648 APPENDIX. 



there 54 inches asunder. The bolts in the 

 joint A could scarcely give way except they 

 were shorn across by the three small links, as 

 they are supported both at their ends and 

 middle, but in the other joint the bolt, which 

 is of the same diameter as the preceding ones, 

 "was unsustained at its ends B and C and 

 supported only at its middle. The links or 

 bars too, being round, only acted at their centers 

 on the bolts, and consequently with a leverage 

 of somewhat more than an inch on each side 

 of D E ; the direct tendency was therefore to 

 break the bolt across; and in this manner 

 fracture took place in it, near to its middle, 

 or half way between B and C* 



To estimate the strength of the bolt so acted 

 upon, supposing it not strained beyond its 

 elastic force. In this case, the extensions and 

 compressions being equal from equal forces, the 

 neutral line would be in the middle, and the 

 formula for the strength (Memoirs, vol. 4, page 

 282, Cor.) is '^^^ = .78b4 sd^ x ^, where 

 s = the absolute strength of the particles in a 

 unity of section, d = the diameter, and / =■ the 

 length. In this case c? z= 2, and Z = 1, .-. 

 strength = ,1854 sd^ x f; but .7854 5 r/^ is the 



♦ The bolt B C is made too long, and D E too narrow, 

 U the figure, but the mistake will create no wrong idea. 



