250 



Rev. J. B. Emmett on the 



[April, 



Sect. III. On Gaseous Bodies. 



Lem?7ia. 



In distances from the particles 

 of bodies, such, that the in- 

 crease of density of the sur- 

 rounding caloric is very small 

 compared with its entire density. 

 If the force of attraction vary 

 inversely as the nth power of 

 the distance, and the elastic 

 force of caloric be as its density, 

 the repulsive force of the calo- 

 rific atmosphere will be inverse- 

 ly as the n — 1th power of the 

 distance. 



Let A P Q be a particle of 

 matter ; produce the radius A S 

 indefinitely ; describe the curve 



DLI, such that its ordinates B D, K L, &c. perpendicular to 

 B S, shall be proportional to the force of attraction at B, K, &c. 

 Let this particle be immersed in an uniformly diffused elastic 

 medium, whose density is B F ; at remote distances A, K, the 

 pressure on K : pressure on k : : S k : S K. 



Through the point F draw F H parallel to B S, and if the 

 medium were not attracted by A P Q, its density at all points 

 A, K, B, 8cc. would be equal to B F. Take C indefinitely near 

 to B ; the specific gravity of the elastic medium at B is as B D 

 x B F ; therefore its pressure atCisasBD x BF x BC; 

 if this pressure be indefinitely less than the whole elastic force 

 of the fluid, its density will be increased by this pressure, by a 

 quantity which is indefinitely small, compared with the whole 

 density, or the fluid may be considered as incompressible by 

 the force acting upon it. At the point K, let the density K M 

 be increased by the superincumbent pressure, by the quantity 

 M O, and let M O be very small compared with K M ; through 

 k draw k o parallel to K O, and O o parallel to K k ; the evanes- 

 cent area K m will be less than the evanescent area K o by the 

 indefinitely small area M o ; therefore the pressure K L x KM 

 x K'A is less than the pressure KL x KO x K k by the 

 quantity K L x M O x K k, which is indefinitely small when 

 compared with either ; therefore the pressure at k will be inde- 

 finitely nearly equal to the sum of all the several pressures K L 

 x K k x B F, C E x B C x B F, &c. ; that is, as the area 



i 

 k B D I x B F. Let the force of attraction be as -r-^- and the 



