OF THE COHESION OF FLUIDS. 335 



For the interior parts of the fluid, the actions of all the 

 particles will be the same as in a fluid of unlimited extent, 



that is, ^ c^Mfy calling the density unity, since its finite 



o 



variations do not enter into the present question. But for 

 the particles within the distance c of the surface, the forces 

 will be able to act on such a number of other particles only, 

 as are contained in a segment of the sphere, of which the 

 verse sine is c-\-Xf the distance from the surface being jr, 

 which are not only fewer than in the whole sphere, but are 

 also at a smaller mean distance from the centre. 



Each of these segments may be divided into two por- 

 tions ; that which is contained between the centre and the 

 spherical circumference, and the cone, which lies between 

 the centre and the plane surface : the variation of the mean 

 distance of the former will be the same as for the whole 

 sphere ; but for the cone, instead of the variation belonging 

 to that of the corresponding portion of the sphere, which 

 will be expressed by the product of its content into ^ of 

 the variation of the radius, we shall have the content of 

 the cone into the variation of its mean distance, or 



— (c2— a;2) X mto \ . — that is, — {c^—x^) x — , 



o c^ — X" u xy 6u 



instead of 2crc(c — x) ~ into \c — -, or ^ (c* — c^x) 5-, the 



difference being — -(3c*— 4c-''a:-f x*) --, for each particle at 

 u ou 



the distance x from the surface ; and in order to find the 



total difference for the whole stratum, we must multiply this 



bv the fluxion of x, and find the fluent, which will be — • 







(3c*^---2c^x^ -fio:^) -or, when:r=c,-^.f c^l^^ rz^c^ -^, 



