326 On the Equililrium of a Comlination of Blocks, 



and by retaining the letter g for the representative centre 

 o^ graviiy of the similar trianiiles of which S is at one of 

 the angles in fig. 2; the lettero, for the intersection of the 

 vertical line dniun through g, with the line SB, SC. SD, 

 &c. and V, for the intersection of the same vertical witU 

 the \mcSd,Sc,Sd, 8cc. 



That is to say, if the blocks are applied to each other ia 

 iig. 3, so that the base line of the trianuie in each shall 

 have a position parallel to its representative in lig. 2, the 

 iinilual forces arisinij from their siraviiv and the resistance 

 of the abutments wifj keep them in equilibrio; because the 

 line SB, which is proportional to one of the forces that 

 lieep the block AB in equilibrio, is also the same which is 

 taken to represent the opposite force which helps to sustain 

 the block BC; action and reaction being equal and oppo- 

 site, — so SC is taken for one of the forces which keep the 

 block BC in equilibrio; as it is also for one of those which 

 leep the block CD in that state, — and so of the rest. 



To find the centre of gravity of the frame. 



From A, fig. 3, in the direction of the sustaining force 

 there (being parallel to SA, fig. i^) draw A^'. From C, in 

 the direction of the sustaining forces there (being parallel 



to SC, fig. 2,) draw C c, till it intersect the line A/ in c. 

 In like manner proceed to draw lines from D, E, F and G, 

 in directions of the forces actine; at those points (being re- 

 spectively parallel to SD, SE, SF, and SG, fig. '■2) which 



will intersect the line A ^, at the points d,e,f, and g. 



From these intersections let fall vertical lines c o, dp, e q, 



fr and g s. In the vertical co will be found the centre of 

 gravity of the two blotks AB and BC. 



For it is known by mechanics, that if a number of bodies 

 be sustained in equilibrio by two forces, tlieir directions 

 must intersect each other in a vertical line thai passes 

 through the common centre of gravity of the bodies. 



It will also be found in the line ah joining their respec- 

 tive centres of gravity; and the intersection o of these lines 

 will be the common centre of gravity of the two blocks. 

 Also, for similar reasons the centre of graviiy of the three 



blocks A to D will be in the vertical dp; it will also be in 

 the line which joins the common centre of gravity of the 

 two first blocks, and that of the third CD, and at the in- 

 tersection p of these lines 'vill be the centre of gravity of 

 the three first blocks. In like maimer the centre of graviiy 



of 



