3. Conceive a fluid mass (Plate LXXX. fig. 1), the particles of which attract one another, but which is sub jected to the action of no other forces, not even to that of gravity; and let an imaginary surface be traced through the fluid, having at every part a depth equal to the utmost range of the corpuscular force. Then a particle placed within the imaginary surface may be considered as occupying the centre of a sphere of the fluid, described with a radius equal to the great est distance to which attraction reaches; whence it is manifest that the particle will be urged with equal forces ih all opposite directions. If the particle be placed between the boundaries of the superficial stratum or film, the sphere of which it is the centre will extend above the fluid's surface; and, on ac count of the defect of matter, the particle will be less attracted outward than inward. Let N be a particle so situated, and suppose that a is another particle as much elevated above the fluid's surface as N is immersed below it; and trace the surface PQ in the fluid as far below N as that particle itself is below the outer boundary of the fluid mass. Then the particle N will be in equilibrium with regard to the attraction of all the fluid above PQ; but it will be urged inward by the force with which it is at tracted by the fluid below PQ; and as the particles at N and n are similarly situated with regard to the whole fluid mass, and the part of it below the sur face PQ, it is manifest that the attraction of the whole mass upon the particle at n is equal to the force which urges the particle at N inward. From this it follows, that all particles placed in a stratum which is every where at the same depth below the fluid's surface, are drawn inward with the same force, equal to that with which the whole mass at tracts a particle placed at an equal height above the fluid's surface.
If now we conceive a canal passing through the interior of the fluid, and terminating both ways in the surface, it follows, from what has been said, that the attraction of the whole mass upon the superficial drops placed at the two orifices, will propagate equal pressures in opposite directions, through the canal. In order to estimate the force of compression, we may denote, by K, the pressure inward, caused by the attraction of the whole fluid upon a square inch of the superficial film ; then a portion of the fluid within the canal will be compressed by the equal forces, K, acting in opposite directions. This is true of all portions of the fluid within the superficial stra tum; between the boundaries of that stratum the compressive force is less, being always of the same intensity at the same depth, but decreasing rapidly in approaching the surface, where it is evanescent.
We may now conceive a fluid mass, whatever be its figure, to consist of a central part, surrounded by an indefinite number of thin beds or strata, placed at equal depths below the surface; and it will follow, from what has been proved, that the compression is constant in all the central part ; and likewise that it is uniformly of the same intensity throughout every superficial stratum, varying from one stratum to another, and decreasing very rapidly near the sur.
face. Such a body of fluid will therefore be in equi librium whatever be its figure ; in other words, the corpuscular attraction will oppose no resistance to a change of figure in the fluid, nor abstract, in any de gree, the perfect mobility of the particles among one another.
It must be observed, however, that the conclusion just obtained is exact only when we confine our at tention to the direct action of the attractive forces, as is done in the theory of the figure of the earth. But there is another effect caused by the direct at traction of the particles of a fluid, to be afterwards considered, which takes place only at the surface, and from which this consequence results, that a body of fluid subjected to no forces but the attraction of its own particles, will no longer be indifferent to any figure, but will arrange itself in a perfect sphere.
A change in the temperature of a fluid mass will produce an alteration in the cohesive force ; but it appears very difficult, if not impossible, to estimate, in any satisfactory manner, the effect arising from this cause.
A variation of temperature will affect the attraction of the particles of a fluid by the change of density which it induces. When two portions of a fluid at. tract one another, if we conceive one of them to have its density changed, while that of the other re mains unaltered, it is evident that their cohesion will be proportional to the number of particles of the first portion placed within the sphere of action of the se cond ; that is, it will vary in the direct proportion of the density. Again, if we now suppose the density of the second portion to vary, the attractive force will, on this account, also suffer a proportional change. Wherefore, when both portions undergo an equal change of temperature, their cohesion will vary as the square of the density.
Again, the variations in the mutual distanoes of the particles of a fluid, caused by changes of tempe rature, must bear a finite proportion to the range of the corpuscular force; and, on this account, a change in the fluid's cohesion will take place, de pending upon the law that attraction follows in re gard to the distance. At a given temperature, and under a given pressure, the particles are separated from one another to a certain distance, at which there is an equilibrium between the attractive force which impels them towards one another, and the re pulsive power attending the action of heat. In these circumstances, the actual cohesion is due to that part only of' the whole corpuscular force which is exerted upon the particles placed beyond the limit of ap proach allowed by the given degree of temperature. The cohesion, too, is diminished not only by the de creased intensity of the attractive force, but also by the increased repulsion of heat. Our ignorance of the laws that regulate the action of these forces makes it impossible to subject to calculation the ef fect of a change of temperature ; but, when we con sider that corpuscular attraction decreases very ra pidly as the distance increases, it is extremely pro bable that the cohesion of a fluid undergoes much greater changes from this cause than from the varia tions of density.