Slocks, &c.; and on the Pohjgon of "Forces. 323 



Now, if the cords BB, CC, were shortened so as to 

 bring the ends of the beams to touch, keeping the latter 



parallel, they would lake the figure A BCD, and the di- 

 rections and value of the forces would remain the same, 

 {f this latter figiue be inverted, or rather the beams thereby 

 represented, it is known that the forces which have been 

 shown to take place, would be merely changed from those 

 of tension to those of con)presslon, and the short lines 



drawn across the angles at A, B, C and D at right angles 

 to the forces which connect the beams, are such as, whea 

 inverted with the beams, their ends should conform to, to 

 attain any degree of stability j but here is no indication of 

 these lines (representing planes) bisecting the angle formed 

 by the contiguous beams, as one author has informed us 

 they ouffht. 



By these remarks, I do not intend in the smallest degree 

 to impute blame to those authors I have had in view, but 

 merely to point out what appears to me erroneous or de- 

 fective. 



I now come to the principal object of this letter. 



Problem. 



To put any number of blocks or pieces of timber, stone. 

 Sec. whose weights and centres of gravity are given ia 

 equilibrio in a vertical plane, in any given order, so that 

 anv two of them' shall have a given ant!;ular position. 



Let AB, BC, CD, DE, EF^and FG, fig. 1. (Plate IX), 

 be the blocks which are reciulred to be placed in equilibrio 

 in the order just mentioned, in such manner that the spires 

 of CD and EF shall be vertical*; and let right lines be 

 drawn from A to B, from B to C, C to D, &c. the termi- 

 nations of which are the points of contact or abutment on 

 each other. Also let the points a, b, c, Sec. be the centres 

 of gravity of the diflcrent blocks. From the extremities of 

 the right line AB draw to the centre of gravity a the right 

 lines A a, B a, and thereby a triangle w ill be formed of 

 which 'AB is the base, and a the vertex. Also from the 

 extremities of the line BC draw to the point b, the lines 

 Bb, Cb forming the triangle BbC, of which the base \i 

 BC, and b the vertex ; and proceed in like manner with 

 the other blocks, forming the triangles CcD, DdE, EeF, 

 and FfG. 



• Which i> equivalent to giving the elevations of thoir base lines, or aiv 

 gular po»iiioii. 



X S Draw 



