OF THE COHESION OF TLUIDS. 333 



mass, or the number\)f particles contained in it. Now the 

 centre of gravity of a spherical surface is situated in the 

 middle of its absciss or verse sine, since the increments of 

 the surface are proportional to those of the verse sine (183). 

 Hence it follows, that the joint force of all the particles in 

 each surface is half what it would be, if they were all 

 situated in the given direction : and the proportion being 

 the same for all the concentric surfaces, it must also remain 

 the same for the whole hemisphere. If we had only to 

 consider the attractions of a series of particles, situated 

 in a circular circumference, upon a central particle, it 

 might be shown, in a similar manner, that they would be 

 together equal to that of a number of particles represented 

 by the chord, supposed to be placed at the middle of the 

 arc. 



Scholium 2. If any of the elastic fluids, with which 

 we are acquainted, be considered as thus constituted, we 

 must suppose the fourth power of the distance r to vary 

 inversely as the density d, since the force V is found to 



F TT 



vary simply as the density, and — = — - dc* Mf is constant. 



It would have been more natural to expect, that if c were 

 not constant, its cube c' would have varied inversely as 

 the density, supposing the number of particles cooperating 

 to be given. But in the Newtonian demonstration the 

 elementary force /is also supposed to vary inversely as the 

 distance, while the number of particles cooperating is in- 

 variable. In this case the number of particles in the space 

 Mu are as dMu, and the elementary forces as dh, the va- 

 riations of the distances, for a given value of ^u, being as 

 i, so that the products of these quantities remain con- 



