of the Law of Mariotte, with Corrections^ Sfc. 337 



had one which showed, that the prop, is true in general, if 

 it is so in any particular case, and that case could easily be 

 derived from experiment. However, in re-considering the 

 subject, I discovered the true demonstration, first proving, 

 from the theory, Mariotte's law, or the 4th prop, in the 

 paper, and then the 2nd as a corollary ; therefore, instead 

 of the 2nd and 4th propositions please to insert as the 2nd 

 the following, which, with the 1st cor., includes them both : 

 the rest of the paper will then remain good, making only 

 one or two very obvious changes in the references. 



Before introducing the new proof, it maybe observed, 

 that in fig. 1, p. 273, the inner concentric spherical vessel 

 V P W is supposed such as to confine the tenacious atoms, 

 but to admit a perfectly free communication to those of the 

 ethereal class. Now, it will easily be seen, that a certain 

 number of tenacious atoms in the inner vessel will form a 

 concentric spherical mass; and, when the number is such, 

 that this sphere has a less radius than that of the vessel, 

 there will be no compression of the tenacious atoms by the 

 re-action of the surface V P W, the density of the tenacious 

 atoms, at that surface, being in this case nothing. But 

 when a greater quantity is introduced, there will arise a 

 compression from the re-action of the surface, preventing 

 the extension of the sphere of tenacious atoms. 



Prop, 2. (prop. 4 of the paper.) If the pressure atT on the 

 exterior vessel, fig. 1 , be given, and a body of tenacious atoms 

 in the inner vessel be compressed by a force, as at the piston 

 P, but such, that the tenacious atoms may be kept apart by 

 intervening ethereal matter ; then, the compressing force at 

 P will vary as the density of the body of tenacious atoms. 



For, suppose the increment of density produced by an 



increment of the compressing force to be divided into a 



number of equal parts, and the increment of pressure into 



the same number of parts, such, that taken in order from 



the beginning, each shall produce one of the equal parts of 



the increment of density : let the number of these parts be 



increased, and, consequently, their magnitude diminished 



without limit. Then, taking u for the compressing force, 



and X for the density, the ultimate, or nascent ratio of the 



d u 

 increments will be -, — in which d x is constant, since all 

 d X 



VOL. IV. 2 



