sphere of activity. Each molecule of a body is in 

 fact surrounded, at an inappreciable distance, by other molecules 

 which receive its repulsive influence, and at the same time behave to 

 it like a screen. And as these molecules are not mathematical points^ 

 and as their dimensions are considerable when compared with the 

 intervals which separate them, the repulsion due to heat an 

 action of surface, exhausting itself on the surface of the body which 

 it affects - - will find itself sensibly reduced beyond the limits of 

 the molecules surrounding each centre of action. We may further 



