﻿366 Canon Moseley on the Mechanical Impossibility of 



Let m' n' be the elementary prism which rests immediately on 

 m n. Draw o n perpendicular to m' n 1 . Then is o n' the distance 

 through which m 1 n' is sheared over m n. Moreover the resist- 

 ance to this shearing is the constant quantity fju mndx; 



.*. work of the horizontal shear of mn=p . mn . on' . dx. 



x, , i , , dmn 



13 ut on' = m'n' — mn=z — 7 — dv : 

 dy J > 



.*. work of horizontal shear of m n 



= }i . mn — - — dx dy. ....... (3') 



But mn = M+*(*-m p+yiV-v)-] . 



abp 



dm~n _ Q3— 7) [>£ + #(«-£)] 

 """ dy ~~ ab/3 '' 



.'. work of horizontal shear of m n 



"Whole work of internal horizontal shear of trapezoid A c 



6/3 2 (a-£) 



In the same manner it may be shown that work of vertical 

 shear of m n 



— dmn 7 7 .... 



== fji mn — — ax ay {41) 



ax 



Whole work of internal vertical shear of trapezoid A c 



= ^fi f" j"[*y + y(|8-7)]W+*(«-|8)]<fcrfy 



