S24: On the 'Equililriunt of a Comllnation of Beams f 



Draw a vej-tical line ACE, &c. fig. 2. on which set oflT 

 AB, BC, CD, &c. proportional to the weights of the blocks 

 rcspectivelv, and in the order in which thev are to he 

 placed \n eqijilibrio ; on the portions AB, BC, CD, &c. of 

 this line as bases erect triangles similar to the oritiinal ones 

 on the blocks, so that the vertices of these similar triangles 

 be on the remote or on the proximate side of their bases, 

 in respect of S, as, on the blocks they are above or below 

 the base lines ; (S beinp; on the same side of the vertical 

 line AG, as the block AB is on in respect of the other 

 blocks) ; and so that the vertex a, which on the block AB 

 is nearer the point B than A, shall, in the erected triangle, 

 fig. 2. be nearer the point A than B ; so that the vertex b, 

 which on the block BC is nearer B than C, shall in the 

 erected triangle be nearer C than B, and so on : thus, the 

 erected triangles, fig. 2, will be reverse of the original ones, 

 though similar. 



Through the vertex c, fig. 2, draw c c towards S crossing 

 the vertical AG in c, so that the angle CcS may be equal 

 to the angle C c m of the spire-block CD. fig. 1 ; c, being 

 at the intersection of a line (which is to be vertical) 

 through the middle of the spire m, with the base line CD. 

 Also, through the vertex e, of the erected triangle EeF, 

 fig. 2, draw ee towards S, crossing the vertical AG in e, 

 so that the angle EeS may be equal to the angle Een of 

 the spire-block EF, fig. l ; e beintr at the intersection of a 

 line (which is also lo be vertical) drawn through the centre 

 of the spire n, with the base line EF. The intersection of 

 these lines ccS and eeS, fig. 2, continued, establishes ihe 

 point S ; from which draw lines to the vertices of the other 

 triangles, as Sa, S/>, Sd, &c. which will respectively be the 

 antjular p'>siti(ms, in respect ot the verticil ot the base lines 

 of~ihe blocks AB. BC, CD, DE, &c. fig. i, when placed 

 together in equilibrio, and then they will take the form as 

 shown fig. 3; wherein AB is parallel to Sa, fig. 2; BC 

 is parallel tn S b ; CD is parallel to Sc, &c. &c ; and the 

 spires m and n are by coii>lruciion vertical. 



From S, ilg. 2. draw also lines SA, SB, SC, &c. which 

 ■will represent the directions and quantities of the forces 

 which sustain the blocks in equilibrio: thus, the block 

 AB, fig. 3, is sustained in its position, by a force acting 

 asiainst its foot at rt, proportional to the line SA, fig. 2, 

 and in a direction parallel to ihe same; by a force 

 acfins against the end B of the same block, propor- 

 tional to the line SB, fig. 2, and in a direction parallel to 

 BS; and by the weight of the block itself, taken propor- 

 tional 



