OF PRESSURE AND EQUILIBRIUM. 101 



will be equal to the sum of the products of 

 each separate force into the respective dis- 

 tances or variations in the lines of their 

 directions. 



Or, V^ui:zlSh', (a); 



V being the joint force, Jm the variation of the distance 

 in its direction, and ISh the sum of the quantities Sh 

 obtained by multiplying each force S by the variation of 

 the line of its direction h, §. 2. P. 7. 



Let s be the distance of the point M from the origin of 

 one of the forces aS^, and let the position of 31 be deter- 

 mined by the three coordinates a:, y, and z, and that of the 

 origin of the force by a, 6, and c ; we have then 5= >/ 



J(a:— -a)2+(y — by-\-{z—cyl, and the portions of iS 



^ fi 



acting in the directions of x, y, and z will be *S.— , 



S.~ , and S, respectively: and it is obvious that, 



s s 



if s be made to vary by the altera- 

 tion of X alone, h will be to ^x as 



X — a to 5, and -r-= . Ac- 



QX s 



cording to the mode of notation commonly adopted, the 

 coefficient of this partial variation is compendiously ex- 

 pressed by the notation ^— , though it would be more cor- 



rect to write it y- , or even j-, in order that the same 



symbol might not be employed for a partial and a total 

 variation : and it is easily found, by taking the fluxion of #, 



