Ottaviano-Fabrizio Mossotti

“ By supposing, indeed, that the mutual repulsive action between the particles of matter is, by a very small quantity, less than that between the particles of the electric fluid, a small balance would be left in favour of the attraction of neutral bodies for one another, which might constitute the very force which operates under the name of gravitation ”

“ If several material molecules, which mutually repel each other, are plunged into an elastic fluid, the atoms of which also mutually repel each other, but are at the same time attracted by the material molecules, and if these attractive and repulsive forces are all directly as the masses, and inversely as the square of the distance, it is proposed to determine whether the actions resulting from these forces are sufficient to bring the molecules into equilibrium, and keep them fixed in that state. ”

“ As the quantity of æther diffused through the immensity of space may be considered as infinite, the atmosphere formed by each molecule for itself is always the same, and its density is only superadded to that which the æther in the same places owes to other causes. According to the nature of the molecular actions, the value of the coefficient should be considered as very great: hence it follows that the density of each atmosphere will be incomparably greater when quite near or in contact with the molecule, and will decrease very rapidly as its distance from the molecule increases. ”

“ If then, with the equilibrium of the fluids, it is desired to find the equilibrium of the masses also, an equal repulsion must be allowed between the molecules; since the bodies would otherwise forcibly attract each other. But such an attraction is contrary to what we learn from experience. He felt at first a strong objection to the admission of such a repulsive force between the material molecules, as being opposed to the idea entertained of their mutual attraction, which was so clearly demonstrated on Newton's principles. ”

“ As the resistance opposed by bodies to compression increases indefinitely with the reduction of their volume, though their molecules have not come into contact with each other, it shows that the force which they exercise is repulsive at the least distances. At a distance greater than these, but still imperceptible, it must vary with great rapidity, and become attractive, in order that a steady equilibrium of the molecules may be possible ”

“ The study of the phænomena of nature has led philosophers to consider bodies as being composed of molecules held in a state of fixed equilibrium at a certain distance from each other. Such a state requires that they should be endued with a certain action. ”

“ If the density of the æther into which the molecules are plunged, or the quantity , becomes greater, the density q given by the equation (6) will increase also; that value of which will satisfy the foregoing equation will consequently become greater, and the molecules will fix themselves in equilibrium at a greater distance. We see in this result that the æther performs the functions of caloric, and that it is to its greater or less density we are to ascribe the temperature and volume of the body. ”

“ If several bodies, being electric conductors, are placed in presence of each other, and thus attain a permanent state, the result of the actions of the layers of electric fluid which cover them, and of the exterior layers of matter which are not yet neutralized, on the electric fluid at a point taken anywhere in the interior of a body, must, in that state, be null ”

“ On my return to Europe I learned, through the reading of some memoirs, and in the course of conversation with men of science, that the attention of geometers was particularly directed to the molecular forces, as being those which may lead us more directly to the knowledge of the intrinsic properties of bodies. ”

“ To apply the formulæ which we have found, for the purpose of representing molecular action, to the phænomena of the interior constitution of bodies, requires methods of calculation which are not yet developed, and which must become still more complicated when the arrangement of the molecules, their form and their density, are taken into consideration. ”

“ The equations which we have just found are those which must take place in case of equilibrium, or in the natural state of a body composed of spherical molecules, if Franklin's hypothesis respecting statical electricity may be applied to the constitution of bodies also. The form in which the equations present themselves shows that this equilibrium takes place exactly as if there existed between each pair of molecules a reciprocal action, in the direction of the straight line which would join their centres of gravity, and would be represented by ”

“ If we conceive this change made, the expression for will be of the same form as that for marked (V) ′, except that , , and will be replaced by , , , and , and , , by , , . Let us then, by approximation, introduce into the differential instead of the coordinates (, , ) of the surface, the coordinates (, , ) of the centre considered as constant; if we perform the integration, which is done by substituting the volume for , the term which stands under the sign in the first of the equations (II) will be represented by . ”

“ When in some particular cases the integrations of the preceding formula shall have been performed by substituting its expression in the equation (III) , the functions and will be determined by comparing them with those of the same order introduced by means of the different expressIons for ; so that this equation may become identical. All being thus determined, the densty given by the formula (2) will be known. ”