PARALLEL FORCES are those forces which act upon a body in directions parallel to eaclt other. Every body, being an assemblage of separate particles, each of which is acted on by gravity, may thus be considered as impressed upon by a system of parallel forces. The following demonstration will exhibit the mode in which the amount and position of the resultant force are found: Let P and Q be two parallel forces acting at the points A and B respectively, either in the same (fig. 1), or in opposite (fig. 2) directions; join AP, and in this line, at the points A and B, apply the equal and forces S and S, which counterbalance each other, and therefore do not affect the system. Find 31 and N (see COMPOSITION AND RESOLUTION OF FORCES), 111d ants of P and S, and Q and S respectively, and produce their directions till they meet in D, at which point let the ants be resolved parallel to their original directions; then there are two equal forces, S and 8, acting parallel to AB, but in site directions, and thus, as they counterbalance each other, they may be removed. Then there remain two forces. P and
'Q, acting at D, in the line DC, parallel to their original directions, and their sum (fig. 1) or difference (fig. 2), represented by 11, is accordingly the resultant of the original faces at A and 13. To the position of C, the point in AB, or AB produced, through which the resultant passes, it is necessary to make use of the well-known property denominated the triangle of forces (q.v.), according to which the three forces S, 31, and P arc tional to the lengths of AC, AD, DC, the sides of the triangle ADC; then S: P:: AC : CD, similarly Q : S :: DC : CB, therefore Q : P AC : BC, and Q f P or It : P:: AC ± BC or AB : BC, from which proportions we derive the principle of the lever,