336 APPENDIX A, 



aDd for the lengths, ~ c%, while the force of the whole 

 Jo 



stratum, of the thickness c, would have been -^ c^c, substi- 



o 



tuting c for M in article 385, and the deficiency is to the 

 whole force as -^ to i, or as 1 to 5). 



Corollary. If the cohesive force C and the repulsive 

 R be in equilibrium for the whole fluid considered as incom- 

 parably greater in thickness than c or r, the diff'erence of 

 the forces with regard to the superficial stratum on each 



side only, will he-~'-^(c^C—r^R): now it has been shown 



that c^C^=:r*i2, consequently c^C—r^R=:c*C{c~r), and 



the joint deficiency in the cohesive force will be — . — c^C 



5 3 



i-ii) 



c y 



( 



Corollary 2. The deficiency being positive when 

 c is greater than r, it follows that if the superficial cohesion 

 prevail in a fluid so constituted, it must be because r is 

 greater than c and the defect is greatest with regard to the 

 repulsive force. In such cases the fluid must be slightly 

 condensed in its interior parts, so as to produce a resist- 

 ance equivalent to the excess of cohesion of the surface. 



Corollary 3. These conclusions are applicable, with 

 slight modifications only, to the case of a repulsion like 

 that of elastic fluids, as assumed by Newton. For we 

 have only to take r equal to the radius of the actual mean 

 sphere of action for the fluid in any given state of com- 

 pression, and the superficial deficiency of the force will be 

 very nearly as determined by this proposition, the distance 

 r becoming in this case somewhat smaller than the whole 

 extent of the sphere of action. The utmost possible cohe- 



